All the Suckers's Bets Decks with, 3, decks, with deck sizes from 3 to, 5
Where No denomination appears in more than one deck (hence there is never a \
tie)
With various different denominations
By Shalosh B. Ekhad
Chapter Number, 1
In this chapter we will consider the set whose deck sizes are, 3, 3, 3
and there are, 5, denominations from 1(Ace) to, 5
Up to obvious cyclic symmetry, there are, 1,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 4
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.016, seconds to generate.
Chapter Number, 2
In this chapter we will consider the set whose deck sizes are, 3, 3, 3
and there are, 6, denominations from 1(Ace) to, 6
Up to obvious cyclic symmetry, there are, 4,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 5
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.031, seconds to generate.
Chapter Number, 3
In this chapter we will consider the set whose deck sizes are, 3, 3, 3
and there are, 7, denominations from 1(Ace) to, 7
Up to obvious cyclic symmetry, there are, 9,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 6
Deck , 2, has denominations , 3, 3, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 5, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 6, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 7, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 8, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 9, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.057, seconds to generate.
Chapter Number, 4
In this chapter we will consider the set whose deck sizes are, 3, 3, 3
and there are, 8, denominations from 1(Ace) to, 8
Up to obvious cyclic symmetry, there are, 10,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 8
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 3, 4, 6
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 3, 4, 7
Deck , 3, has denominations , 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 5, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 6, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 7, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 8, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 9, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 5, 6
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 10, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.062, seconds to generate.
Chapter Number, 5
In this chapter we will consider the set whose deck sizes are, 3, 3, 3
and there are, 9, denominations from 1(Ace) to, 9
Up to obvious cyclic symmetry, there are, 5,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 5, 9
Deck , 2, has denominations , 3, 4, 8
Deck , 3, has denominations , 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 3, 5, 7
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 4, 5, 7
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 3, 5, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 5, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.051, seconds to generate.
Chapter Number, 6
In this chapter we will consider the set whose deck sizes are, 3, 3, 4
and there are, 5, denominations from 1(Ace) to, 5
Up to obvious cyclic symmetry, there are, 1,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 4
Deck , 2, has denominations , 3, 3, 3, 3
Deck , 3, has denominations , 2, 2, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.022, seconds to generate.
Chapter Number, 7
In this chapter we will consider the set whose deck sizes are, 3, 3, 4
and there are, 6, denominations from 1(Ace) to, 6
Up to obvious cyclic symmetry, there are, 5,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 5
Deck , 2, has denominations , 3, 3, 3, 3
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 3, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 4, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 4, 4, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 5, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 4, 4, 4, 4
Deck , 3, has denominations , 2, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.080, seconds to generate.
Chapter Number, 8
In this chapter we will consider the set whose deck sizes are, 3, 3, 4
and there are, 7, denominations from 1(Ace) to, 7
Up to obvious cyclic symmetry, there are, 13,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 6
Deck , 2, has denominations , 3, 3, 3, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 3, 3, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 3, 4, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 4, 4, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 5, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 4, 4, 4, 4
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 6, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 3, 4, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 7, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 4, 4, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 8, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 4, 5, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 9, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 5, 5, 5
Deck , 3, has denominations , 2, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 10, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 4, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 11, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 5, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 12, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 5, 5, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 13, is as follows
Deck , 1, has denominations , 1, 4, 4, 7
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 7/12
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.152, seconds to generate.
Chapter Number, 9
In this chapter we will consider the set whose deck sizes are, 3, 3, 4
and there are, 8, denominations from 1(Ace) to, 8
Up to obvious cyclic symmetry, there are, 21,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 3, 3, 4, 6
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 3, 4, 4, 6
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 4, 4, 4, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 5, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 3, 4, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 6, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 4, 4, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 7, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 4, 5, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 8, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 5, 5, 5
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 9, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 4, 4, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 10, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 4, 5, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 11, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 5, 5, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 12, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 4, 5, 6
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 13, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 5, 5, 6
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 14, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 5, 6, 6
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 15, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 4, 5, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 16, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 5, 5, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 17, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 5, 6, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 18, is as follows
Deck , 1, has denominations , 1, 4, 4, 8
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 19, is as follows
Deck , 1, has denominations , 1, 4, 5, 8
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 20, is as follows
Deck , 1, has denominations , 1, 4, 7, 7
Deck , 2, has denominations , 3, 6, 6
Deck , 3, has denominations , 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 21, is as follows
Deck , 1, has denominations , 1, 5, 5, 8
Deck , 2, has denominations , 3, 4, 7
Deck , 3, has denominations , 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 7/12
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.191, seconds to generate.
Chapter Number, 10
In this chapter we will consider the set whose deck sizes are, 3, 3, 4
and there are, 9, denominations from 1(Ace) to, 9
Up to obvious cyclic symmetry, there are, 19,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 3, 4, 7
Deck , 3, has denominations , 2, 2, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 4, 4, 7
Deck , 3, has denominations , 2, 3, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 3, 4, 5, 7
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 3, 5, 5, 7
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 5, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 4, 4, 5, 7
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 6, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 4, 5, 5, 7
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 7, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 3, 4, 5, 6
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 8, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 3, 5, 5, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 9, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 3, 5, 6, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 10, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 4, 4, 5, 6
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 11, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 4, 5, 5, 6
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 12, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 4, 5, 6, 6
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 13, is as follows
Deck , 1, has denominations , 1, 8, 8
Deck , 2, has denominations , 3, 5, 6, 7
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 14, is as follows
Deck , 1, has denominations , 1, 8, 8
Deck , 2, has denominations , 4, 5, 6, 7
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 15, is as follows
Deck , 1, has denominations , 1, 4, 5, 9
Deck , 2, has denominations , 3, 3, 8
Deck , 3, has denominations , 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 16, is as follows
Deck , 1, has denominations , 1, 4, 7, 8
Deck , 2, has denominations , 3, 6, 6
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 17, is as follows
Deck , 1, has denominations , 1, 4, 8, 8
Deck , 2, has denominations , 3, 6, 7
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 18, is as follows
Deck , 1, has denominations , 1, 5, 5, 9
Deck , 2, has denominations , 3, 4, 8
Deck , 3, has denominations , 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 19, is as follows
Deck , 1, has denominations , 1, 5, 6, 9
Deck , 2, has denominations , 3, 4, 8
Deck , 3, has denominations , 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 7/12
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.264, seconds to generate.
Chapter Number, 11
In this chapter we will consider the set whose deck sizes are, 3, 3, 5
and there are, 5, denominations from 1(Ace) to, 5
Up to obvious cyclic symmetry, there are, 3,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 4
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 4, 4
Deck , 2, has denominations , 3, 3, 3, 3, 3
Deck , 3, has denominations , 2, 2, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 1, 4, 4, 4
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.031, seconds to generate.
Chapter Number, 12
In this chapter we will consider the set whose deck sizes are, 3, 3, 5
and there are, 6, denominations from 1(Ace) to, 6
Up to obvious cyclic symmetry, there are, 24,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 4
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 4, 4
Deck , 2, has denominations , 3, 3, 3, 3, 5
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 4, 4
Deck , 2, has denominations , 3, 3, 3, 3, 6
Deck , 3, has denominations , 2, 2, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 4, 5
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 5, is as follows
Deck , 1, has denominations , 1, 4, 5
Deck , 2, has denominations , 3, 3, 3, 3, 3
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 6, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 7, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 8, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 9, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 10, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 2, 4, 4, 4, 4
Deck , 3, has denominations , 3, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 11, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 3, 3, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 12, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 3, 4, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 13, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 4, 4, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 14, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 4, 4, 4, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 15, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 4, 4, 4, 4, 4
Deck , 3, has denominations , 2, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 16, is as follows
Deck , 1, has denominations , 1, 1, 4, 4, 5
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 17, is as follows
Deck , 1, has denominations , 1, 1, 4, 4, 6
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 18, is as follows
Deck , 1, has denominations , 1, 1, 4, 5, 5
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 19, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 20, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 21, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 22, is as follows
Deck , 1, has denominations , 1, 2, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 3, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 23, is as follows
Deck , 1, has denominations , 1, 3, 3, 6, 6
Deck , 2, has denominations , 2, 5, 5
Deck , 3, has denominations , 4, 4, 4
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 24, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 4
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.163, seconds to generate.
Chapter Number, 13
In this chapter we will consider the set whose deck sizes are, 3, 3, 5
and there are, 7, denominations from 1(Ace) to, 7
Up to obvious cyclic symmetry, there are, 92,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 5
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 4, 5
Deck , 2, has denominations , 3, 3, 3, 3, 6
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 4, 5
Deck , 2, has denominations , 3, 3, 3, 3, 7
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 4, 6
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 5, is as follows
Deck , 1, has denominations , 1, 4, 6
Deck , 2, has denominations , 3, 3, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 6, is as follows
Deck , 1, has denominations , 1, 4, 6
Deck , 2, has denominations , 3, 3, 3, 3, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 7, is as follows
Deck , 1, has denominations , 1, 4, 6
Deck , 2, has denominations , 3, 3, 3, 5, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 8, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 2, 5, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 9, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 3, 6, 6
Deck , 3, has denominations , 2, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 10, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 11, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 12, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 13, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 14, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 2, 4, 4, 4, 6
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 15, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 2, 4, 4, 4, 7
Deck , 3, has denominations , 3, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 16, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 3, 4, 6
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 17, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 3, 4, 7
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 18, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 4, 4, 6
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 19, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 4, 4, 7
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 20, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 4, 4, 4, 6
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 21, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 4, 4, 4, 7
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 22, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 4, 4, 4, 4, 6
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 23, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 4, 4, 4, 4, 7
Deck , 3, has denominations , 2, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 24, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 25, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 26, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 27, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 28, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 2, 4, 4, 4, 4
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 29, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 3, 3, 3, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 30, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 3, 3, 4, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 31, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 3, 4, 4, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 32, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 4, 4, 4, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 33, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 4, 4, 4, 4, 4
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 34, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 35, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 2, 4, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 36, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 37, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 38, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 39, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 40, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 3, 4, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 41, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 2, 4, 4, 4, 5
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 42, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 2, 4, 4, 5, 5
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 43, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 2, 4, 5, 5, 5
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 44, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 2, 5, 5, 5, 5
Deck , 3, has denominations , 3, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 45, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 3, 3, 4, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 46, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 3, 4, 4, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 47, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 3, 4, 5, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 48, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 3, 5, 5, 5
Deck , 3, has denominations , 2, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 49, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 4, 4, 4, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 50, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 4, 4, 5, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 51, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 4, 5, 5, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 52, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 5, 5, 5, 5
Deck , 3, has denominations , 2, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 53, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 4, 4, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 54, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 4, 5, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 55, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 5, 5, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 56, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 5, 5, 5, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 57, is as follows
Deck , 1, has denominations , 1, 1, 4, 5, 6
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 58, is as follows
Deck , 1, has denominations , 1, 1, 4, 5, 7
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 59, is as follows
Deck , 1, has denominations , 1, 1, 4, 6, 6
Deck , 2, has denominations , 3, 3, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 60, is as follows
Deck , 1, has denominations , 1, 1, 4, 7, 7
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 61, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 62, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 63, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 64, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 7
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 65, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 7
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 66, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 7
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 67, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 68, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 69, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 70, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 71, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 72, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 73, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 74, is as follows
Deck , 1, has denominations , 1, 2, 5, 5, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 75, is as follows
Deck , 1, has denominations , 1, 2, 5, 5, 7
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 3, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 76, is as follows
Deck , 1, has denominations , 1, 2, 5, 6, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 77, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 78, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 79, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 3, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 80, is as follows
Deck , 1, has denominations , 1, 3, 3, 6, 7
Deck , 2, has denominations , 2, 5, 5
Deck , 3, has denominations , 4, 4, 4
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 81, is as follows
Deck , 1, has denominations , 1, 3, 3, 7, 7
Deck , 2, has denominations , 2, 5, 6
Deck , 3, has denominations , 4, 4, 4
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 82, is as follows
Deck , 1, has denominations , 1, 3, 3, 7, 7
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 4, 4, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 83, is as follows
Deck , 1, has denominations , 1, 3, 3, 7, 7
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 4, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 84, is as follows
Deck , 1, has denominations , 1, 3, 4, 7, 7
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 5, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 85, is as follows
Deck , 1, has denominations , 1, 3, 6, 6, 6
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 86, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 4
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 87, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 5
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 88, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 6
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 89, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 7
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 90, is as follows
Deck , 1, has denominations , 1, 4, 4, 5, 5
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 91, is as follows
Deck , 1, has denominations , 1, 4, 5, 5, 5
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 92, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 5
Deck , 2, has denominations , 3, 4, 7
Deck , 3, has denominations , 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.223, seconds to generate.
Chapter Number, 14
In this chapter we will consider the set whose deck sizes are, 3, 3, 5
and there are, 8, denominations from 1(Ace) to, 8
Up to obvious cyclic symmetry, there are, 210,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 6
Deck , 2, has denominations , 3, 3, 5
Deck , 3, has denominations , 2, 2, 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 5
Deck , 3, has denominations , 2, 2, 2, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 2, 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 2, 5, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 5, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 3, 5, 6
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 6, is as follows
Deck , 1, has denominations , 1, 4, 8
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 2, 5, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 7, is as follows
Deck , 1, has denominations , 1, 4, 8
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 5, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 8, is as follows
Deck , 1, has denominations , 1, 4, 8
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 5, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 9, is as follows
Deck , 1, has denominations , 1, 4, 8
Deck , 2, has denominations , 3, 3, 3, 6, 7
Deck , 3, has denominations , 2, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 10, is as follows
Deck , 1, has denominations , 1, 4, 8
Deck , 2, has denominations , 3, 3, 3, 7, 7
Deck , 3, has denominations , 2, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 11, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 12, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 13, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 14, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 15, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 2, 4, 4, 4, 7
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 16, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 2, 4, 4, 4, 8
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 17, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 3, 3, 4, 7
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 18, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 3, 3, 4, 8
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 19, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 3, 4, 4, 7
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 20, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 3, 4, 4, 8
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 21, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 4, 4, 4, 7
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 22, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 4, 4, 4, 8
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 23, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 4, 4, 4, 4, 7
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 24, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 4, 4, 4, 4, 8
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 25, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 26, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 27, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 3, 4, 6
Deck , 3, has denominations , 2, 2, 2, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 28, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 29, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 30, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 2, 2, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 31, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 2, 3, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 32, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 2, 4, 4, 4, 6
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 33, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 2, 4, 4, 6, 6
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 34, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 3, 3, 3, 4, 6
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 35, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 3, 3, 4, 4, 6
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 36, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 3, 3, 4, 6, 6
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 37, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 3, 4, 4, 4, 6
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 38, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 3, 4, 4, 6, 6
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 39, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 4, 4, 4, 4, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 40, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 4, 4, 4, 6, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 41, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 3, 4, 7
Deck , 3, has denominations , 2, 2, 6, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 42, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 4, 4, 7
Deck , 3, has denominations , 2, 3, 6, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 43, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 2, 4, 4, 7, 7
Deck , 3, has denominations , 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 44, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 3, 3, 4, 7, 7
Deck , 3, has denominations , 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 45, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 3, 4, 4, 7, 7
Deck , 3, has denominations , 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 46, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 47, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 2, 4, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 48, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 2, 3, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 49, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 3, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 50, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 2, 3, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 51, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 3, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 52, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 3, 4, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 53, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 2, 4, 4, 5, 7
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 54, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 2, 4, 4, 5, 8
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 55, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 2, 4, 5, 5, 7
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 56, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 2, 4, 5, 5, 8
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 57, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 2, 5, 5, 5, 7
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 58, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 2, 5, 5, 5, 8
Deck , 3, has denominations , 3, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 59, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 3, 3, 5, 8
Deck , 3, has denominations , 2, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 60, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 3, 4, 5, 7
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 61, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 3, 4, 5, 8
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 62, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 3, 5, 5, 7
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 63, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 3, 5, 5, 8
Deck , 3, has denominations , 2, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 64, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 4, 4, 5, 7
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 65, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 4, 4, 5, 8
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 66, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 4, 5, 5, 7
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 67, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 4, 5, 5, 8
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 68, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 5, 5, 5, 7
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 69, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 5, 5, 5, 8
Deck , 3, has denominations , 2, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 70, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 4, 5, 7
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 71, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 4, 5, 8
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 72, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 5, 5, 7
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 73, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 5, 5, 8
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 74, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 5, 5, 5, 7
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 75, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 5, 5, 5, 8
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 76, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 2, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 77, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 2, 4, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 78, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 2, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 79, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 80, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 2, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 81, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 82, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 3, 4, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 83, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 2, 4, 4, 4, 5
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 84, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 2, 4, 4, 5, 5
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 85, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 2, 4, 5, 5, 5
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 86, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 2, 5, 5, 5, 5
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 87, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 3, 3, 4, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 88, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 3, 4, 4, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 89, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 3, 4, 5, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 90, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 3, 5, 5, 5
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 91, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 4, 4, 4, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 92, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 4, 4, 5, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 93, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 4, 5, 5, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 94, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 5, 5, 5, 5
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 95, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 4, 4, 4, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 96, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 4, 4, 5, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 97, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 4, 5, 5, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 98, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 5, 5, 5, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 99, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 5, 6
Deck , 3, has denominations , 2, 2, 4, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 100, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 2, 2, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 101, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 2, 3, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 102, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 6, 6
Deck , 3, has denominations , 2, 3, 5, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 103, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 5, 5, 6
Deck , 3, has denominations , 2, 3, 4, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 104, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 5, 6, 6
Deck , 3, has denominations , 2, 3, 4, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 105, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 2, 4, 4, 5, 6
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 106, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 2, 4, 5, 5, 6
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 107, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 2, 4, 5, 6, 6
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 108, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 2, 5, 5, 5, 6
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 109, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 2, 5, 5, 6, 6
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 110, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 2, 5, 6, 6, 6
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 111, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 3, 4, 5, 6
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 112, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 3, 5, 5, 6
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 113, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 3, 5, 6, 6
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 114, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 4, 4, 5, 6
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 115, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 4, 5, 5, 6
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 116, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 4, 5, 6, 6
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 117, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 4, 6, 6, 6
Deck , 3, has denominations , 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 118, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 5, 5, 5, 6
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 119, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 5, 5, 6, 6
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 120, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 5, 6, 6, 6
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 121, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 4, 4, 5, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 122, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 4, 5, 5, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 123, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 4, 5, 6, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 124, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 5, 5, 5, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 125, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 5, 5, 6, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 126, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 5, 6, 6, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 127, is as follows
Deck , 1, has denominations , 1, 1, 4, 6, 7
Deck , 2, has denominations , 3, 3, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 128, is as follows
Deck , 1, has denominations , 1, 1, 4, 6, 8
Deck , 2, has denominations , 3, 3, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 129, is as follows
Deck , 1, has denominations , 1, 1, 4, 7, 8
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 130, is as follows
Deck , 1, has denominations , 1, 1, 4, 8, 8
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 131, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 7
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 132, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 7
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 133, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 7
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 134, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 8
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 135, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 8
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 136, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 8
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 137, is as follows
Deck , 1, has denominations , 1, 1, 5, 7, 7
Deck , 2, has denominations , 3, 4, 6
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 138, is as follows
Deck , 1, has denominations , 1, 1, 5, 7, 7
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 139, is as follows
Deck , 1, has denominations , 1, 1, 5, 8, 8
Deck , 2, has denominations , 3, 4, 7
Deck , 3, has denominations , 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 140, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 7
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 141, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 7
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 142, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 7
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 143, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 7
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 144, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 8
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 145, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 8
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 146, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 8
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 147, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 8
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 148, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 7
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 149, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 7
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 150, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 7
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 151, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 7
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 152, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 7
Deck , 2, has denominations , 3, 5, 6
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 153, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 7
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 154, is as follows
Deck , 1, has denominations , 1, 2, 5, 6, 7
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 155, is as follows
Deck , 1, has denominations , 1, 2, 5, 6, 8
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 156, is as follows
Deck , 1, has denominations , 1, 2, 5, 7, 7
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 157, is as follows
Deck , 1, has denominations , 1, 2, 5, 8, 8
Deck , 2, has denominations , 4, 4, 7
Deck , 3, has denominations , 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 158, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 7
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 159, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 7
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 160, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 7
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 161, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 8
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 162, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 8
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 163, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 8
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 3, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 164, is as follows
Deck , 1, has denominations , 1, 2, 6, 7, 7
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 165, is as follows
Deck , 1, has denominations , 1, 2, 6, 7, 7
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 166, is as follows
Deck , 1, has denominations , 1, 2, 6, 7, 7
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 167, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 7
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 168, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 7
Deck , 2, has denominations , 4, 6, 6
Deck , 3, has denominations , 3, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 169, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 7
Deck , 2, has denominations , 5, 5, 6
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 170, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 7
Deck , 2, has denominations , 5, 6, 6
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 171, is as follows
Deck , 1, has denominations , 1, 3, 3, 7, 8
Deck , 2, has denominations , 2, 5, 6
Deck , 3, has denominations , 4, 4, 4
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 172, is as follows
Deck , 1, has denominations , 1, 3, 3, 7, 8
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 4, 4, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 173, is as follows
Deck , 1, has denominations , 1, 3, 3, 7, 8
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 4, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 174, is as follows
Deck , 1, has denominations , 1, 3, 3, 8, 8
Deck , 2, has denominations , 2, 5, 7
Deck , 3, has denominations , 4, 4, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 175, is as follows
Deck , 1, has denominations , 1, 3, 3, 8, 8
Deck , 2, has denominations , 2, 6, 7
Deck , 3, has denominations , 4, 4, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 176, is as follows
Deck , 1, has denominations , 1, 3, 3, 8, 8
Deck , 2, has denominations , 2, 6, 7
Deck , 3, has denominations , 4, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 177, is as follows
Deck , 1, has denominations , 1, 3, 3, 8, 8
Deck , 2, has denominations , 2, 7, 7
Deck , 3, has denominations , 4, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 178, is as follows
Deck , 1, has denominations , 1, 3, 4, 7, 8
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 5, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 179, is as follows
Deck , 1, has denominations , 1, 3, 4, 8, 8
Deck , 2, has denominations , 2, 6, 7
Deck , 3, has denominations , 5, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 180, is as follows
Deck , 1, has denominations , 1, 3, 4, 8, 8
Deck , 2, has denominations , 2, 7, 7
Deck , 3, has denominations , 5, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 181, is as follows
Deck , 1, has denominations , 1, 3, 4, 8, 8
Deck , 2, has denominations , 2, 7, 7
Deck , 3, has denominations , 5, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 182, is as follows
Deck , 1, has denominations , 1, 3, 5, 8, 8
Deck , 2, has denominations , 2, 7, 7
Deck , 3, has denominations , 4, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 183, is as follows
Deck , 1, has denominations , 1, 3, 6, 6, 7
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 184, is as follows
Deck , 1, has denominations , 1, 3, 6, 7, 7
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 185, is as follows
Deck , 1, has denominations , 1, 3, 7, 7, 7
Deck , 2, has denominations , 4, 6, 6
Deck , 3, has denominations , 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 186, is as follows
Deck , 1, has denominations , 1, 3, 7, 7, 7
Deck , 2, has denominations , 5, 5, 6
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 187, is as follows
Deck , 1, has denominations , 1, 3, 7, 7, 7
Deck , 2, has denominations , 5, 6, 6
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 188, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 5
Deck , 2, has denominations , 3, 3, 8
Deck , 3, has denominations , 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 189, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 6
Deck , 2, has denominations , 3, 3, 8
Deck , 3, has denominations , 2, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 190, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 7
Deck , 2, has denominations , 3, 3, 8
Deck , 3, has denominations , 2, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 191, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 8
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 192, is as follows
Deck , 1, has denominations , 1, 4, 4, 5, 5
Deck , 2, has denominations , 3, 3, 8
Deck , 3, has denominations , 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 193, is as follows
Deck , 1, has denominations , 1, 4, 4, 5, 6
Deck , 2, has denominations , 3, 3, 8
Deck , 3, has denominations , 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 194, is as follows
Deck , 1, has denominations , 1, 4, 4, 5, 7
Deck , 2, has denominations , 3, 3, 8
Deck , 3, has denominations , 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 195, is as follows
Deck , 1, has denominations , 1, 4, 4, 5, 8
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 196, is as follows
Deck , 1, has denominations , 1, 4, 4, 6, 6
Deck , 2, has denominations , 3, 3, 8
Deck , 3, has denominations , 2, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 197, is as follows
Deck , 1, has denominations , 1, 4, 4, 7, 7
Deck , 2, has denominations , 3, 6, 6
Deck , 3, has denominations , 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 198, is as follows
Deck , 1, has denominations , 1, 4, 5, 5, 5
Deck , 2, has denominations , 3, 3, 8
Deck , 3, has denominations , 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 199, is as follows
Deck , 1, has denominations , 1, 4, 5, 5, 6
Deck , 2, has denominations , 3, 3, 8
Deck , 3, has denominations , 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 200, is as follows
Deck , 1, has denominations , 1, 4, 5, 5, 7
Deck , 2, has denominations , 3, 3, 8
Deck , 3, has denominations , 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 201, is as follows
Deck , 1, has denominations , 1, 4, 5, 5, 8
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 202, is as follows
Deck , 1, has denominations , 1, 4, 5, 6, 6
Deck , 2, has denominations , 3, 3, 8
Deck , 3, has denominations , 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 203, is as follows
Deck , 1, has denominations , 1, 4, 6, 6, 6
Deck , 2, has denominations , 3, 3, 8
Deck , 3, has denominations , 2, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 204, is as follows
Deck , 1, has denominations , 1, 4, 7, 7, 7
Deck , 2, has denominations , 3, 6, 6
Deck , 3, has denominations , 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 205, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 5
Deck , 2, has denominations , 3, 4, 8
Deck , 3, has denominations , 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 206, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 6
Deck , 2, has denominations , 3, 4, 8
Deck , 3, has denominations , 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 207, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 7
Deck , 2, has denominations , 3, 4, 8
Deck , 3, has denominations , 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 208, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 8
Deck , 2, has denominations , 3, 4, 7
Deck , 3, has denominations , 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 209, is as follows
Deck , 1, has denominations , 1, 5, 5, 6, 6
Deck , 2, has denominations , 3, 4, 8
Deck , 3, has denominations , 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 210, is as follows
Deck , 1, has denominations , 1, 5, 6, 6, 6
Deck , 2, has denominations , 3, 4, 8
Deck , 3, has denominations , 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.625, seconds to generate.
Chapter Number, 15
In this chapter we will consider the set whose deck sizes are, 3, 3, 5
and there are, 9, denominations from 1(Ace) to, 9
Up to obvious cyclic symmetry, there are, 291,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 8
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 5, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 4, 9
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 5, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 4, 9
Deck , 2, has denominations , 3, 3, 8
Deck , 3, has denominations , 2, 2, 5, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 4, 9
Deck , 2, has denominations , 3, 3, 3, 6, 8
Deck , 3, has denominations , 2, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 5, is as follows
Deck , 1, has denominations , 1, 4, 9
Deck , 2, has denominations , 3, 3, 3, 7, 8
Deck , 3, has denominations , 2, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 6, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 3, 4, 6
Deck , 3, has denominations , 2, 2, 2, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 7, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 2, 2, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 8, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 2, 3, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 9, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 4, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 10, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 3, 4, 6
Deck , 3, has denominations , 2, 2, 2, 7, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 11, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 3, 4, 7
Deck , 3, has denominations , 2, 2, 2, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 12, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 3, 4, 7
Deck , 3, has denominations , 2, 2, 6, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 13, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 2, 2, 3, 7, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 14, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 2, 3, 3, 7, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 15, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 4, 4, 7
Deck , 3, has denominations , 2, 2, 3, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 16, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 4, 4, 7
Deck , 3, has denominations , 2, 3, 3, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 17, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 4, 4, 7
Deck , 3, has denominations , 2, 3, 6, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 18, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 2, 4, 4, 6, 7
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 19, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 3, 3, 4, 6, 7
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 20, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 3, 4, 4, 6, 7
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 21, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 4, 4, 4, 6, 7
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 22, is as follows
Deck , 1, has denominations , 1, 5, 9
Deck , 2, has denominations , 3, 4, 7
Deck , 3, has denominations , 2, 2, 6, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 23, is as follows
Deck , 1, has denominations , 1, 5, 9
Deck , 2, has denominations , 3, 4, 8
Deck , 3, has denominations , 2, 2, 6, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 24, is as follows
Deck , 1, has denominations , 1, 5, 9
Deck , 2, has denominations , 3, 4, 8
Deck , 3, has denominations , 2, 2, 6, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 25, is as follows
Deck , 1, has denominations , 1, 5, 9
Deck , 2, has denominations , 4, 4, 7
Deck , 3, has denominations , 2, 3, 6, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 26, is as follows
Deck , 1, has denominations , 1, 5, 9
Deck , 2, has denominations , 4, 4, 8
Deck , 3, has denominations , 2, 3, 6, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 27, is as follows
Deck , 1, has denominations , 1, 5, 9
Deck , 2, has denominations , 4, 4, 8
Deck , 3, has denominations , 2, 3, 6, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 28, is as follows
Deck , 1, has denominations , 1, 5, 9
Deck , 2, has denominations , 2, 4, 4, 7, 8
Deck , 3, has denominations , 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 29, is as follows
Deck , 1, has denominations , 1, 5, 9
Deck , 2, has denominations , 2, 4, 4, 8, 8
Deck , 3, has denominations , 3, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 30, is as follows
Deck , 1, has denominations , 1, 5, 9
Deck , 2, has denominations , 3, 3, 4, 7, 8
Deck , 3, has denominations , 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 31, is as follows
Deck , 1, has denominations , 1, 5, 9
Deck , 2, has denominations , 3, 3, 4, 8, 8
Deck , 3, has denominations , 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 32, is as follows
Deck , 1, has denominations , 1, 5, 9
Deck , 2, has denominations , 3, 4, 4, 7, 8
Deck , 3, has denominations , 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 33, is as follows
Deck , 1, has denominations , 1, 5, 9
Deck , 2, has denominations , 3, 4, 4, 8, 8
Deck , 3, has denominations , 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 34, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 2, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 35, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 2, 4, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 36, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 2, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 37, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 38, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 2, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 39, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 40, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 3, 4, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 41, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 2, 4, 4, 5, 8
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 42, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 2, 4, 4, 5, 9
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 43, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 2, 4, 5, 5, 8
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 44, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 2, 4, 5, 5, 9
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 45, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 2, 5, 5, 5, 8
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 46, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 2, 5, 5, 5, 9
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 47, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 3, 3, 5, 9
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 48, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 3, 4, 5, 8
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 49, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 3, 4, 5, 9
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 50, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 3, 5, 5, 8
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 51, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 3, 5, 5, 9
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 52, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 4, 4, 5, 8
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 53, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 4, 4, 5, 9
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 54, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 4, 5, 5, 8
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 55, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 4, 5, 5, 9
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 56, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 5, 5, 5, 8
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 57, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 5, 5, 5, 9
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 58, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 4, 4, 5, 8
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 59, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 4, 4, 5, 9
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 60, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 4, 5, 5, 8
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 61, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 4, 5, 5, 9
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 62, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 5, 5, 5, 8
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 63, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 5, 5, 5, 9
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 64, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 2, 7, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 65, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 2, 4, 7, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 66, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 3, 5, 7
Deck , 3, has denominations , 2, 2, 4, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 67, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 2, 3, 7, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 68, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 3, 7, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 69, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 2, 3, 7, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 70, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 3, 7, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 71, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 4, 5, 7
Deck , 3, has denominations , 2, 2, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 72, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 4, 5, 7
Deck , 3, has denominations , 2, 3, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 73, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 3, 4, 7, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 74, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 5, 5, 7
Deck , 3, has denominations , 2, 3, 4, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 75, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 2, 4, 4, 5, 7
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 76, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 2, 4, 5, 5, 7
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 77, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 2, 4, 5, 7, 7
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 78, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 2, 5, 5, 5, 7
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 79, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 2, 5, 5, 7, 7
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 80, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 3, 3, 4, 5, 7
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 81, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 3, 3, 5, 5, 7
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 82, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 3, 3, 5, 7, 7
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 83, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 3, 4, 4, 5, 7
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 84, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 3, 4, 5, 5, 7
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 85, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 3, 4, 5, 7, 7
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 86, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 3, 5, 5, 5, 7
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 87, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 3, 5, 5, 7, 7
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 88, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 4, 4, 4, 5, 7
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 89, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 4, 4, 5, 5, 7
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 90, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 4, 4, 5, 7, 7
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 91, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 4, 5, 5, 5, 7
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 92, is as follows
Deck , 1, has denominations , 1, 6, 8
Deck , 2, has denominations , 4, 5, 5, 7, 7
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 93, is as follows
Deck , 1, has denominations , 1, 6, 9
Deck , 2, has denominations , 3, 5, 8
Deck , 3, has denominations , 2, 4, 7, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 94, is as follows
Deck , 1, has denominations , 1, 6, 9
Deck , 2, has denominations , 4, 5, 8
Deck , 3, has denominations , 2, 3, 7, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 5/9
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 95, is as follows
Deck , 1, has denominations , 1, 6, 9
Deck , 2, has denominations , 2, 4, 5, 8, 8
Deck , 3, has denominations , 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 96, is as follows
Deck , 1, has denominations , 1, 6, 9
Deck , 2, has denominations , 3, 4, 5, 8, 8
Deck , 3, has denominations , 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 97, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 5, 6
Deck , 3, has denominations , 2, 2, 4, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 98, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 2, 2, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 99, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 2, 3, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 100, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 6, 6
Deck , 3, has denominations , 2, 3, 5, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 101, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 5, 5, 6
Deck , 3, has denominations , 2, 3, 4, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 102, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 5, 6, 6
Deck , 3, has denominations , 2, 3, 4, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 103, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 2, 4, 5, 6, 8
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 104, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 2, 4, 5, 6, 9
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 105, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 2, 4, 6, 6, 9
Deck , 3, has denominations , 3, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 106, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 2, 5, 5, 6, 8
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 107, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 2, 5, 5, 6, 9
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 108, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 2, 5, 6, 6, 8
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 109, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 2, 5, 6, 6, 9
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 110, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 3, 4, 6, 9
Deck , 3, has denominations , 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 111, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 3, 5, 6, 8
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 112, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 3, 5, 6, 9
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 113, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 4, 4, 6, 9
Deck , 3, has denominations , 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 114, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 4, 5, 6, 8
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 115, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 4, 5, 6, 9
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 116, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 4, 6, 6, 8
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 117, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 4, 6, 6, 9
Deck , 3, has denominations , 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 118, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 5, 5, 6, 8
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 119, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 5, 5, 6, 9
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 120, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 5, 6, 6, 8
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 121, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 5, 6, 6, 9
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 122, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 4, 5, 6, 8
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 123, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 4, 5, 6, 9
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 124, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 5, 5, 6, 8
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 125, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 5, 5, 6, 9
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 126, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 5, 6, 6, 8
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 127, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 5, 6, 6, 9
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 128, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 3, 5, 6
Deck , 3, has denominations , 2, 2, 4, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 129, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 2, 2, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 130, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 2, 3, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 131, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 4, 6, 6
Deck , 3, has denominations , 2, 3, 5, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 132, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 5, 5, 6
Deck , 3, has denominations , 2, 3, 4, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 133, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 5, 6, 6
Deck , 3, has denominations , 2, 3, 4, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 134, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 2, 4, 4, 5, 6
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 135, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 2, 4, 5, 5, 6
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 136, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 2, 4, 5, 6, 6
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 137, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 2, 5, 5, 5, 6
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 138, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 2, 5, 5, 6, 6
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 139, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 2, 5, 6, 6, 6
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 140, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 3, 3, 4, 5, 6
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 141, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 3, 3, 5, 5, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 142, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 3, 3, 5, 6, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 143, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 3, 4, 4, 5, 6
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 144, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 3, 4, 5, 5, 6
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 145, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 3, 4, 5, 6, 6
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 146, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 3, 4, 6, 6, 6
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 147, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 3, 5, 5, 5, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 148, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 3, 5, 5, 6, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 149, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 3, 5, 6, 6, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 150, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 4, 4, 4, 5, 6
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 151, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 4, 4, 5, 5, 6
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 152, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 4, 4, 5, 6, 6
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 153, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 4, 5, 5, 5, 6
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 154, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 4, 5, 5, 6, 6
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 155, is as follows
Deck , 1, has denominations , 1, 7, 8
Deck , 2, has denominations , 4, 5, 6, 6, 6
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 156, is as follows
Deck , 1, has denominations , 1, 8, 8
Deck , 2, has denominations , 4, 6, 7
Deck , 3, has denominations , 2, 3, 5, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 157, is as follows
Deck , 1, has denominations , 1, 8, 8
Deck , 2, has denominations , 5, 6, 7
Deck , 3, has denominations , 2, 3, 4, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 158, is as follows
Deck , 1, has denominations , 1, 8, 8
Deck , 2, has denominations , 2, 4, 5, 6, 7
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 159, is as follows
Deck , 1, has denominations , 1, 8, 8
Deck , 2, has denominations , 2, 5, 5, 6, 7
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 160, is as follows
Deck , 1, has denominations , 1, 8, 8
Deck , 2, has denominations , 2, 5, 6, 6, 7
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 161, is as follows
Deck , 1, has denominations , 1, 8, 8
Deck , 2, has denominations , 2, 5, 6, 7, 7
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 162, is as follows
Deck , 1, has denominations , 1, 8, 8
Deck , 2, has denominations , 3, 3, 5, 6, 7
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 163, is as follows
Deck , 1, has denominations , 1, 8, 8
Deck , 2, has denominations , 3, 4, 5, 6, 7
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 164, is as follows
Deck , 1, has denominations , 1, 8, 8
Deck , 2, has denominations , 3, 4, 6, 6, 7
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 165, is as follows
Deck , 1, has denominations , 1, 8, 8
Deck , 2, has denominations , 3, 4, 6, 7, 7
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 166, is as follows
Deck , 1, has denominations , 1, 8, 8
Deck , 2, has denominations , 3, 5, 5, 6, 7
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 167, is as follows
Deck , 1, has denominations , 1, 8, 8
Deck , 2, has denominations , 3, 5, 6, 6, 7
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 168, is as follows
Deck , 1, has denominations , 1, 8, 8
Deck , 2, has denominations , 3, 5, 6, 7, 7
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 169, is as follows
Deck , 1, has denominations , 1, 8, 8
Deck , 2, has denominations , 4, 4, 5, 6, 7
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 170, is as follows
Deck , 1, has denominations , 1, 8, 8
Deck , 2, has denominations , 4, 5, 5, 6, 7
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 171, is as follows
Deck , 1, has denominations , 1, 8, 8
Deck , 2, has denominations , 4, 5, 6, 6, 7
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 172, is as follows
Deck , 1, has denominations , 1, 8, 8
Deck , 2, has denominations , 4, 5, 6, 7, 7
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 5/9
-------------------------------------------------------
Set Number, 173, is as follows
Deck , 1, has denominations , 1, 1, 4, 8, 9
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 174, is as follows
Deck , 1, has denominations , 1, 1, 5, 7, 8
Deck , 2, has denominations , 3, 4, 6
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 175, is as follows
Deck , 1, has denominations , 1, 1, 5, 7, 8
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 176, is as follows
Deck , 1, has denominations , 1, 1, 5, 7, 9
Deck , 2, has denominations , 3, 4, 6
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 177, is as follows
Deck , 1, has denominations , 1, 1, 5, 7, 9
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 178, is as follows
Deck , 1, has denominations , 1, 1, 5, 8, 9
Deck , 2, has denominations , 3, 4, 7
Deck , 3, has denominations , 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 179, is as follows
Deck , 1, has denominations , 1, 1, 5, 9, 9
Deck , 2, has denominations , 3, 4, 8
Deck , 3, has denominations , 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 180, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 8
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 181, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 8
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 182, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 8
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 183, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 8
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 184, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 9
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 185, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 9
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 186, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 9
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 187, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 9
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 188, is as follows
Deck , 1, has denominations , 1, 1, 6, 8, 8
Deck , 2, has denominations , 3, 5, 7
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 189, is as follows
Deck , 1, has denominations , 1, 1, 6, 8, 8
Deck , 2, has denominations , 4, 5, 7
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 190, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 8
Deck , 2, has denominations , 3, 5, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 191, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 8
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 192, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 9
Deck , 2, has denominations , 3, 5, 6
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 193, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 9
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 194, is as follows
Deck , 1, has denominations , 1, 1, 7, 8, 8
Deck , 2, has denominations , 3, 5, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 195, is as follows
Deck , 1, has denominations , 1, 1, 7, 8, 8
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 196, is as follows
Deck , 1, has denominations , 1, 2, 5, 7, 8
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 197, is as follows
Deck , 1, has denominations , 1, 2, 5, 7, 9
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 198, is as follows
Deck , 1, has denominations , 1, 2, 5, 8, 9
Deck , 2, has denominations , 4, 4, 7
Deck , 3, has denominations , 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 199, is as follows
Deck , 1, has denominations , 1, 2, 5, 9, 9
Deck , 2, has denominations , 4, 4, 8
Deck , 3, has denominations , 3, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 200, is as follows
Deck , 1, has denominations , 1, 2, 6, 7, 8
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 201, is as follows
Deck , 1, has denominations , 1, 2, 6, 7, 8
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 202, is as follows
Deck , 1, has denominations , 1, 2, 6, 7, 8
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 203, is as follows
Deck , 1, has denominations , 1, 2, 6, 7, 9
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 204, is as follows
Deck , 1, has denominations , 1, 2, 6, 7, 9
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 205, is as follows
Deck , 1, has denominations , 1, 2, 6, 7, 9
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 206, is as follows
Deck , 1, has denominations , 1, 2, 6, 8, 8
Deck , 2, has denominations , 4, 5, 7
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 207, is as follows
Deck , 1, has denominations , 1, 2, 6, 8, 8
Deck , 2, has denominations , 5, 5, 7
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 208, is as follows
Deck , 1, has denominations , 1, 2, 6, 9, 9
Deck , 2, has denominations , 4, 5, 8
Deck , 3, has denominations , 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 209, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 8
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 210, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 8
Deck , 2, has denominations , 4, 6, 6
Deck , 3, has denominations , 3, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 211, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 8
Deck , 2, has denominations , 5, 5, 6
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 212, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 8
Deck , 2, has denominations , 5, 6, 6
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 213, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 9
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 214, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 9
Deck , 2, has denominations , 4, 6, 6
Deck , 3, has denominations , 3, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 215, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 9
Deck , 2, has denominations , 5, 5, 6
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 216, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 9
Deck , 2, has denominations , 5, 6, 6
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 217, is as follows
Deck , 1, has denominations , 1, 2, 7, 8, 8
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 218, is as follows
Deck , 1, has denominations , 1, 2, 7, 8, 8
Deck , 2, has denominations , 4, 6, 6
Deck , 3, has denominations , 3, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 219, is as follows
Deck , 1, has denominations , 1, 2, 7, 8, 8
Deck , 2, has denominations , 5, 5, 6
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 220, is as follows
Deck , 1, has denominations , 1, 2, 7, 8, 8
Deck , 2, has denominations , 5, 6, 6
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 221, is as follows
Deck , 1, has denominations , 1, 2, 8, 8, 8
Deck , 2, has denominations , 4, 6, 7
Deck , 3, has denominations , 3, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 222, is as follows
Deck , 1, has denominations , 1, 2, 8, 8, 8
Deck , 2, has denominations , 5, 6, 7
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 223, is as follows
Deck , 1, has denominations , 1, 3, 3, 8, 9
Deck , 2, has denominations , 2, 5, 7
Deck , 3, has denominations , 4, 4, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 224, is as follows
Deck , 1, has denominations , 1, 3, 3, 8, 9
Deck , 2, has denominations , 2, 6, 7
Deck , 3, has denominations , 4, 4, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 225, is as follows
Deck , 1, has denominations , 1, 3, 3, 8, 9
Deck , 2, has denominations , 2, 6, 7
Deck , 3, has denominations , 4, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 226, is as follows
Deck , 1, has denominations , 1, 3, 3, 8, 9
Deck , 2, has denominations , 2, 7, 7
Deck , 3, has denominations , 4, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 227, is as follows
Deck , 1, has denominations , 1, 3, 3, 9, 9
Deck , 2, has denominations , 2, 6, 8
Deck , 3, has denominations , 4, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 228, is as follows
Deck , 1, has denominations , 1, 3, 3, 9, 9
Deck , 2, has denominations , 2, 7, 8
Deck , 3, has denominations , 4, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 229, is as follows
Deck , 1, has denominations , 1, 3, 4, 8, 9
Deck , 2, has denominations , 2, 6, 7
Deck , 3, has denominations , 5, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 230, is as follows
Deck , 1, has denominations , 1, 3, 4, 8, 9
Deck , 2, has denominations , 2, 7, 7
Deck , 3, has denominations , 5, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 231, is as follows
Deck , 1, has denominations , 1, 3, 4, 8, 9
Deck , 2, has denominations , 2, 7, 7
Deck , 3, has denominations , 5, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 232, is as follows
Deck , 1, has denominations , 1, 3, 4, 9, 9
Deck , 2, has denominations , 2, 6, 8
Deck , 3, has denominations , 5, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 233, is as follows
Deck , 1, has denominations , 1, 3, 4, 9, 9
Deck , 2, has denominations , 2, 7, 8
Deck , 3, has denominations , 5, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 234, is as follows
Deck , 1, has denominations , 1, 3, 4, 9, 9
Deck , 2, has denominations , 2, 7, 8
Deck , 3, has denominations , 5, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 235, is as follows
Deck , 1, has denominations , 1, 3, 4, 9, 9
Deck , 2, has denominations , 2, 8, 8
Deck , 3, has denominations , 5, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 236, is as follows
Deck , 1, has denominations , 1, 3, 5, 8, 9
Deck , 2, has denominations , 2, 7, 7
Deck , 3, has denominations , 4, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 237, is as follows
Deck , 1, has denominations , 1, 3, 5, 9, 9
Deck , 2, has denominations , 2, 7, 8
Deck , 3, has denominations , 4, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 238, is as follows
Deck , 1, has denominations , 1, 3, 5, 9, 9
Deck , 2, has denominations , 2, 8, 8
Deck , 3, has denominations , 4, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 239, is as follows
Deck , 1, has denominations , 1, 3, 6, 6, 9
Deck , 2, has denominations , 2, 5, 8
Deck , 3, has denominations , 4, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 240, is as follows
Deck , 1, has denominations , 1, 3, 6, 7, 8
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 241, is as follows
Deck , 1, has denominations , 1, 3, 6, 8, 8
Deck , 2, has denominations , 5, 5, 7
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 242, is as follows
Deck , 1, has denominations , 1, 3, 7, 7, 8
Deck , 2, has denominations , 4, 6, 6
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 243, is as follows
Deck , 1, has denominations , 1, 3, 7, 7, 8
Deck , 2, has denominations , 5, 5, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 244, is as follows
Deck , 1, has denominations , 1, 3, 7, 7, 8
Deck , 2, has denominations , 5, 6, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 245, is as follows
Deck , 1, has denominations , 1, 3, 7, 8, 8
Deck , 2, has denominations , 4, 6, 6
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 246, is as follows
Deck , 1, has denominations , 1, 3, 7, 8, 8
Deck , 2, has denominations , 5, 5, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 247, is as follows
Deck , 1, has denominations , 1, 3, 7, 8, 8
Deck , 2, has denominations , 5, 6, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 248, is as follows
Deck , 1, has denominations , 1, 3, 8, 8, 8
Deck , 2, has denominations , 4, 6, 7
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 249, is as follows
Deck , 1, has denominations , 1, 3, 8, 8, 8
Deck , 2, has denominations , 5, 6, 7
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 250, is as follows
Deck , 1, has denominations , 1, 4, 4, 5, 6
Deck , 2, has denominations , 3, 3, 9
Deck , 3, has denominations , 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 251, is as follows
Deck , 1, has denominations , 1, 4, 4, 5, 7
Deck , 2, has denominations , 3, 3, 9
Deck , 3, has denominations , 2, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 252, is as follows
Deck , 1, has denominations , 1, 4, 4, 5, 8
Deck , 2, has denominations , 3, 3, 9
Deck , 3, has denominations , 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 253, is as follows
Deck , 1, has denominations , 1, 4, 4, 5, 9
Deck , 2, has denominations , 3, 3, 8
Deck , 3, has denominations , 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 254, is as follows
Deck , 1, has denominations , 1, 4, 4, 6, 7
Deck , 2, has denominations , 3, 3, 9
Deck , 3, has denominations , 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 255, is as follows
Deck , 1, has denominations , 1, 4, 4, 6, 8
Deck , 2, has denominations , 3, 3, 9
Deck , 3, has denominations , 2, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 256, is as follows
Deck , 1, has denominations , 1, 4, 4, 6, 9
Deck , 2, has denominations , 3, 3, 8
Deck , 3, has denominations , 2, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 257, is as follows
Deck , 1, has denominations , 1, 4, 4, 7, 8
Deck , 2, has denominations , 3, 6, 6
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 258, is as follows
Deck , 1, has denominations , 1, 4, 4, 7, 9
Deck , 2, has denominations , 3, 6, 6
Deck , 3, has denominations , 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 259, is as follows
Deck , 1, has denominations , 1, 4, 4, 8, 8
Deck , 2, has denominations , 3, 6, 7
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 260, is as follows
Deck , 1, has denominations , 1, 4, 5, 5, 6
Deck , 2, has denominations , 3, 3, 9
Deck , 3, has denominations , 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 261, is as follows
Deck , 1, has denominations , 1, 4, 5, 5, 7
Deck , 2, has denominations , 3, 3, 9
Deck , 3, has denominations , 2, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 262, is as follows
Deck , 1, has denominations , 1, 4, 5, 5, 8
Deck , 2, has denominations , 3, 3, 9
Deck , 3, has denominations , 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 263, is as follows
Deck , 1, has denominations , 1, 4, 5, 5, 9
Deck , 2, has denominations , 3, 3, 8
Deck , 3, has denominations , 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 264, is as follows
Deck , 1, has denominations , 1, 4, 5, 6, 6
Deck , 2, has denominations , 3, 3, 9
Deck , 3, has denominations , 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 265, is as follows
Deck , 1, has denominations , 1, 4, 5, 6, 7
Deck , 2, has denominations , 3, 3, 9
Deck , 3, has denominations , 2, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 266, is as follows
Deck , 1, has denominations , 1, 4, 5, 6, 8
Deck , 2, has denominations , 3, 3, 9
Deck , 3, has denominations , 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 267, is as follows
Deck , 1, has denominations , 1, 4, 5, 6, 9
Deck , 2, has denominations , 3, 3, 8
Deck , 3, has denominations , 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 268, is as follows
Deck , 1, has denominations , 1, 4, 5, 7, 7
Deck , 2, has denominations , 3, 3, 9
Deck , 3, has denominations , 2, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 269, is as follows
Deck , 1, has denominations , 1, 4, 5, 8, 8
Deck , 2, has denominations , 3, 7, 7
Deck , 3, has denominations , 2, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 270, is as follows
Deck , 1, has denominations , 1, 4, 6, 6, 7
Deck , 2, has denominations , 3, 3, 9
Deck , 3, has denominations , 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 271, is as follows
Deck , 1, has denominations , 1, 4, 6, 6, 9
Deck , 2, has denominations , 3, 5, 8
Deck , 3, has denominations , 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 272, is as follows
Deck , 1, has denominations , 1, 4, 6, 7, 7
Deck , 2, has denominations , 3, 3, 9
Deck , 3, has denominations , 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 273, is as follows
Deck , 1, has denominations , 1, 4, 6, 8, 8
Deck , 2, has denominations , 3, 7, 7
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 274, is as follows
Deck , 1, has denominations , 1, 4, 7, 7, 8
Deck , 2, has denominations , 3, 6, 6
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 275, is as follows
Deck , 1, has denominations , 1, 4, 7, 8, 8
Deck , 2, has denominations , 3, 6, 6
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 276, is as follows
Deck , 1, has denominations , 1, 4, 8, 8, 8
Deck , 2, has denominations , 3, 6, 7
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 277, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 6
Deck , 2, has denominations , 3, 4, 9
Deck , 3, has denominations , 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 278, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 7
Deck , 2, has denominations , 3, 4, 9
Deck , 3, has denominations , 2, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 279, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 8
Deck , 2, has denominations , 3, 4, 9
Deck , 3, has denominations , 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 280, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 9
Deck , 2, has denominations , 3, 4, 8
Deck , 3, has denominations , 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 281, is as follows
Deck , 1, has denominations , 1, 5, 5, 6, 6
Deck , 2, has denominations , 3, 4, 9
Deck , 3, has denominations , 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 282, is as follows
Deck , 1, has denominations , 1, 5, 5, 6, 7
Deck , 2, has denominations , 3, 4, 9
Deck , 3, has denominations , 2, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 283, is as follows
Deck , 1, has denominations , 1, 5, 5, 6, 8
Deck , 2, has denominations , 3, 4, 9
Deck , 3, has denominations , 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 284, is as follows
Deck , 1, has denominations , 1, 5, 5, 6, 9
Deck , 2, has denominations , 3, 4, 8
Deck , 3, has denominations , 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 285, is as follows
Deck , 1, has denominations , 1, 5, 5, 7, 7
Deck , 2, has denominations , 3, 4, 9
Deck , 3, has denominations , 2, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 286, is as follows
Deck , 1, has denominations , 1, 5, 6, 6, 6
Deck , 2, has denominations , 3, 4, 9
Deck , 3, has denominations , 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 287, is as follows
Deck , 1, has denominations , 1, 5, 6, 6, 7
Deck , 2, has denominations , 3, 4, 9
Deck , 3, has denominations , 2, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 288, is as follows
Deck , 1, has denominations , 1, 5, 6, 6, 8
Deck , 2, has denominations , 3, 4, 9
Deck , 3, has denominations , 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 289, is as follows
Deck , 1, has denominations , 1, 5, 6, 6, 9
Deck , 2, has denominations , 3, 4, 8
Deck , 3, has denominations , 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 290, is as follows
Deck , 1, has denominations , 1, 5, 6, 7, 7
Deck , 2, has denominations , 3, 4, 9
Deck , 3, has denominations , 2, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 291, is as follows
Deck , 1, has denominations , 1, 5, 7, 7, 7
Deck , 2, has denominations , 3, 4, 9
Deck , 3, has denominations , 2, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 5/9
yet Deck, 3, beats deck 1, with probability , 8/15
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 1.451, seconds to generate.
Chapter Number, 16
In this chapter we will consider the set whose deck sizes are, 3, 4, 4
and there are, 8, denominations from 1(Ace) to, 8
Up to obvious cyclic symmetry, there are, 4,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 3, 6
Deck , 3, has denominations , 2, 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 9/16
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 4, 4, 7
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 9/16
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 4, 7, 7
Deck , 2, has denominations , 3, 6, 6
Deck , 3, has denominations , 2, 5, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 9/16
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 4, 7, 7
Deck , 2, has denominations , 3, 6, 6, 6
Deck , 3, has denominations , 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 9/16
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 7/12
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.955, seconds to generate.
Chapter Number, 17
In this chapter we will consider the set whose deck sizes are, 3, 4, 4
and there are, 9, denominations from 1(Ace) to, 9
Up to obvious cyclic symmetry, there are, 12,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 3, 3, 4, 7
Deck , 3, has denominations , 2, 2, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 9/16
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 3, 4, 4, 7
Deck , 3, has denominations , 2, 2, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 9/16
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 4, 4, 4, 7
Deck , 3, has denominations , 2, 3, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 9/16
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 4, 5, 8
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 9/16
-------------------------------------------------------
Set Number, 5, is as follows
Deck , 1, has denominations , 1, 4, 7, 8
Deck , 2, has denominations , 3, 6, 6
Deck , 3, has denominations , 2, 5, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 9/16
-------------------------------------------------------
Set Number, 6, is as follows
Deck , 1, has denominations , 1, 4, 7, 8
Deck , 2, has denominations , 3, 6, 6, 6
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 9/16
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 7, is as follows
Deck , 1, has denominations , 1, 4, 8, 8
Deck , 2, has denominations , 3, 6, 7
Deck , 3, has denominations , 2, 5, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 9/16
-------------------------------------------------------
Set Number, 8, is as follows
Deck , 1, has denominations , 1, 4, 8, 8
Deck , 2, has denominations , 3, 7, 7
Deck , 3, has denominations , 2, 5, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 9/16
-------------------------------------------------------
Set Number, 9, is as follows
Deck , 1, has denominations , 1, 4, 8, 8
Deck , 2, has denominations , 3, 6, 6, 7
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 9/16
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 10, is as follows
Deck , 1, has denominations , 1, 4, 8, 8
Deck , 2, has denominations , 3, 6, 7, 7
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 9/16
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 11, is as follows
Deck , 1, has denominations , 1, 5, 5, 8
Deck , 2, has denominations , 3, 4, 7
Deck , 3, has denominations , 2, 2, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 9/16
-------------------------------------------------------
Set Number, 12, is as follows
Deck , 1, has denominations , 1, 5, 5, 8
Deck , 2, has denominations , 4, 4, 7
Deck , 3, has denominations , 2, 3, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 9/16
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.760, seconds to generate.
Chapter Number, 18
In this chapter we will consider the set whose deck sizes are, 3, 4, 4
and there are, 10, denominations from 1(Ace) to, 10
Up to obvious cyclic symmetry, there are, 12,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 6, 9
Deck , 2, has denominations , 3, 4, 5, 8
Deck , 3, has denominations , 2, 2, 7, 10
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 9/16
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 6, 9
Deck , 2, has denominations , 4, 4, 5, 8
Deck , 3, has denominations , 2, 3, 7, 10
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 9/16
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 6, 9
Deck , 2, has denominations , 4, 5, 5, 8
Deck , 3, has denominations , 2, 3, 7, 10
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 9/16
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 4, 8, 9
Deck , 2, has denominations , 3, 6, 7
Deck , 3, has denominations , 2, 5, 5, 10
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 9/16
-------------------------------------------------------
Set Number, 5, is as follows
Deck , 1, has denominations , 1, 4, 8, 9
Deck , 2, has denominations , 3, 7, 7
Deck , 3, has denominations , 2, 5, 6, 10
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 9/16
-------------------------------------------------------
Set Number, 6, is as follows
Deck , 1, has denominations , 1, 4, 8, 9
Deck , 2, has denominations , 3, 6, 6, 7
Deck , 3, has denominations , 2, 5, 10
It is readily seen that
Deck , 1, beats deck , 2, with probability , 9/16
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 7, is as follows
Deck , 1, has denominations , 1, 4, 8, 9
Deck , 2, has denominations , 3, 6, 7, 7
Deck , 3, has denominations , 2, 5, 10
It is readily seen that
Deck , 1, beats deck , 2, with probability , 9/16
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 8, is as follows
Deck , 1, has denominations , 1, 4, 9, 9
Deck , 2, has denominations , 3, 7, 8
Deck , 3, has denominations , 2, 5, 6, 10
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 9/16
-------------------------------------------------------
Set Number, 9, is as follows
Deck , 1, has denominations , 1, 4, 9, 9
Deck , 2, has denominations , 3, 6, 7, 8
Deck , 3, has denominations , 2, 5, 10
It is readily seen that
Deck , 1, beats deck , 2, with probability , 9/16
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 10, is as follows
Deck , 1, has denominations , 1, 5, 6, 9
Deck , 2, has denominations , 3, 4, 8
Deck , 3, has denominations , 2, 2, 7, 10
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 9/16
-------------------------------------------------------
Set Number, 11, is as follows
Deck , 1, has denominations , 1, 5, 6, 9
Deck , 2, has denominations , 4, 4, 8
Deck , 3, has denominations , 2, 3, 7, 10
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 9/16
-------------------------------------------------------
Set Number, 12, is as follows
Deck , 1, has denominations , 1, 6, 6, 9
Deck , 2, has denominations , 4, 5, 8
Deck , 3, has denominations , 2, 3, 7, 10
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 9/16
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.660, seconds to generate.
Chapter Number, 19
In this chapter we will consider the set whose deck sizes are, 3, 4, 4
and there are, 11, denominations from 1(Ace) to, 11
Up to obvious cyclic symmetry, there are, 4,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 7, 10
Deck , 2, has denominations , 4, 5, 6, 9
Deck , 3, has denominations , 2, 3, 8, 11
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 9/16
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 4, 9, 10
Deck , 2, has denominations , 3, 7, 8
Deck , 3, has denominations , 2, 5, 6, 11
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 9/16
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 4, 9, 10
Deck , 2, has denominations , 3, 6, 7, 8
Deck , 3, has denominations , 2, 5, 11
It is readily seen that
Deck , 1, beats deck , 2, with probability , 9/16
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 6, 7, 10
Deck , 2, has denominations , 4, 5, 9
Deck , 3, has denominations , 2, 3, 8, 11
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 9/16
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.239, seconds to generate.
There do not exist Sucker's Bets Sets of Decks with, 3, decks, with deck sizes,
3, 4, 4, using , 12, denominations labelled from 1 to, 12
Chapter Number, 21
In this chapter we will consider the set whose deck sizes are, 3, 4, 5
and there are, 5, denominations from 1(Ace) to, 5
Up to obvious cyclic symmetry, there are, 2,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 4, 4
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 1, 4, 4, 4
Deck , 2, has denominations , 3, 3, 3, 3
Deck , 3, has denominations , 2, 2, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.042, seconds to generate.
Chapter Number, 22
In this chapter we will consider the set whose deck sizes are, 3, 4, 5
and there are, 6, denominations from 1(Ace) to, 6
Up to obvious cyclic symmetry, there are, 16,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 4
Deck , 2, has denominations , 3, 3, 3, 3, 6
Deck , 3, has denominations , 2, 2, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 4, 4, 4
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 4, 4, 5
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 4, 5, 5
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 5, is as follows
Deck , 1, has denominations , 1, 5, 5, 5
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 6, is as follows
Deck , 1, has denominations , 1, 5, 5, 5
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 7, is as follows
Deck , 1, has denominations , 1, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 8, is as follows
Deck , 1, has denominations , 1, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 9, is as follows
Deck , 1, has denominations , 1, 1, 4, 4, 5
Deck , 2, has denominations , 3, 3, 3, 3
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 10, is as follows
Deck , 1, has denominations , 1, 1, 4, 4, 6
Deck , 2, has denominations , 3, 3, 3, 3
Deck , 3, has denominations , 2, 2, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 11, is as follows
Deck , 1, has denominations , 1, 1, 4, 5, 5
Deck , 2, has denominations , 3, 3, 3, 3
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 12, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 3, 3, 3, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 13, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 3, 3, 4, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 14, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 3, 4, 4, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 15, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4, 4
Deck , 3, has denominations , 2, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 16, is as follows
Deck , 1, has denominations , 1, 2, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4, 4
Deck , 3, has denominations , 3, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.120, seconds to generate.
Chapter Number, 23
In this chapter we will consider the set whose deck sizes are, 3, 4, 5
and there are, 7, denominations from 1(Ace) to, 7
Up to obvious cyclic symmetry, there are, 65,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 4
Deck , 2, has denominations , 3, 3, 3, 3, 6
Deck , 3, has denominations , 2, 2, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 4, 4
Deck , 2, has denominations , 3, 3, 3, 3, 7
Deck , 3, has denominations , 2, 2, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 4, 5
Deck , 2, has denominations , 3, 3, 3, 3, 7
Deck , 3, has denominations , 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 3, 6, 6
Deck , 3, has denominations , 2, 5, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 5, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 3, 4, 7
Deck , 3, has denominations , 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 6, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 4, 4, 7
Deck , 3, has denominations , 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 7, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 4, 4, 4, 7
Deck , 3, has denominations , 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 8, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 4, 4, 4, 4, 7
Deck , 3, has denominations , 2, 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 9, is as follows
Deck , 1, has denominations , 1, 3, 6, 6
Deck , 2, has denominations , 2, 5, 5
Deck , 3, has denominations , 4, 4, 4, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 10, is as follows
Deck , 1, has denominations , 1, 4, 4, 5
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 11, is as follows
Deck , 1, has denominations , 1, 4, 4, 6
Deck , 2, has denominations , 3, 3, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 12, is as follows
Deck , 1, has denominations , 1, 4, 4, 7
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 2, 5, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 13, is as follows
Deck , 1, has denominations , 1, 4, 5, 5
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 14, is as follows
Deck , 1, has denominations , 1, 4, 5, 6
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 15, is as follows
Deck , 1, has denominations , 1, 4, 6, 6
Deck , 2, has denominations , 3, 3, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 16, is as follows
Deck , 1, has denominations , 1, 4, 6, 6
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 17, is as follows
Deck , 1, has denominations , 1, 5, 5, 5
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 18, is as follows
Deck , 1, has denominations , 1, 5, 5, 5
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 19, is as follows
Deck , 1, has denominations , 1, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 20, is as follows
Deck , 1, has denominations , 1, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 21, is as follows
Deck , 1, has denominations , 1, 5, 5, 6
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 22, is as follows
Deck , 1, has denominations , 1, 5, 5, 6
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 23, is as follows
Deck , 1, has denominations , 1, 5, 5, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 24, is as follows
Deck , 1, has denominations , 1, 5, 5, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 25, is as follows
Deck , 1, has denominations , 1, 5, 6, 6
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 26, is as follows
Deck , 1, has denominations , 1, 5, 6, 6
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 27, is as follows
Deck , 1, has denominations , 1, 5, 6, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 28, is as follows
Deck , 1, has denominations , 1, 5, 6, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 29, is as follows
Deck , 1, has denominations , 1, 6, 6, 6
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 30, is as follows
Deck , 1, has denominations , 1, 6, 6, 6
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 2, 4, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 31, is as follows
Deck , 1, has denominations , 1, 6, 6, 6
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 32, is as follows
Deck , 1, has denominations , 1, 6, 6, 6
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 33, is as follows
Deck , 1, has denominations , 1, 6, 6, 6
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 34, is as follows
Deck , 1, has denominations , 1, 6, 6, 6
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 35, is as follows
Deck , 1, has denominations , 1, 6, 6, 6
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 3, 4, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 36, is as follows
Deck , 1, has denominations , 1, 1, 4, 5, 6
Deck , 2, has denominations , 3, 3, 3, 3
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 37, is as follows
Deck , 1, has denominations , 1, 1, 4, 5, 7
Deck , 2, has denominations , 3, 3, 3, 3
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 38, is as follows
Deck , 1, has denominations , 1, 1, 4, 6, 6
Deck , 2, has denominations , 3, 3, 3, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 39, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 3, 3, 3, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 40, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 3, 3, 4, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 41, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 3, 4, 4, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 42, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 4, 4, 4, 4
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 43, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 7
Deck , 2, has denominations , 3, 3, 3, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 44, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 7
Deck , 2, has denominations , 3, 3, 4, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 45, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 7
Deck , 2, has denominations , 3, 4, 4, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 46, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 7
Deck , 2, has denominations , 4, 4, 4, 4
Deck , 3, has denominations , 2, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 47, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 3, 3, 3, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 48, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 3, 3, 4, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 49, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 3, 4, 4, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 50, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 4, 4, 4, 4
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 51, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 3, 4, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 52, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 4, 4, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 53, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 4, 5, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 54, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 5, 5, 5
Deck , 3, has denominations , 2, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 55, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 4, 4, 4, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 56, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 4, 4, 5, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 57, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 4, 5, 5, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 58, is as follows
Deck , 1, has denominations , 1, 2, 5, 5, 6
Deck , 2, has denominations , 4, 4, 4, 4
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 59, is as follows
Deck , 1, has denominations , 1, 2, 5, 5, 7
Deck , 2, has denominations , 4, 4, 4, 4
Deck , 3, has denominations , 3, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 60, is as follows
Deck , 1, has denominations , 1, 2, 5, 6, 6
Deck , 2, has denominations , 4, 4, 4, 4
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 61, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 4, 4, 4, 5
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 62, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 4, 4, 5, 5
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 63, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 4, 5, 5, 5
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 64, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 5, 5, 5, 5
Deck , 3, has denominations , 3, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 65, is as follows
Deck , 1, has denominations , 1, 3, 6, 6, 6
Deck , 2, has denominations , 5, 5, 5, 5
Deck , 3, has denominations , 2, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.410, seconds to generate.
Chapter Number, 24
In this chapter we will consider the set whose deck sizes are, 3, 4, 5
and there are, 8, denominations from 1(Ace) to, 8
Up to obvious cyclic symmetry, there are, 171,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 5
Deck , 2, has denominations , 3, 3, 3, 3, 7
Deck , 3, has denominations , 2, 2, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 4, 5
Deck , 2, has denominations , 3, 3, 3, 3, 8
Deck , 3, has denominations , 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 4, 6
Deck , 2, has denominations , 3, 3, 3, 3, 7
Deck , 3, has denominations , 2, 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 4, 6
Deck , 2, has denominations , 3, 3, 3, 3, 8
Deck , 3, has denominations , 2, 2, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 5, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 3, 3, 6
Deck , 3, has denominations , 2, 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 6, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 3, 6, 6
Deck , 3, has denominations , 2, 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 7, is as follows
Deck , 1, has denominations , 1, 4, 8
Deck , 2, has denominations , 3, 3, 3, 6, 7
Deck , 3, has denominations , 2, 5, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 8, is as follows
Deck , 1, has denominations , 1, 4, 8
Deck , 2, has denominations , 3, 3, 3, 7, 7
Deck , 3, has denominations , 2, 5, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 9, is as follows
Deck , 1, has denominations , 1, 4, 8
Deck , 2, has denominations , 3, 3, 3, 7, 7
Deck , 3, has denominations , 2, 5, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 10, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 3, 4, 7
Deck , 3, has denominations , 2, 2, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 11, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 3, 4, 8
Deck , 3, has denominations , 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 12, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 4, 4, 7
Deck , 3, has denominations , 2, 2, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 13, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 4, 4, 8
Deck , 3, has denominations , 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 14, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 4, 4, 4, 7
Deck , 3, has denominations , 2, 2, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 15, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 4, 4, 4, 8
Deck , 3, has denominations , 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 16, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 4, 4, 4, 4, 7
Deck , 3, has denominations , 2, 3, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 17, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 4, 4, 4, 4, 8
Deck , 3, has denominations , 2, 3, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 18, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 3, 3, 4, 8
Deck , 3, has denominations , 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 19, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 3, 4, 4, 8
Deck , 3, has denominations , 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 20, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 4, 4, 4, 8
Deck , 3, has denominations , 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 21, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 4, 4, 4, 4, 8
Deck , 3, has denominations , 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 22, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 3, 3, 4, 7, 7
Deck , 3, has denominations , 2, 6, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 23, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 3, 4, 4, 7, 7
Deck , 3, has denominations , 2, 6, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 24, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 3, 4, 5, 8
Deck , 3, has denominations , 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 25, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 4, 4, 5, 8
Deck , 3, has denominations , 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 26, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 4, 5, 5, 8
Deck , 3, has denominations , 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 27, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 5, 5, 5, 8
Deck , 3, has denominations , 2, 4, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 28, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 4, 5, 8
Deck , 3, has denominations , 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 29, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 5, 5, 8
Deck , 3, has denominations , 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 30, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 5, 5, 5, 8
Deck , 3, has denominations , 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 31, is as follows
Deck , 1, has denominations , 1, 3, 6, 7
Deck , 2, has denominations , 2, 5, 5
Deck , 3, has denominations , 4, 4, 4, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 32, is as follows
Deck , 1, has denominations , 1, 3, 6, 8
Deck , 2, has denominations , 2, 5, 5
Deck , 3, has denominations , 4, 4, 4, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 33, is as follows
Deck , 1, has denominations , 1, 3, 7, 7
Deck , 2, has denominations , 2, 5, 6
Deck , 3, has denominations , 4, 4, 4, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 34, is as follows
Deck , 1, has denominations , 1, 3, 7, 7
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 4, 4, 4, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 35, is as follows
Deck , 1, has denominations , 1, 3, 7, 7
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 4, 4, 5, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 36, is as follows
Deck , 1, has denominations , 1, 3, 7, 7
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 4, 5, 5, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 37, is as follows
Deck , 1, has denominations , 1, 4, 4, 6
Deck , 2, has denominations , 3, 3, 5
Deck , 3, has denominations , 2, 2, 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 38, is as follows
Deck , 1, has denominations , 1, 4, 4, 7
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 2, 5, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 39, is as follows
Deck , 1, has denominations , 1, 4, 4, 8
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 2, 5, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 40, is as follows
Deck , 1, has denominations , 1, 4, 4, 8
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 5, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 41, is as follows
Deck , 1, has denominations , 1, 4, 4, 8
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 5, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 42, is as follows
Deck , 1, has denominations , 1, 4, 5, 6
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 43, is as follows
Deck , 1, has denominations , 1, 4, 5, 7
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 2, 2, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 44, is as follows
Deck , 1, has denominations , 1, 4, 5, 8
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 6, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 45, is as follows
Deck , 1, has denominations , 1, 4, 6, 6
Deck , 2, has denominations , 3, 3, 5
Deck , 3, has denominations , 2, 2, 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 46, is as follows
Deck , 1, has denominations , 1, 4, 6, 6
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 2, 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 47, is as follows
Deck , 1, has denominations , 1, 4, 6, 7
Deck , 2, has denominations , 3, 3, 5
Deck , 3, has denominations , 2, 2, 2, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 48, is as follows
Deck , 1, has denominations , 1, 4, 6, 7
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 2, 2, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 49, is as follows
Deck , 1, has denominations , 1, 4, 7, 7
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 3, 5, 5, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 50, is as follows
Deck , 1, has denominations , 1, 4, 7, 7
Deck , 2, has denominations , 3, 5, 6
Deck , 3, has denominations , 2, 2, 2, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 51, is as follows
Deck , 1, has denominations , 1, 4, 7, 7
Deck , 2, has denominations , 3, 6, 6
Deck , 3, has denominations , 2, 2, 5, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 52, is as follows
Deck , 1, has denominations , 1, 4, 7, 7
Deck , 2, has denominations , 3, 6, 6
Deck , 3, has denominations , 2, 5, 5, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 53, is as follows
Deck , 1, has denominations , 1, 5, 5, 6
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 54, is as follows
Deck , 1, has denominations , 1, 5, 5, 6
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 55, is as follows
Deck , 1, has denominations , 1, 5, 5, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 56, is as follows
Deck , 1, has denominations , 1, 5, 5, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 57, is as follows
Deck , 1, has denominations , 1, 5, 5, 7
Deck , 2, has denominations , 3, 4, 6
Deck , 3, has denominations , 2, 2, 2, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 58, is as follows
Deck , 1, has denominations , 1, 5, 5, 7
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 2, 2, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 59, is as follows
Deck , 1, has denominations , 1, 5, 5, 7
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 2, 3, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 60, is as follows
Deck , 1, has denominations , 1, 5, 5, 8
Deck , 2, has denominations , 3, 4, 7
Deck , 3, has denominations , 2, 2, 6, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 61, is as follows
Deck , 1, has denominations , 1, 5, 5, 8
Deck , 2, has denominations , 4, 4, 7
Deck , 3, has denominations , 2, 3, 6, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 62, is as follows
Deck , 1, has denominations , 1, 5, 6, 6
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 63, is as follows
Deck , 1, has denominations , 1, 5, 6, 6
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 64, is as follows
Deck , 1, has denominations , 1, 5, 6, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 65, is as follows
Deck , 1, has denominations , 1, 5, 6, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 66, is as follows
Deck , 1, has denominations , 1, 5, 6, 7
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 67, is as follows
Deck , 1, has denominations , 1, 5, 6, 7
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 68, is as follows
Deck , 1, has denominations , 1, 5, 6, 7
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 69, is as follows
Deck , 1, has denominations , 1, 5, 6, 7
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 70, is as follows
Deck , 1, has denominations , 1, 5, 7, 7
Deck , 2, has denominations , 3, 4, 6
Deck , 3, has denominations , 2, 2, 2, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 71, is as follows
Deck , 1, has denominations , 1, 5, 7, 7
Deck , 2, has denominations , 3, 6, 6
Deck , 3, has denominations , 2, 2, 4, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 72, is as follows
Deck , 1, has denominations , 1, 5, 7, 7
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 2, 2, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 73, is as follows
Deck , 1, has denominations , 1, 5, 7, 7
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 2, 3, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 74, is as follows
Deck , 1, has denominations , 1, 5, 7, 7
Deck , 2, has denominations , 4, 6, 6
Deck , 3, has denominations , 2, 2, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 75, is as follows
Deck , 1, has denominations , 1, 5, 7, 7
Deck , 2, has denominations , 4, 6, 6
Deck , 3, has denominations , 2, 3, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 76, is as follows
Deck , 1, has denominations , 1, 6, 6, 6
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 77, is as follows
Deck , 1, has denominations , 1, 6, 6, 6
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 2, 4, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 78, is as follows
Deck , 1, has denominations , 1, 6, 6, 6
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 2, 3, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 79, is as follows
Deck , 1, has denominations , 1, 6, 6, 6
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 3, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 80, is as follows
Deck , 1, has denominations , 1, 6, 6, 6
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 2, 3, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 81, is as follows
Deck , 1, has denominations , 1, 6, 6, 6
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 3, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 82, is as follows
Deck , 1, has denominations , 1, 6, 6, 6
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 3, 4, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 83, is as follows
Deck , 1, has denominations , 1, 6, 6, 7
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 2, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 84, is as follows
Deck , 1, has denominations , 1, 6, 6, 7
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 2, 4, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 85, is as follows
Deck , 1, has denominations , 1, 6, 6, 7
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 2, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 86, is as follows
Deck , 1, has denominations , 1, 6, 6, 7
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 87, is as follows
Deck , 1, has denominations , 1, 6, 6, 7
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 2, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 88, is as follows
Deck , 1, has denominations , 1, 6, 6, 7
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 89, is as follows
Deck , 1, has denominations , 1, 6, 6, 7
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 3, 4, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 90, is as follows
Deck , 1, has denominations , 1, 6, 7, 7
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 2, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 91, is as follows
Deck , 1, has denominations , 1, 6, 7, 7
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 2, 4, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 92, is as follows
Deck , 1, has denominations , 1, 6, 7, 7
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 2, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 93, is as follows
Deck , 1, has denominations , 1, 6, 7, 7
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 94, is as follows
Deck , 1, has denominations , 1, 6, 7, 7
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 2, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 95, is as follows
Deck , 1, has denominations , 1, 6, 7, 7
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 96, is as follows
Deck , 1, has denominations , 1, 6, 7, 7
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 3, 4, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 97, is as follows
Deck , 1, has denominations , 1, 7, 7, 7
Deck , 2, has denominations , 3, 5, 6
Deck , 3, has denominations , 2, 2, 4, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 98, is as follows
Deck , 1, has denominations , 1, 7, 7, 7
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 2, 2, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 99, is as follows
Deck , 1, has denominations , 1, 7, 7, 7
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 2, 3, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 100, is as follows
Deck , 1, has denominations , 1, 7, 7, 7
Deck , 2, has denominations , 4, 6, 6
Deck , 3, has denominations , 2, 3, 5, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 101, is as follows
Deck , 1, has denominations , 1, 7, 7, 7
Deck , 2, has denominations , 5, 5, 6
Deck , 3, has denominations , 2, 3, 4, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 102, is as follows
Deck , 1, has denominations , 1, 7, 7, 7
Deck , 2, has denominations , 5, 6, 6
Deck , 3, has denominations , 2, 3, 4, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 103, is as follows
Deck , 1, has denominations , 1, 1, 4, 6, 7
Deck , 2, has denominations , 3, 3, 3, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 104, is as follows
Deck , 1, has denominations , 1, 1, 4, 6, 8
Deck , 2, has denominations , 3, 3, 3, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 105, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 7
Deck , 2, has denominations , 3, 3, 3, 4
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 106, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 7
Deck , 2, has denominations , 3, 3, 4, 4
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 107, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 7
Deck , 2, has denominations , 3, 4, 4, 4
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 108, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 7
Deck , 2, has denominations , 4, 4, 4, 4
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 109, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 8
Deck , 2, has denominations , 3, 3, 3, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 110, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 8
Deck , 2, has denominations , 3, 3, 4, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 111, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 8
Deck , 2, has denominations , 3, 4, 4, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 112, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 8
Deck , 2, has denominations , 4, 4, 4, 4
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 113, is as follows
Deck , 1, has denominations , 1, 1, 5, 7, 7
Deck , 2, has denominations , 3, 3, 4, 6
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 114, is as follows
Deck , 1, has denominations , 1, 1, 5, 7, 7
Deck , 2, has denominations , 3, 4, 4, 6
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 115, is as follows
Deck , 1, has denominations , 1, 1, 5, 7, 7
Deck , 2, has denominations , 4, 4, 4, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 116, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 7
Deck , 2, has denominations , 3, 3, 4, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 117, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 7
Deck , 2, has denominations , 3, 4, 4, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 118, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 7
Deck , 2, has denominations , 3, 4, 5, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 119, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 7
Deck , 2, has denominations , 3, 5, 5, 5
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 120, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 7
Deck , 2, has denominations , 4, 4, 4, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 121, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 7
Deck , 2, has denominations , 4, 4, 5, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 122, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 7
Deck , 2, has denominations , 4, 5, 5, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 123, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 8
Deck , 2, has denominations , 3, 3, 4, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 124, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 8
Deck , 2, has denominations , 3, 4, 4, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 125, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 8
Deck , 2, has denominations , 3, 4, 5, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 126, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 8
Deck , 2, has denominations , 3, 5, 5, 5
Deck , 3, has denominations , 2, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 127, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 8
Deck , 2, has denominations , 4, 4, 4, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 128, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 8
Deck , 2, has denominations , 4, 4, 5, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 129, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 8
Deck , 2, has denominations , 4, 5, 5, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 130, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 7
Deck , 2, has denominations , 3, 3, 4, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 131, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 7
Deck , 2, has denominations , 3, 4, 4, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 132, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 7
Deck , 2, has denominations , 3, 4, 5, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 133, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 7
Deck , 2, has denominations , 3, 5, 5, 5
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 134, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 7
Deck , 2, has denominations , 4, 4, 4, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 135, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 7
Deck , 2, has denominations , 4, 4, 5, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 136, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 7
Deck , 2, has denominations , 4, 5, 5, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 137, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 7
Deck , 2, has denominations , 3, 4, 5, 6
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 138, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 7
Deck , 2, has denominations , 3, 5, 5, 6
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 139, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 7
Deck , 2, has denominations , 3, 5, 6, 6
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 140, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 7
Deck , 2, has denominations , 4, 4, 5, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 141, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 7
Deck , 2, has denominations , 4, 5, 5, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 142, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 7
Deck , 2, has denominations , 4, 5, 6, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 143, is as follows
Deck , 1, has denominations , 1, 2, 5, 6, 7
Deck , 2, has denominations , 4, 4, 4, 4
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 144, is as follows
Deck , 1, has denominations , 1, 2, 5, 6, 8
Deck , 2, has denominations , 4, 4, 4, 4
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 145, is as follows
Deck , 1, has denominations , 1, 2, 5, 7, 7
Deck , 2, has denominations , 4, 4, 4, 6
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 146, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 7
Deck , 2, has denominations , 4, 4, 4, 5
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 147, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 7
Deck , 2, has denominations , 4, 4, 5, 5
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 148, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 7
Deck , 2, has denominations , 4, 5, 5, 5
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 149, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 7
Deck , 2, has denominations , 5, 5, 5, 5
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 150, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 8
Deck , 2, has denominations , 4, 4, 4, 5
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 151, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 8
Deck , 2, has denominations , 4, 4, 5, 5
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 152, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 8
Deck , 2, has denominations , 4, 5, 5, 5
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 153, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 8
Deck , 2, has denominations , 5, 5, 5, 5
Deck , 3, has denominations , 3, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 154, is as follows
Deck , 1, has denominations , 1, 2, 6, 7, 7
Deck , 2, has denominations , 4, 4, 4, 5
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 155, is as follows
Deck , 1, has denominations , 1, 2, 6, 7, 7
Deck , 2, has denominations , 4, 4, 5, 5
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 156, is as follows
Deck , 1, has denominations , 1, 2, 6, 7, 7
Deck , 2, has denominations , 4, 5, 5, 5
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 157, is as follows
Deck , 1, has denominations , 1, 2, 6, 7, 7
Deck , 2, has denominations , 5, 5, 5, 5
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 158, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 7
Deck , 2, has denominations , 4, 4, 5, 6
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 159, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 7
Deck , 2, has denominations , 4, 5, 5, 6
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 160, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 7
Deck , 2, has denominations , 4, 5, 6, 6
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 161, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 7
Deck , 2, has denominations , 4, 6, 6, 6
Deck , 3, has denominations , 3, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 162, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 7
Deck , 2, has denominations , 5, 5, 5, 6
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 163, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 7
Deck , 2, has denominations , 5, 5, 6, 6
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 164, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 7
Deck , 2, has denominations , 5, 6, 6, 6
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 165, is as follows
Deck , 1, has denominations , 1, 3, 6, 6, 7
Deck , 2, has denominations , 5, 5, 5, 5
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 166, is as follows
Deck , 1, has denominations , 1, 3, 6, 7, 7
Deck , 2, has denominations , 5, 5, 5, 5
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 167, is as follows
Deck , 1, has denominations , 1, 3, 7, 7, 7
Deck , 2, has denominations , 4, 6, 6, 6
Deck , 3, has denominations , 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 168, is as follows
Deck , 1, has denominations , 1, 3, 7, 7, 7
Deck , 2, has denominations , 5, 5, 5, 6
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 169, is as follows
Deck , 1, has denominations , 1, 3, 7, 7, 7
Deck , 2, has denominations , 5, 5, 6, 6
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 170, is as follows
Deck , 1, has denominations , 1, 3, 7, 7, 7
Deck , 2, has denominations , 5, 6, 6, 6
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 171, is as follows
Deck , 1, has denominations , 1, 4, 7, 7, 7
Deck , 2, has denominations , 3, 6, 6, 6
Deck , 3, has denominations , 2, 5, 8
It is readily seen that
13
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 8/15
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 1.902, seconds to generate.
Chapter Number, 25
In this chapter we will consider the set whose deck sizes are, 3, 4, 5
and there are, 9, denominations from 1(Ace) to, 9
Up to obvious cyclic symmetry, there are, 293,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 8
Deck , 2, has denominations , 3, 3, 3, 5, 7
Deck , 3, has denominations , 2, 2, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 4, 8
Deck , 2, has denominations , 3, 3, 3, 6, 7
Deck , 3, has denominations , 2, 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 4, 9
Deck , 2, has denominations , 3, 3, 3, 7, 8
Deck , 3, has denominations , 2, 5, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 4, 9
Deck , 2, has denominations , 3, 3, 3, 7, 8
Deck , 3, has denominations , 2, 5, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 5, is as follows
Deck , 1, has denominations , 1, 4, 9
Deck , 2, has denominations , 3, 3, 3, 8, 8
Deck , 3, has denominations , 2, 5, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 6, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 3, 3, 4, 8
Deck , 3, has denominations , 2, 2, 7, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 7, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 3, 3, 4, 9
Deck , 3, has denominations , 2, 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 8, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 3, 4, 4, 8
Deck , 3, has denominations , 2, 2, 7, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 9, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 3, 4, 4, 9
Deck , 3, has denominations , 2, 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 10, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 4, 4, 4, 8
Deck , 3, has denominations , 2, 2, 7, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 11, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 4, 4, 4, 9
Deck , 3, has denominations , 2, 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 12, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 4, 4, 4, 4, 8
Deck , 3, has denominations , 2, 3, 7, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 13, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 4, 4, 4, 4, 9
Deck , 3, has denominations , 2, 3, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 14, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 3, 3, 3, 4, 8
Deck , 3, has denominations , 2, 2, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 15, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 3, 3, 3, 4, 9
Deck , 3, has denominations , 2, 2, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 16, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 3, 3, 4, 4, 8
Deck , 3, has denominations , 2, 2, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 17, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 3, 3, 4, 4, 9
Deck , 3, has denominations , 2, 2, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 18, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 3, 4, 4, 4, 8
Deck , 3, has denominations , 2, 2, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 19, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 3, 4, 4, 4, 9
Deck , 3, has denominations , 2, 2, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 20, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 4, 4, 4, 4, 8
Deck , 3, has denominations , 2, 3, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 21, is as follows
Deck , 1, has denominations , 1, 5, 7
Deck , 2, has denominations , 4, 4, 4, 4, 9
Deck , 3, has denominations , 2, 3, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 22, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 3, 3, 3, 4, 7
Deck , 3, has denominations , 2, 2, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 23, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 3, 3, 4, 4, 7
Deck , 3, has denominations , 2, 2, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 24, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 3, 3, 4, 7, 7
Deck , 3, has denominations , 2, 2, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 25, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 3, 4, 4, 4, 7
Deck , 3, has denominations , 2, 2, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 26, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 3, 4, 4, 7, 7
Deck , 3, has denominations , 2, 2, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 27, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 4, 4, 4, 4, 7
Deck , 3, has denominations , 2, 3, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 28, is as follows
Deck , 1, has denominations , 1, 5, 8
Deck , 2, has denominations , 4, 4, 4, 7, 7
Deck , 3, has denominations , 2, 3, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 29, is as follows
Deck , 1, has denominations , 1, 5, 9
Deck , 2, has denominations , 3, 3, 4, 7, 8
Deck , 3, has denominations , 2, 6, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 30, is as follows
Deck , 1, has denominations , 1, 5, 9
Deck , 2, has denominations , 3, 3, 4, 8, 8
Deck , 3, has denominations , 2, 6, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 31, is as follows
Deck , 1, has denominations , 1, 5, 9
Deck , 2, has denominations , 3, 3, 4, 8, 8
Deck , 3, has denominations , 2, 6, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 32, is as follows
Deck , 1, has denominations , 1, 5, 9
Deck , 2, has denominations , 3, 4, 4, 7, 8
Deck , 3, has denominations , 2, 6, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 33, is as follows
Deck , 1, has denominations , 1, 5, 9
Deck , 2, has denominations , 3, 4, 4, 8, 8
Deck , 3, has denominations , 2, 6, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 34, is as follows
Deck , 1, has denominations , 1, 5, 9
Deck , 2, has denominations , 3, 4, 4, 8, 8
Deck , 3, has denominations , 2, 6, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 35, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 3, 4, 5, 8
Deck , 3, has denominations , 2, 2, 7, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 36, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 3, 4, 5, 9
Deck , 3, has denominations , 2, 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 37, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 4, 4, 5, 8
Deck , 3, has denominations , 2, 2, 7, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 38, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 4, 4, 5, 9
Deck , 3, has denominations , 2, 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 39, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 4, 5, 5, 8
Deck , 3, has denominations , 2, 2, 7, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 40, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 4, 5, 5, 9
Deck , 3, has denominations , 2, 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 41, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 5, 5, 5, 9
Deck , 3, has denominations , 2, 4, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 42, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 4, 5, 8
Deck , 3, has denominations , 2, 3, 7, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 43, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 4, 5, 9
Deck , 3, has denominations , 2, 3, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 44, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 5, 5, 8
Deck , 3, has denominations , 2, 3, 7, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 45, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 5, 5, 9
Deck , 3, has denominations , 2, 3, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 46, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 5, 5, 5, 8
Deck , 3, has denominations , 2, 3, 7, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 47, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 5, 5, 5, 9
Deck , 3, has denominations , 2, 3, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 48, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 3, 4, 5, 9
Deck , 3, has denominations , 2, 2, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 49, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 4, 4, 5, 9
Deck , 3, has denominations , 2, 2, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 50, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 4, 5, 5, 9
Deck , 3, has denominations , 2, 2, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 51, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 3, 5, 5, 5, 9
Deck , 3, has denominations , 2, 4, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 52, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 4, 4, 5, 9
Deck , 3, has denominations , 2, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 53, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 4, 5, 5, 9
Deck , 3, has denominations , 2, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 54, is as follows
Deck , 1, has denominations , 1, 6, 7
Deck , 2, has denominations , 4, 5, 5, 5, 9
Deck , 3, has denominations , 2, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 55, is as follows
Deck , 1, has denominations , 1, 6, 9
Deck , 2, has denominations , 3, 4, 5, 8, 8
Deck , 3, has denominations , 2, 7, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 7/12
-------------------------------------------------------
Set Number, 56, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 4, 5, 6, 9
Deck , 3, has denominations , 2, 2, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 57, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 5, 5, 6, 9
Deck , 3, has denominations , 2, 4, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 58, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 3, 5, 6, 6, 9
Deck , 3, has denominations , 2, 4, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
20
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 59, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 4, 5, 6, 9
Deck , 3, has denominations , 2, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 60, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 5, 5, 6, 9
Deck , 3, has denominations , 2, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 61, is as follows
Deck , 1, has denominations , 1, 7, 7
Deck , 2, has denominations , 4, 5, 6, 6, 9
Deck , 3, has denominations , 2, 3, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 62, is as follows
Deck , 1, has denominations , 1, 3, 7, 8
Deck , 2, has denominations , 2, 5, 6
Deck , 3, has denominations , 4, 4, 4, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 63, is as follows
Deck , 1, has denominations , 1, 3, 7, 8
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 4, 4, 4, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 64, is as follows
Deck , 1, has denominations , 1, 3, 7, 8
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 4, 4, 5, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 65, is as follows
Deck , 1, has denominations , 1, 3, 7, 8
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 4, 5, 5, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 66, is as follows
Deck , 1, has denominations , 1, 3, 7, 9
Deck , 2, has denominations , 2, 5, 6
Deck , 3, has denominations , 4, 4, 4, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 67, is as follows
Deck , 1, has denominations , 1, 3, 7, 9
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 4, 4, 4, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 68, is as follows
Deck , 1, has denominations , 1, 3, 7, 9
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 4, 4, 5, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 69, is as follows
Deck , 1, has denominations , 1, 3, 7, 9
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 4, 5, 5, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 70, is as follows
Deck , 1, has denominations , 1, 3, 8, 8
Deck , 2, has denominations , 2, 6, 7
Deck , 3, has denominations , 4, 4, 4, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 71, is as follows
Deck , 1, has denominations , 1, 3, 8, 8
Deck , 2, has denominations , 2, 6, 7
Deck , 3, has denominations , 4, 4, 5, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 72, is as follows
Deck , 1, has denominations , 1, 3, 8, 8
Deck , 2, has denominations , 2, 6, 7
Deck , 3, has denominations , 4, 5, 5, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 73, is as follows
Deck , 1, has denominations , 1, 3, 8, 8
Deck , 2, has denominations , 2, 7, 7
Deck , 3, has denominations , 4, 4, 5, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 74, is as follows
Deck , 1, has denominations , 1, 3, 8, 8
Deck , 2, has denominations , 2, 7, 7
Deck , 3, has denominations , 4, 5, 5, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 75, is as follows
Deck , 1, has denominations , 1, 3, 8, 8
Deck , 2, has denominations , 2, 7, 7
Deck , 3, has denominations , 4, 5, 6, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 76, is as follows
Deck , 1, has denominations , 1, 4, 4, 8
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 5, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 77, is as follows
Deck , 1, has denominations , 1, 4, 4, 9
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 5, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 78, is as follows
Deck , 1, has denominations , 1, 4, 4, 9
Deck , 2, has denominations , 3, 3, 8
Deck , 3, has denominations , 2, 2, 5, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 79, is as follows
Deck , 1, has denominations , 1, 4, 5, 7
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 2, 2, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 80, is as follows
Deck , 1, has denominations , 1, 4, 5, 8
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 6, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 81, is as follows
Deck , 1, has denominations , 1, 4, 5, 9
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 6, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 82, is as follows
Deck , 1, has denominations , 1, 4, 5, 9
Deck , 2, has denominations , 3, 3, 8
Deck , 3, has denominations , 2, 2, 6, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 83, is as follows
Deck , 1, has denominations , 1, 4, 5, 9
Deck , 2, has denominations , 3, 3, 8
Deck , 3, has denominations , 2, 2, 6, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 84, is as follows
Deck , 1, has denominations , 1, 4, 6, 7
Deck , 2, has denominations , 3, 3, 5
Deck , 3, has denominations , 2, 2, 2, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 85, is as follows
Deck , 1, has denominations , 1, 4, 6, 7
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 2, 2, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 86, is as follows
Deck , 1, has denominations , 1, 4, 7, 7
Deck , 2, has denominations , 3, 5, 6
Deck , 3, has denominations , 2, 2, 2, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 87, is as follows
Deck , 1, has denominations , 1, 4, 7, 7
Deck , 2, has denominations , 3, 6, 6
Deck , 3, has denominations , 2, 2, 5, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 88, is as follows
Deck , 1, has denominations , 1, 4, 7, 8
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 3, 5, 5, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 89, is as follows
Deck , 1, has denominations , 1, 4, 7, 8
Deck , 2, has denominations , 3, 5, 6
Deck , 3, has denominations , 2, 2, 2, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 90, is as follows
Deck , 1, has denominations , 1, 4, 7, 8
Deck , 2, has denominations , 3, 6, 6
Deck , 3, has denominations , 2, 2, 5, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 91, is as follows
Deck , 1, has denominations , 1, 4, 7, 8
Deck , 2, has denominations , 3, 6, 6
Deck , 3, has denominations , 2, 5, 5, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 92, is as follows
Deck , 1, has denominations , 1, 4, 8, 8
Deck , 2, has denominations , 2, 6, 7
Deck , 3, has denominations , 3, 5, 5, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 93, is as follows
Deck , 1, has denominations , 1, 4, 8, 8
Deck , 2, has denominations , 2, 7, 7
Deck , 3, has denominations , 3, 5, 5, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 94, is as follows
Deck , 1, has denominations , 1, 4, 8, 8
Deck , 2, has denominations , 2, 7, 7
Deck , 3, has denominations , 3, 5, 6, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 95, is as follows
Deck , 1, has denominations , 1, 4, 8, 8
Deck , 2, has denominations , 3, 6, 7
Deck , 3, has denominations , 2, 2, 5, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 96, is as follows
Deck , 1, has denominations , 1, 4, 8, 8
Deck , 2, has denominations , 3, 6, 7
Deck , 3, has denominations , 2, 5, 5, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 97, is as follows
Deck , 1, has denominations , 1, 4, 8, 8
Deck , 2, has denominations , 3, 7, 7
Deck , 3, has denominations , 2, 5, 5, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 98, is as follows
Deck , 1, has denominations , 1, 4, 8, 8
Deck , 2, has denominations , 3, 7, 7
Deck , 3, has denominations , 2, 5, 6, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 99, is as follows
Deck , 1, has denominations , 1, 5, 5, 7
Deck , 2, has denominations , 3, 4, 6
Deck , 3, has denominations , 2, 2, 2, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 100, is as follows
Deck , 1, has denominations , 1, 5, 5, 7
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 2, 2, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 101, is as follows
Deck , 1, has denominations , 1, 5, 5, 7
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 2, 3, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 102, is as follows
Deck , 1, has denominations , 1, 5, 5, 8
Deck , 2, has denominations , 3, 4, 7
Deck , 3, has denominations , 2, 2, 6, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 103, is as follows
Deck , 1, has denominations , 1, 5, 5, 8
Deck , 2, has denominations , 4, 4, 7
Deck , 3, has denominations , 2, 3, 6, 6, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 104, is as follows
Deck , 1, has denominations , 1, 5, 5, 9
Deck , 2, has denominations , 3, 4, 7
Deck , 3, has denominations , 2, 2, 6, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 105, is as follows
Deck , 1, has denominations , 1, 5, 5, 9
Deck , 2, has denominations , 3, 4, 8
Deck , 3, has denominations , 2, 2, 6, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 106, is as follows
Deck , 1, has denominations , 1, 5, 5, 9
Deck , 2, has denominations , 3, 4, 8
Deck , 3, has denominations , 2, 2, 6, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 107, is as follows
Deck , 1, has denominations , 1, 5, 5, 9
Deck , 2, has denominations , 4, 4, 7
Deck , 3, has denominations , 2, 3, 6, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 108, is as follows
Deck , 1, has denominations , 1, 5, 5, 9
Deck , 2, has denominations , 4, 4, 8
Deck , 3, has denominations , 2, 3, 6, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 109, is as follows
Deck , 1, has denominations , 1, 5, 5, 9
Deck , 2, has denominations , 4, 4, 8
Deck , 3, has denominations , 2, 3, 6, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 110, is as follows
Deck , 1, has denominations , 1, 5, 6, 7
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 111, is as follows
Deck , 1, has denominations , 1, 5, 6, 7
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 112, is as follows
Deck , 1, has denominations , 1, 5, 6, 7
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 113, is as follows
Deck , 1, has denominations , 1, 5, 6, 7
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 114, is as follows
Deck , 1, has denominations , 1, 5, 6, 8
Deck , 2, has denominations , 3, 4, 7
Deck , 3, has denominations , 2, 2, 2, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 115, is as follows
Deck , 1, has denominations , 1, 5, 6, 8
Deck , 2, has denominations , 4, 4, 7
Deck , 3, has denominations , 2, 2, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 116, is as follows
Deck , 1, has denominations , 1, 5, 6, 8
Deck , 2, has denominations , 4, 4, 7
Deck , 3, has denominations , 2, 3, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 117, is as follows
Deck , 1, has denominations , 1, 5, 6, 9
Deck , 2, has denominations , 3, 4, 8
Deck , 3, has denominations , 2, 2, 7, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 118, is as follows
Deck , 1, has denominations , 1, 5, 6, 9
Deck , 2, has denominations , 4, 4, 8
Deck , 3, has denominations , 2, 3, 7, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 119, is as follows
Deck , 1, has denominations , 1, 5, 7, 7
Deck , 2, has denominations , 3, 4, 6
Deck , 3, has denominations , 2, 2, 2, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 120, is as follows
Deck , 1, has denominations , 1, 5, 7, 7
Deck , 2, has denominations , 3, 6, 6
Deck , 3, has denominations , 2, 2, 4, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 121, is as follows
Deck , 1, has denominations , 1, 5, 7, 7
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 2, 2, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 122, is as follows
Deck , 1, has denominations , 1, 5, 7, 7
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 2, 3, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 123, is as follows
Deck , 1, has denominations , 1, 5, 7, 7
Deck , 2, has denominations , 4, 6, 6
Deck , 3, has denominations , 2, 2, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 124, is as follows
Deck , 1, has denominations , 1, 5, 7, 7
Deck , 2, has denominations , 4, 6, 6
Deck , 3, has denominations , 2, 3, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 125, is as follows
Deck , 1, has denominations , 1, 5, 7, 8
Deck , 2, has denominations , 3, 4, 6
Deck , 3, has denominations , 2, 2, 2, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 126, is as follows
Deck , 1, has denominations , 1, 5, 7, 8
Deck , 2, has denominations , 3, 6, 6
Deck , 3, has denominations , 2, 2, 4, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 127, is as follows
Deck , 1, has denominations , 1, 5, 7, 8
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 2, 2, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 128, is as follows
Deck , 1, has denominations , 1, 5, 7, 8
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 2, 3, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 129, is as follows
Deck , 1, has denominations , 1, 5, 7, 8
Deck , 2, has denominations , 4, 6, 6
Deck , 3, has denominations , 2, 2, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 130, is as follows
Deck , 1, has denominations , 1, 5, 7, 8
Deck , 2, has denominations , 4, 6, 6
Deck , 3, has denominations , 2, 3, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 131, is as follows
Deck , 1, has denominations , 1, 5, 8, 8
Deck , 2, has denominations , 3, 6, 7
Deck , 3, has denominations , 2, 2, 4, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 132, is as follows
Deck , 1, has denominations , 1, 5, 8, 8
Deck , 2, has denominations , 4, 6, 7
Deck , 3, has denominations , 2, 2, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 133, is as follows
Deck , 1, has denominations , 1, 5, 8, 8
Deck , 2, has denominations , 4, 6, 7
Deck , 3, has denominations , 2, 3, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 134, is as follows
Deck , 1, has denominations , 1, 5, 8, 8
Deck , 2, has denominations , 4, 7, 7
Deck , 3, has denominations , 2, 3, 6, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 135, is as follows
Deck , 1, has denominations , 1, 6, 6, 7
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 2, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 136, is as follows
Deck , 1, has denominations , 1, 6, 6, 7
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 2, 4, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 137, is as follows
Deck , 1, has denominations , 1, 6, 6, 7
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 2, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 138, is as follows
Deck , 1, has denominations , 1, 6, 6, 7
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 139, is as follows
Deck , 1, has denominations , 1, 6, 6, 7
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 2, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 140, is as follows
Deck , 1, has denominations , 1, 6, 6, 7
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 141, is as follows
Deck , 1, has denominations , 1, 6, 6, 7
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 3, 4, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 142, is as follows
Deck , 1, has denominations , 1, 6, 6, 8
Deck , 2, has denominations , 3, 5, 7
Deck , 3, has denominations , 2, 2, 4, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 143, is as follows
Deck , 1, has denominations , 1, 6, 6, 8
Deck , 2, has denominations , 4, 5, 7
Deck , 3, has denominations , 2, 2, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 144, is as follows
Deck , 1, has denominations , 1, 6, 6, 8
Deck , 2, has denominations , 4, 5, 7
Deck , 3, has denominations , 2, 3, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 145, is as follows
Deck , 1, has denominations , 1, 6, 6, 8
Deck , 2, has denominations , 5, 5, 7
Deck , 3, has denominations , 2, 3, 4, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 146, is as follows
Deck , 1, has denominations , 1, 6, 6, 9
Deck , 2, has denominations , 3, 5, 8
Deck , 3, has denominations , 2, 4, 7, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 147, is as follows
Deck , 1, has denominations , 1, 6, 6, 9
Deck , 2, has denominations , 4, 5, 8
Deck , 3, has denominations , 2, 3, 7, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 148, is as follows
Deck , 1, has denominations , 1, 6, 7, 7
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 2, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 149, is as follows
Deck , 1, has denominations , 1, 6, 7, 7
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 2, 4, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 150, is as follows
Deck , 1, has denominations , 1, 6, 7, 7
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 2, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 151, is as follows
Deck , 1, has denominations , 1, 6, 7, 7
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 152, is as follows
Deck , 1, has denominations , 1, 6, 7, 7
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 2, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 153, is as follows
Deck , 1, has denominations , 1, 6, 7, 7
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 154, is as follows
Deck , 1, has denominations , 1, 6, 7, 7
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 3, 4, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 155, is as follows
Deck , 1, has denominations , 1, 6, 7, 8
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 2, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 156, is as follows
Deck , 1, has denominations , 1, 6, 7, 8
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 2, 4, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 157, is as follows
Deck , 1, has denominations , 1, 6, 7, 8
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 2, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 158, is as follows
Deck , 1, has denominations , 1, 6, 7, 8
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 159, is as follows
Deck , 1, has denominations , 1, 6, 7, 8
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 2, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 160, is as follows
Deck , 1, has denominations , 1, 6, 7, 8
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 161, is as follows
Deck , 1, has denominations , 1, 6, 7, 8
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 3, 4, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 162, is as follows
Deck , 1, has denominations , 1, 6, 8, 8
Deck , 2, has denominations , 3, 5, 7
Deck , 3, has denominations , 2, 2, 4, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 163, is as follows
Deck , 1, has denominations , 1, 6, 8, 8
Deck , 2, has denominations , 4, 5, 7
Deck , 3, has denominations , 2, 2, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 164, is as follows
Deck , 1, has denominations , 1, 6, 8, 8
Deck , 2, has denominations , 4, 5, 7
Deck , 3, has denominations , 2, 3, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 165, is as follows
Deck , 1, has denominations , 1, 6, 8, 8
Deck , 2, has denominations , 4, 7, 7
Deck , 3, has denominations , 2, 3, 5, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 166, is as follows
Deck , 1, has denominations , 1, 6, 8, 8
Deck , 2, has denominations , 5, 5, 7
Deck , 3, has denominations , 2, 3, 4, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 167, is as follows
Deck , 1, has denominations , 1, 6, 8, 8
Deck , 2, has denominations , 5, 7, 7
Deck , 3, has denominations , 2, 3, 4, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 7/12
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 168, is as follows
Deck , 1, has denominations , 1, 7, 7, 7
Deck , 2, has denominations , 3, 5, 6
Deck , 3, has denominations , 2, 2, 4, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 169, is as follows
Deck , 1, has denominations , 1, 7, 7, 7
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 2, 2, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 170, is as follows
Deck , 1, has denominations , 1, 7, 7, 7
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 2, 3, 3, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 171, is as follows
Deck , 1, has denominations , 1, 7, 7, 7
Deck , 2, has denominations , 4, 6, 6
Deck , 3, has denominations , 2, 3, 5, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 172, is as follows
Deck , 1, has denominations , 1, 7, 7, 7
Deck , 2, has denominations , 5, 5, 6
Deck , 3, has denominations , 2, 3, 4, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 173, is as follows
Deck , 1, has denominations , 1, 7, 7, 7
Deck , 2, has denominations , 5, 6, 6
Deck , 3, has denominations , 2, 3, 4, 8, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 174, is as follows
Deck , 1, has denominations , 1, 7, 7, 8
Deck , 2, has denominations , 3, 5, 6
Deck , 3, has denominations , 2, 2, 4, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 175, is as follows
Deck , 1, has denominations , 1, 7, 7, 8
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 2, 2, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 176, is as follows
Deck , 1, has denominations , 1, 7, 7, 8
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 2, 3, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 177, is as follows
Deck , 1, has denominations , 1, 7, 7, 8
Deck , 2, has denominations , 4, 6, 6
Deck , 3, has denominations , 2, 3, 5, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 178, is as follows
Deck , 1, has denominations , 1, 7, 7, 8
Deck , 2, has denominations , 5, 5, 6
Deck , 3, has denominations , 2, 3, 4, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 179, is as follows
Deck , 1, has denominations , 1, 7, 7, 8
Deck , 2, has denominations , 5, 6, 6
Deck , 3, has denominations , 2, 3, 4, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 180, is as follows
Deck , 1, has denominations , 1, 7, 8, 8
Deck , 2, has denominations , 3, 5, 6
Deck , 3, has denominations , 2, 2, 4, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 181, is as follows
Deck , 1, has denominations , 1, 7, 8, 8
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 2, 2, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 182, is as follows
Deck , 1, has denominations , 1, 7, 8, 8
Deck , 2, has denominations , 4, 5, 6
Deck , 3, has denominations , 2, 3, 3, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 183, is as follows
Deck , 1, has denominations , 1, 7, 8, 8
Deck , 2, has denominations , 4, 6, 6
Deck , 3, has denominations , 2, 3, 5, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 184, is as follows
Deck , 1, has denominations , 1, 7, 8, 8
Deck , 2, has denominations , 5, 5, 6
Deck , 3, has denominations , 2, 3, 4, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 185, is as follows
Deck , 1, has denominations , 1, 7, 8, 8
Deck , 2, has denominations , 5, 6, 6
Deck , 3, has denominations , 2, 3, 4, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 186, is as follows
Deck , 1, has denominations , 1, 8, 8, 8
Deck , 2, has denominations , 4, 6, 7
Deck , 3, has denominations , 2, 3, 5, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 8/15
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 187, is as follows
Deck , 1, has denominations , 1, 8, 8, 8
Deck , 2, has denominations , 5, 6, 7
Deck , 3, has denominations , 2, 3, 4, 9, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/4
Deck , 2, beats deck , 3, with probability , 3/5
11
yet Deck, 3, beats deck 1, with probability , --
20
-------------------------------------------------------
Set Number, 188, is as follows
Deck , 1, has denominations , 1, 1, 5, 7, 8
Deck , 2, has denominations , 3, 3, 4, 6
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 189, is as follows
Deck , 1, has denominations , 1, 1, 5, 7, 8
Deck , 2, has denominations , 3, 4, 4, 6
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 190, is as follows
Deck , 1, has denominations , 1, 1, 5, 7, 8
Deck , 2, has denominations , 4, 4, 4, 6
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 191, is as follows
Deck , 1, has denominations , 1, 1, 5, 7, 9
Deck , 2, has denominations , 3, 3, 4, 6
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 192, is as follows
Deck , 1, has denominations , 1, 1, 5, 7, 9
Deck , 2, has denominations , 3, 4, 4, 6
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 193, is as follows
Deck , 1, has denominations , 1, 1, 5, 7, 9
Deck , 2, has denominations , 4, 4, 4, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 194, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 8
Deck , 2, has denominations , 3, 3, 4, 5
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 195, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 8
Deck , 2, has denominations , 3, 4, 4, 5
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 196, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 8
Deck , 2, has denominations , 3, 4, 5, 5
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 197, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 8
Deck , 2, has denominations , 3, 5, 5, 5
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 198, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 8
Deck , 2, has denominations , 4, 4, 4, 5
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 199, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 8
Deck , 2, has denominations , 4, 4, 5, 5
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 200, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 8
Deck , 2, has denominations , 4, 5, 5, 5
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 201, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 9
Deck , 2, has denominations , 3, 3, 4, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 202, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 9
Deck , 2, has denominations , 3, 4, 4, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 203, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 9
Deck , 2, has denominations , 3, 4, 5, 5
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 204, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 9
Deck , 2, has denominations , 3, 5, 5, 5
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 205, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 9
Deck , 2, has denominations , 4, 4, 4, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 206, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 9
Deck , 2, has denominations , 4, 4, 5, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 207, is as follows
Deck , 1, has denominations , 1, 1, 6, 7, 9
Deck , 2, has denominations , 4, 5, 5, 5
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 208, is as follows
Deck , 1, has denominations , 1, 1, 6, 8, 8
Deck , 2, has denominations , 3, 4, 5, 7
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 209, is as follows
Deck , 1, has denominations , 1, 1, 6, 8, 8
Deck , 2, has denominations , 3, 5, 5, 7
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 210, is as follows
Deck , 1, has denominations , 1, 1, 6, 8, 8
Deck , 2, has denominations , 4, 4, 5, 7
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 211, is as follows
Deck , 1, has denominations , 1, 1, 6, 8, 8
Deck , 2, has denominations , 4, 5, 5, 7
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 212, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 8
Deck , 2, has denominations , 3, 4, 5, 6
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 213, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 8
Deck , 2, has denominations , 3, 5, 5, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 214, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 8
Deck , 2, has denominations , 3, 5, 6, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 215, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 8
Deck , 2, has denominations , 4, 4, 5, 6
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 216, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 8
Deck , 2, has denominations , 4, 5, 5, 6
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 217, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 8
Deck , 2, has denominations , 4, 5, 6, 6
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 218, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 9
Deck , 2, has denominations , 3, 4, 5, 6
Deck , 3, has denominations , 2, 2, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 219, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 9
Deck , 2, has denominations , 3, 5, 5, 6
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 220, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 9
Deck , 2, has denominations , 3, 5, 6, 6
Deck , 3, has denominations , 2, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 221, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 9
Deck , 2, has denominations , 4, 4, 5, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 222, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 9
Deck , 2, has denominations , 4, 5, 5, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 223, is as follows
Deck , 1, has denominations , 1, 1, 7, 7, 9
Deck , 2, has denominations , 4, 5, 6, 6
Deck , 3, has denominations , 2, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 224, is as follows
Deck , 1, has denominations , 1, 1, 7, 8, 8
Deck , 2, has denominations , 3, 4, 5, 6
Deck , 3, has denominations , 2, 2, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 225, is as follows
Deck , 1, has denominations , 1, 1, 7, 8, 8
Deck , 2, has denominations , 3, 5, 5, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 226, is as follows
Deck , 1, has denominations , 1, 1, 7, 8, 8
Deck , 2, has denominations , 3, 5, 6, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 227, is as follows
Deck , 1, has denominations , 1, 1, 7, 8, 8
Deck , 2, has denominations , 4, 4, 5, 6
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 228, is as follows
Deck , 1, has denominations , 1, 1, 7, 8, 8
Deck , 2, has denominations , 4, 5, 5, 6
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 229, is as follows
Deck , 1, has denominations , 1, 1, 7, 8, 8
Deck , 2, has denominations , 4, 5, 6, 6
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 230, is as follows
Deck , 1, has denominations , 1, 1, 8, 8, 8
Deck , 2, has denominations , 3, 5, 6, 7
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 231, is as follows
Deck , 1, has denominations , 1, 1, 8, 8, 8
Deck , 2, has denominations , 4, 5, 6, 7
Deck , 3, has denominations , 2, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 232, is as follows
Deck , 1, has denominations , 1, 2, 5, 7, 8
Deck , 2, has denominations , 4, 4, 4, 6
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 233, is as follows
Deck , 1, has denominations , 1, 2, 5, 7, 9
Deck , 2, has denominations , 4, 4, 4, 6
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 234, is as follows
Deck , 1, has denominations , 1, 2, 6, 7, 8
Deck , 2, has denominations , 4, 4, 4, 5
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 235, is as follows
Deck , 1, has denominations , 1, 2, 6, 7, 8
Deck , 2, has denominations , 4, 4, 5, 5
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 236, is as follows
Deck , 1, has denominations , 1, 2, 6, 7, 8
Deck , 2, has denominations , 4, 5, 5, 5
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 237, is as follows
Deck , 1, has denominations , 1, 2, 6, 7, 8
Deck , 2, has denominations , 5, 5, 5, 5
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 238, is as follows
Deck , 1, has denominations , 1, 2, 6, 7, 9
Deck , 2, has denominations , 4, 4, 4, 5
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 239, is as follows
Deck , 1, has denominations , 1, 2, 6, 7, 9
Deck , 2, has denominations , 4, 4, 5, 5
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 240, is as follows
Deck , 1, has denominations , 1, 2, 6, 7, 9
Deck , 2, has denominations , 4, 5, 5, 5
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 241, is as follows
Deck , 1, has denominations , 1, 2, 6, 7, 9
Deck , 2, has denominations , 5, 5, 5, 5
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 242, is as follows
Deck , 1, has denominations , 1, 2, 6, 8, 8
Deck , 2, has denominations , 4, 4, 5, 7
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 243, is as follows
Deck , 1, has denominations , 1, 2, 6, 8, 8
Deck , 2, has denominations , 4, 5, 5, 7
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 244, is as follows
Deck , 1, has denominations , 1, 2, 6, 8, 8
Deck , 2, has denominations , 5, 5, 5, 7
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 245, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 8
Deck , 2, has denominations , 4, 4, 5, 6
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 246, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 8
Deck , 2, has denominations , 4, 5, 5, 6
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 247, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 8
Deck , 2, has denominations , 4, 5, 6, 6
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 248, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 8
Deck , 2, has denominations , 4, 6, 6, 6
Deck , 3, has denominations , 3, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 249, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 8
Deck , 2, has denominations , 5, 5, 5, 6
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 250, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 8
Deck , 2, has denominations , 5, 5, 6, 6
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 251, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 8
Deck , 2, has denominations , 5, 6, 6, 6
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 252, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 9
Deck , 2, has denominations , 4, 4, 5, 6
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 253, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 9
Deck , 2, has denominations , 4, 5, 5, 6
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 254, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 9
Deck , 2, has denominations , 4, 5, 6, 6
Deck , 3, has denominations , 3, 3, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 255, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 9
Deck , 2, has denominations , 4, 6, 6, 6
Deck , 3, has denominations , 3, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 256, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 9
Deck , 2, has denominations , 5, 5, 5, 6
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 257, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 9
Deck , 2, has denominations , 5, 5, 6, 6
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 258, is as follows
Deck , 1, has denominations , 1, 2, 7, 7, 9
Deck , 2, has denominations , 5, 6, 6, 6
Deck , 3, has denominations , 3, 4, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 259, is as follows
Deck , 1, has denominations , 1, 2, 7, 8, 8
Deck , 2, has denominations , 4, 4, 5, 6
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 260, is as follows
Deck , 1, has denominations , 1, 2, 7, 8, 8
Deck , 2, has denominations , 4, 5, 5, 6
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 261, is as follows
Deck , 1, has denominations , 1, 2, 7, 8, 8
Deck , 2, has denominations , 4, 5, 6, 6
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 262, is as follows
Deck , 1, has denominations , 1, 2, 7, 8, 8
Deck , 2, has denominations , 4, 6, 6, 6
Deck , 3, has denominations , 3, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 263, is as follows
Deck , 1, has denominations , 1, 2, 7, 8, 8
Deck , 2, has denominations , 5, 5, 5, 6
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 264, is as follows
Deck , 1, has denominations , 1, 2, 7, 8, 8
Deck , 2, has denominations , 5, 5, 6, 6
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 265, is as follows
Deck , 1, has denominations , 1, 2, 7, 8, 8
Deck , 2, has denominations , 5, 6, 6, 6
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 266, is as follows
Deck , 1, has denominations , 1, 2, 8, 8, 8
Deck , 2, has denominations , 4, 5, 6, 7
Deck , 3, has denominations , 3, 3, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 267, is as follows
Deck , 1, has denominations , 1, 2, 8, 8, 8
Deck , 2, has denominations , 4, 6, 6, 7
Deck , 3, has denominations , 3, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 268, is as follows
Deck , 1, has denominations , 1, 2, 8, 8, 8
Deck , 2, has denominations , 4, 6, 7, 7
Deck , 3, has denominations , 3, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 269, is as follows
Deck , 1, has denominations , 1, 2, 8, 8, 8
Deck , 2, has denominations , 5, 5, 6, 7
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 270, is as follows
Deck , 1, has denominations , 1, 2, 8, 8, 8
Deck , 2, has denominations , 5, 6, 6, 7
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 271, is as follows
Deck , 1, has denominations , 1, 2, 8, 8, 8
Deck , 2, has denominations , 5, 6, 7, 7
Deck , 3, has denominations , 3, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 272, is as follows
Deck , 1, has denominations , 1, 3, 6, 6, 9
Deck , 2, has denominations , 2, 5, 5, 8
Deck , 3, has denominations , 4, 4, 7
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 273, is as follows
Deck , 1, has denominations , 1, 3, 6, 7, 8
Deck , 2, has denominations , 5, 5, 5, 5
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 274, is as follows
Deck , 1, has denominations , 1, 3, 6, 8, 8
Deck , 2, has denominations , 5, 5, 5, 7
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 275, is as follows
Deck , 1, has denominations , 1, 3, 6, 9, 9
Deck , 2, has denominations , 2, 5, 8, 8
Deck , 3, has denominations , 4, 7, 7
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 276, is as follows
Deck , 1, has denominations , 1, 3, 7, 7, 8
Deck , 2, has denominations , 4, 6, 6, 6
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 277, is as follows
Deck , 1, has denominations , 1, 3, 7, 7, 8
Deck , 2, has denominations , 5, 5, 5, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 278, is as follows
Deck , 1, has denominations , 1, 3, 7, 7, 8
Deck , 2, has denominations , 5, 5, 6, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 279, is as follows
Deck , 1, has denominations , 1, 3, 7, 7, 8
Deck , 2, has denominations , 5, 6, 6, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 280, is as follows
Deck , 1, has denominations , 1, 3, 7, 8, 8
Deck , 2, has denominations , 4, 6, 6, 6
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 281, is as follows
Deck , 1, has denominations , 1, 3, 7, 8, 8
Deck , 2, has denominations , 5, 5, 5, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 282, is as follows
Deck , 1, has denominations , 1, 3, 7, 8, 8
Deck , 2, has denominations , 5, 5, 6, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 283, is as follows
Deck , 1, has denominations , 1, 3, 7, 8, 8
Deck , 2, has denominations , 5, 6, 6, 6
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 284, is as follows
Deck , 1, has denominations , 1, 3, 8, 8, 8
Deck , 2, has denominations , 4, 6, 6, 7
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 285, is as follows
Deck , 1, has denominations , 1, 3, 8, 8, 8
Deck , 2, has denominations , 4, 6, 7, 7
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 286, is as follows
Deck , 1, has denominations , 1, 3, 8, 8, 8
Deck , 2, has denominations , 5, 5, 6, 7
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 287, is as follows
Deck , 1, has denominations , 1, 3, 8, 8, 8
Deck , 2, has denominations , 5, 6, 6, 7
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 288, is as follows
Deck , 1, has denominations , 1, 3, 8, 8, 8
Deck , 2, has denominations , 5, 6, 7, 7
Deck , 3, has denominations , 2, 4, 9
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 289, is as follows
Deck , 1, has denominations , 1, 4, 7, 7, 7
Deck , 2, has denominations , 3, 3, 6, 9
Deck , 3, has denominations , 2, 5, 8
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 290, is as follows
Deck , 1, has denominations , 1, 4, 7, 7, 8
Deck , 2, has denominations , 3, 6, 6, 6
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
13
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 291, is as follows
Deck , 1, has denominations , 1, 4, 7, 8, 8
Deck , 2, has denominations , 3, 6, 6, 6
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
13
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 292, is as follows
Deck , 1, has denominations , 1, 4, 8, 8, 8
Deck , 2, has denominations , 3, 6, 6, 7
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
13
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 293, is as follows
Deck , 1, has denominations , 1, 4, 8, 8, 8
Deck , 2, has denominations , 3, 6, 7, 7
Deck , 3, has denominations , 2, 5, 9
It is readily seen that
13
Deck , 1, beats deck , 2, with probability , --
20
Deck , 2, beats deck , 3, with probability , 7/12
yet Deck, 3, beats deck 1, with probability , 8/15
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 4.274, seconds to generate.
Chapter Number, 26
In this chapter we will consider the set whose deck sizes are, 3, 5, 5
and there are, 5, denominations from 1(Ace) to, 5
Up to obvious cyclic symmetry, there are, 5,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 4
Deck , 2, has denominations , 3, 3, 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 1, 4, 4, 4
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 2, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 1, 4, 4, 4
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 1, 4, 4, 4
Deck , 2, has denominations , 3, 3, 3, 3, 3
Deck , 3, has denominations , 2, 2, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 5, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 4
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.056, seconds to generate.
Chapter Number, 27
In this chapter we will consider the set whose deck sizes are, 3, 5, 5
and there are, 6, denominations from 1(Ace) to, 6
Up to obvious cyclic symmetry, there are, 54,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 4
Deck , 2, has denominations , 3, 3, 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 4, 4
Deck , 2, has denominations , 3, 3, 3, 3, 5
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 4, 4
Deck , 2, has denominations , 3, 3, 3, 3, 6
Deck , 3, has denominations , 2, 2, 2, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
17
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 4, 4
Deck , 2, has denominations , 3, 3, 3, 3, 6
Deck , 3, has denominations , 2, 2, 5, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
13
Deck , 2, beats deck , 3, with probability , --
25
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 5, is as follows
Deck , 1, has denominations , 1, 4, 5
Deck , 2, has denominations , 3, 3, 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 6, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 7, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 8, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 4, 4, 4
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 9, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 4, 4, 4, 4
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 10, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 4, 4, 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 11, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 4, 4, 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 12, is as follows
Deck , 1, has denominations , 1, 1, 4, 4, 4
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 13, is as follows
Deck , 1, has denominations , 1, 1, 4, 4, 5
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 14, is as follows
Deck , 1, has denominations , 1, 1, 4, 4, 5
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 15, is as follows
Deck , 1, has denominations , 1, 1, 4, 4, 5
Deck , 2, has denominations , 3, 3, 3, 3, 3
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 16, is as follows
Deck , 1, has denominations , 1, 1, 4, 4, 6
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
14
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 17, is as follows
Deck , 1, has denominations , 1, 1, 4, 4, 6
Deck , 2, has denominations , 3, 3, 3, 3, 3
Deck , 3, has denominations , 2, 2, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 18, is as follows
Deck , 1, has denominations , 1, 1, 4, 5, 5
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 19, is as follows
Deck , 1, has denominations , 1, 1, 4, 5, 5
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 20, is as follows
Deck , 1, has denominations , 1, 1, 4, 5, 5
Deck , 2, has denominations , 3, 3, 3, 3, 3
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 21, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 2, 4, 4
Deck , 3, has denominations , 3, 3, 3, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 22, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 4, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 23, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 24, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 25, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 26, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 27, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 2, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 28, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 29, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 30, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 31, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 32, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 2, 4, 4, 4, 4
Deck , 3, has denominations , 3, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 33, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 3, 3, 3, 3, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 34, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 3, 3, 3, 4, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 35, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 3, 3, 4, 4, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 36, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 3, 4, 4, 4, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 37, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4, 4, 4
Deck , 3, has denominations , 2, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 38, is as follows
Deck , 1, has denominations , 1, 2, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 3, 3, 3, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 39, is as follows
Deck , 1, has denominations , 1, 2, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 3, 3, 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 40, is as follows
Deck , 1, has denominations , 1, 2, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4, 4, 4
Deck , 3, has denominations , 3, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 41, is as follows
Deck , 1, has denominations , 1, 3, 3, 6, 6
Deck , 2, has denominations , 2, 5, 5
Deck , 3, has denominations , 4, 4, 4, 4, 4
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 42, is as follows
Deck , 1, has denominations , 1, 3, 3, 6, 6
Deck , 2, has denominations , 2, 2, 5, 5, 5
Deck , 3, has denominations , 4, 4, 4
It is readily seen that
14
Deck , 1, beats deck , 2, with probability , --
25
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 43, is as follows
Deck , 1, has denominations , 1, 3, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 44, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 4
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 45, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 4
Deck , 2, has denominations , 3, 3, 5
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 46, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 4
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 2, 2, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 47, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 4
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 2, 5, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
17
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 48, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 5
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 49, is as follows
Deck , 1, has denominations , 1, 4, 4, 5, 5
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 50, is as follows
Deck , 1, has denominations , 1, 4, 5, 5, 5
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 51, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 5
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 52, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 5
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 53, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 54, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 0.176, seconds to generate.
Chapter Number, 28
In this chapter we will consider the set whose deck sizes are, 3, 5, 5
and there are, 7, denominations from 1(Ace) to, 7
Up to obvious cyclic symmetry, there are, 293,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 4
Deck , 2, has denominations , 3, 3, 3, 3, 5
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 4, 4
Deck , 2, has denominations , 3, 3, 3, 3, 6
Deck , 3, has denominations , 2, 2, 2, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
16
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 4, 4
Deck , 2, has denominations , 3, 3, 3, 3, 7
Deck , 3, has denominations , 2, 2, 2, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
17
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 4, 4
Deck , 2, has denominations , 3, 3, 3, 3, 7
Deck , 3, has denominations , 2, 2, 5, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
13
Deck , 2, beats deck , 3, with probability , --
25
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 5, is as follows
Deck , 1, has denominations , 1, 4, 4
Deck , 2, has denominations , 3, 3, 3, 3, 7
Deck , 3, has denominations , 2, 2, 5, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
13
Deck , 2, beats deck , 3, with probability , --
25
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 6, is as follows
Deck , 1, has denominations , 1, 4, 5
Deck , 2, has denominations , 3, 3, 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 7, is as follows
Deck , 1, has denominations , 1, 4, 5
Deck , 2, has denominations , 3, 3, 3, 3, 6
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 8, is as follows
Deck , 1, has denominations , 1, 4, 5
Deck , 2, has denominations , 3, 3, 3, 3, 7
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
17
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 9, is as follows
Deck , 1, has denominations , 1, 4, 5
Deck , 2, has denominations , 3, 3, 3, 3, 7
Deck , 3, has denominations , 2, 2, 6, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
13
Deck , 2, beats deck , 3, with probability , --
25
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 10, is as follows
Deck , 1, has denominations , 1, 4, 6
Deck , 2, has denominations , 3, 3, 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 11, is as follows
Deck , 1, has denominations , 1, 4, 6
Deck , 2, has denominations , 3, 3, 3, 3, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 12, is as follows
Deck , 1, has denominations , 1, 4, 6
Deck , 2, has denominations , 3, 3, 3, 3, 7
Deck , 3, has denominations , 2, 2, 5, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
13
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 13, is as follows
Deck , 1, has denominations , 1, 4, 6
Deck , 2, has denominations , 3, 3, 3, 5, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 14, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 3, 3, 6
Deck , 3, has denominations , 2, 2, 5, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
13
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 15, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 3, 6, 6
Deck , 3, has denominations , 2, 2, 5, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
16
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 16, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 3, 6, 6
Deck , 3, has denominations , 2, 5, 5, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
13
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 17, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 2, 4, 4, 4, 7
Deck , 3, has denominations , 3, 3, 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
14
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 18, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 19, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 3, 3, 7
Deck , 3, has denominations , 2, 2, 4, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
13
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 20, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 21, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 3, 4, 6
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 22, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 3, 4, 7
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
17
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 23, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 3, 4, 7
Deck , 3, has denominations , 2, 2, 6, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
13
Deck , 2, beats deck , 3, with probability , --
25
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 24, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 4, 4, 4
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 25, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 4, 4, 6
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 26, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 4, 4, 7
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
17
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 27, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 3, 4, 4, 7
Deck , 3, has denominations , 2, 2, 6, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
13
Deck , 2, beats deck , 3, with probability , --
25
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 28, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 4, 4, 4, 4
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 29, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 4, 4, 4, 6
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 30, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 4, 4, 4, 7
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
17
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 31, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 3, 4, 4, 4, 7
Deck , 3, has denominations , 2, 2, 6, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
13
Deck , 2, beats deck , 3, with probability , --
25
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 32, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 4, 4, 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 33, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 4, 4, 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 34, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 4, 4, 4, 4, 6
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 35, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 4, 4, 4, 4, 6
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 36, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 4, 4, 4, 4, 7
Deck , 3, has denominations , 2, 2, 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
17
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 37, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 4, 4, 4, 4, 7
Deck , 3, has denominations , 2, 3, 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
17
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 38, is as follows
Deck , 1, has denominations , 1, 5, 5
Deck , 2, has denominations , 4, 4, 4, 4, 7
Deck , 3, has denominations , 2, 3, 6, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
13
Deck , 2, beats deck , 3, with probability , --
25
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 39, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 3, 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 40, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 3, 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 41, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 3, 4, 4, 4
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 42, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 3, 4, 4, 4, 4
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 43, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 4, 4, 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 44, is as follows
Deck , 1, has denominations , 1, 5, 6
Deck , 2, has denominations , 4, 4, 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 45, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 3, 3, 4, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 46, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 3, 4, 4, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 47, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 3, 4, 5, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 48, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 3, 5, 5, 5
Deck , 3, has denominations , 2, 2, 4, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
13
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 49, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 4, 4, 4, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 50, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 4, 4, 5, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 51, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 4, 5, 5, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 52, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 5, 5, 5, 5
Deck , 3, has denominations , 2, 2, 4, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
14
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 53, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 3, 5, 5, 5, 5
Deck , 3, has denominations , 2, 4, 4, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
13
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 54, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 4, 4, 5
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 55, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 4, 4, 5
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 56, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 4, 5, 5
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 57, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 4, 5, 5
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 58, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 5, 5, 5
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 59, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 4, 5, 5, 5
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 60, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 5, 5, 5, 5
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 61, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 4, 5, 5, 5, 5
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 62, is as follows
Deck , 1, has denominations , 1, 6, 6
Deck , 2, has denominations , 5, 5, 5, 5, 5
Deck , 3, has denominations , 2, 3, 4, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 63, is as follows
Deck , 1, has denominations , 1, 1, 4, 4, 5
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 64, is as follows
Deck , 1, has denominations , 1, 1, 4, 4, 6
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 65, is as follows
Deck , 1, has denominations , 1, 1, 4, 4, 6
Deck , 2, has denominations , 3, 3, 3, 3, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
13
Deck , 1, beats deck , 2, with probability , --
25
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 66, is as follows
Deck , 1, has denominations , 1, 1, 4, 4, 7
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
14
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 67, is as follows
Deck , 1, has denominations , 1, 1, 4, 4, 7
Deck , 2, has denominations , 3, 3, 3, 3, 5
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
13
Deck , 1, beats deck , 2, with probability , --
25
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 68, is as follows
Deck , 1, has denominations , 1, 1, 4, 4, 7
Deck , 2, has denominations , 3, 3, 3, 3, 6
Deck , 3, has denominations , 2, 2, 5
It is readily seen that
13
Deck , 1, beats deck , 2, with probability , --
25
11
Deck , 2, beats deck , 3, with probability , --
15
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 69, is as follows
Deck , 1, has denominations , 1, 1, 4, 5, 5
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 70, is as follows
Deck , 1, has denominations , 1, 1, 4, 5, 6
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 71, is as follows
Deck , 1, has denominations , 1, 1, 4, 5, 6
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 72, is as follows
Deck , 1, has denominations , 1, 1, 4, 5, 6
Deck , 2, has denominations , 3, 3, 3, 3, 3
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 73, is as follows
Deck , 1, has denominations , 1, 1, 4, 5, 7
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
14
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 74, is as follows
Deck , 1, has denominations , 1, 1, 4, 5, 7
Deck , 2, has denominations , 3, 3, 3, 3, 3
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 75, is as follows
Deck , 1, has denominations , 1, 1, 4, 6, 6
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
14
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 76, is as follows
Deck , 1, has denominations , 1, 1, 4, 6, 6
Deck , 2, has denominations , 3, 3, 5
Deck , 3, has denominations , 2, 2, 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 77, is as follows
Deck , 1, has denominations , 1, 1, 4, 6, 6
Deck , 2, has denominations , 3, 3, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 78, is as follows
Deck , 1, has denominations , 1, 1, 4, 6, 6
Deck , 2, has denominations , 3, 3, 3, 3, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
14
Deck , 1, beats deck , 2, with probability , --
25
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 79, is as follows
Deck , 1, has denominations , 1, 1, 4, 6, 6
Deck , 2, has denominations , 3, 3, 3, 5, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
13
Deck , 1, beats deck , 2, with probability , --
25
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 80, is as follows
Deck , 1, has denominations , 1, 1, 4, 7, 7
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 2, 5, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 81, is as follows
Deck , 1, has denominations , 1, 1, 4, 7, 7
Deck , 2, has denominations , 3, 3, 3, 6, 6
Deck , 3, has denominations , 2, 5, 5
It is readily seen that
13
Deck , 1, beats deck , 2, with probability , --
25
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 82, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 83, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 84, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 85, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 86, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 2, 4, 4
Deck , 3, has denominations , 3, 3, 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 87, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 88, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 89, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 90, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 91, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 92, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 93, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 94, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 95, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 96, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 97, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 2, 4, 4, 4, 4
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 98, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 3, 3, 3, 3, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 99, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 3, 3, 3, 4, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 100, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 3, 3, 4, 4, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 101, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 3, 4, 4, 4, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 102, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 6
Deck , 2, has denominations , 4, 4, 4, 4, 4
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 103, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 7
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
14
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 104, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 7
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
14
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 105, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 7
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
14
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 106, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 7
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
14
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 107, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 7
Deck , 2, has denominations , 2, 4, 4, 4, 4
Deck , 3, has denominations , 3, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 108, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 7
Deck , 2, has denominations , 3, 3, 3, 3, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 109, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 7
Deck , 2, has denominations , 3, 3, 3, 4, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 110, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 7
Deck , 2, has denominations , 3, 3, 4, 4, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 111, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 7
Deck , 2, has denominations , 3, 4, 4, 4, 4
Deck , 3, has denominations , 2, 2, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 112, is as follows
Deck , 1, has denominations , 1, 1, 5, 5, 7
Deck , 2, has denominations , 4, 4, 4, 4, 4
Deck , 3, has denominations , 2, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 113, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 2, 4, 4
Deck , 3, has denominations , 3, 3, 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 114, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 115, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 116, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 117, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 118, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 119, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 120, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 121, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 122, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 123, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 124, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 2, 4, 4, 4, 4
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 125, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 3, 3, 3, 3, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 126, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 3, 3, 3, 4, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 127, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 3, 3, 4, 4, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 128, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 3, 4, 4, 4, 4
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 129, is as follows
Deck , 1, has denominations , 1, 1, 5, 6, 6
Deck , 2, has denominations , 4, 4, 4, 4, 4
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 130, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 2, 4, 5
Deck , 3, has denominations , 3, 3, 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 131, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 2, 5, 5
Deck , 3, has denominations , 3, 3, 3, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 132, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 2, 5, 5
Deck , 3, has denominations , 3, 3, 4, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 133, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 2, 5, 5
Deck , 3, has denominations , 3, 4, 4, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 134, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 135, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 3, 5
Deck , 3, has denominations , 2, 2, 2, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 136, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 3, 5
Deck , 3, has denominations , 2, 2, 4, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 137, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 138, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 139, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 140, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 2, 2, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
11
Deck , 2, beats deck , 3, with probability , --
15
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 141, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 2, 4, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 142, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 2, 4, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 143, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 4, 4, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 144, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 145, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 146, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 2, 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 147, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 2, 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 148, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 149, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 150, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 151, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 2, 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 152, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 2, 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 153, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 154, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 155, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 156, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 2, 3, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 157, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 3, 3, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 158, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 3, 4, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 159, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 3, 4, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 160, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 2, 4, 4, 4, 5
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 161, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 2, 4, 4, 5, 5
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 162, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 2, 4, 5, 5, 5
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 163, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 2, 5, 5, 5, 5
Deck , 3, has denominations , 3, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 164, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 3, 3, 4, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 165, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 3, 4, 4, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 166, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 3, 4, 5, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 167, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 3, 5, 5, 5
Deck , 3, has denominations , 2, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 168, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 4, 4, 4, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 169, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 4, 4, 5, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 170, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 4, 5, 5, 5
Deck , 3, has denominations , 2, 2, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 171, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 3, 5, 5, 5, 5
Deck , 3, has denominations , 2, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 172, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 4, 4, 4, 4, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 173, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 4, 4, 4, 5, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 174, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 4, 4, 5, 5, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 175, is as follows
Deck , 1, has denominations , 1, 1, 6, 6, 6
Deck , 2, has denominations , 4, 5, 5, 5, 5
Deck , 3, has denominations , 2, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 176, is as follows
Deck , 1, has denominations , 1, 2, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 3, 3, 3, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 177, is as follows
Deck , 1, has denominations , 1, 2, 5, 5, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 3, 3, 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 178, is as follows
Deck , 1, has denominations , 1, 2, 5, 5, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 3, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 179, is as follows
Deck , 1, has denominations , 1, 2, 5, 5, 6
Deck , 2, has denominations , 4, 4, 4, 4, 4
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 180, is as follows
Deck , 1, has denominations , 1, 2, 5, 5, 7
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 3, 3, 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
14
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 181, is as follows
Deck , 1, has denominations , 1, 2, 5, 5, 7
Deck , 2, has denominations , 4, 4, 4, 4, 4
Deck , 3, has denominations , 3, 3, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 182, is as follows
Deck , 1, has denominations , 1, 2, 5, 6, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 3, 3, 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 183, is as follows
Deck , 1, has denominations , 1, 2, 5, 6, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 3, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 184, is as follows
Deck , 1, has denominations , 1, 2, 5, 6, 6
Deck , 2, has denominations , 4, 4, 4, 4, 4
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 185, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 4, 4, 4, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 186, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 3, 3, 3, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 187, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 3, 3, 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 188, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 3, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 189, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 3, 3, 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 190, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 3, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 191, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 3, 3, 3, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 192, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 3, 3, 4, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 193, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 3, 3, 4, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 194, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 3, 4, 4, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 4/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 195, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 3, 4, 4, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
16
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 196, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 3, 5, 5, 5, 5
Deck , 3, has denominations , 4, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 197, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 4, 4, 4, 4, 5
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 198, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 4, 4, 4, 5, 5
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 199, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 4, 4, 5, 5, 5
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 200, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 4, 5, 5, 5, 5
Deck , 3, has denominations , 3, 3, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 201, is as follows
Deck , 1, has denominations , 1, 2, 6, 6, 6
Deck , 2, has denominations , 5, 5, 5, 5, 5
Deck , 3, has denominations , 3, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 202, is as follows
Deck , 1, has denominations , 1, 3, 3, 6, 6
Deck , 2, has denominations , 2, 5, 5
Deck , 3, has denominations , 4, 4, 4, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
17
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 203, is as follows
Deck , 1, has denominations , 1, 3, 3, 6, 7
Deck , 2, has denominations , 2, 5, 5
Deck , 3, has denominations , 4, 4, 4, 4, 4
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 204, is as follows
Deck , 1, has denominations , 1, 3, 3, 6, 7
Deck , 2, has denominations , 2, 2, 5, 5, 5
Deck , 3, has denominations , 4, 4, 4
It is readily seen that
14
Deck , 1, beats deck , 2, with probability , --
25
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 205, is as follows
Deck , 1, has denominations , 1, 3, 3, 7, 7
Deck , 2, has denominations , 2, 5, 5
Deck , 3, has denominations , 4, 4, 4, 4, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 206, is as follows
Deck , 1, has denominations , 1, 3, 3, 7, 7
Deck , 2, has denominations , 2, 5, 6
Deck , 3, has denominations , 4, 4, 4, 4, 4
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 207, is as follows
Deck , 1, has denominations , 1, 3, 3, 7, 7
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 4, 4, 4, 4, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 208, is as follows
Deck , 1, has denominations , 1, 3, 3, 7, 7
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 4, 4, 4, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 209, is as follows
Deck , 1, has denominations , 1, 3, 3, 7, 7
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 4, 4, 5, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 210, is as follows
Deck , 1, has denominations , 1, 3, 3, 7, 7
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 4, 5, 5, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 211, is as follows
Deck , 1, has denominations , 1, 3, 3, 7, 7
Deck , 2, has denominations , 2, 2, 5, 5, 6
Deck , 3, has denominations , 4, 4, 4
It is readily seen that
14
Deck , 1, beats deck , 2, with probability , --
25
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 212, is as follows
Deck , 1, has denominations , 1, 3, 3, 7, 7
Deck , 2, has denominations , 2, 2, 5, 6, 6
Deck , 3, has denominations , 4, 4, 4
It is readily seen that
14
Deck , 1, beats deck , 2, with probability , --
25
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 213, is as follows
Deck , 1, has denominations , 1, 3, 3, 7, 7
Deck , 2, has denominations , 2, 2, 6, 6, 6
Deck , 3, has denominations , 4, 4, 5
It is readily seen that
14
Deck , 1, beats deck , 2, with probability , --
25
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 214, is as follows
Deck , 1, has denominations , 1, 3, 3, 7, 7
Deck , 2, has denominations , 2, 2, 6, 6, 6
Deck , 3, has denominations , 4, 5, 5
It is readily seen that
14
Deck , 1, beats deck , 2, with probability , --
25
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 215, is as follows
Deck , 1, has denominations , 1, 3, 4, 7, 7
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 5, 5, 5, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 216, is as follows
Deck , 1, has denominations , 1, 3, 4, 7, 7
Deck , 2, has denominations , 2, 2, 6, 6, 6
Deck , 3, has denominations , 5, 5, 5
It is readily seen that
14
Deck , 1, beats deck , 2, with probability , --
25
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 217, is as follows
Deck , 1, has denominations , 1, 3, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 218, is as follows
Deck , 1, has denominations , 1, 3, 5, 5, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 219, is as follows
Deck , 1, has denominations , 1, 3, 5, 6, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 220, is as follows
Deck , 1, has denominations , 1, 3, 6, 6, 6
Deck , 2, has denominations , 2, 5, 5
Deck , 3, has denominations , 4, 4, 4, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 8/15
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 221, is as follows
Deck , 1, has denominations , 1, 3, 6, 6, 6
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 222, is as follows
Deck , 1, has denominations , 1, 3, 6, 6, 6
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 223, is as follows
Deck , 1, has denominations , 1, 3, 6, 6, 6
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 2, 4, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
14
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 224, is as follows
Deck , 1, has denominations , 1, 3, 6, 6, 6
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 4, 4, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 225, is as follows
Deck , 1, has denominations , 1, 3, 6, 6, 6
Deck , 2, has denominations , 2, 5, 5, 5, 5
Deck , 3, has denominations , 4, 4, 7
It is readily seen that
16
Deck , 1, beats deck , 2, with probability , --
25
Deck , 2, beats deck , 3, with probability , 8/15
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 226, is as follows
Deck , 1, has denominations , 1, 3, 6, 6, 6
Deck , 2, has denominations , 5, 5, 5, 5, 5
Deck , 3, has denominations , 2, 4, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 2/3
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 227, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 4
Deck , 2, has denominations , 3, 3, 5
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 228, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 4
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 2, 2, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 229, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 4
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 2, 5, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
17
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 230, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 4
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 2, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 231, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 4
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 5, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
17
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 232, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 4
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 5, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
17
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 233, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 5
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 234, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 5
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 235, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 5
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 236, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 5
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 6, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
17
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 237, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 6
Deck , 2, has denominations , 3, 3, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 238, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 6
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 5, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
14
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 239, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 7
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 2, 5, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
14
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 240, is as follows
Deck , 1, has denominations , 1, 4, 4, 4, 7
Deck , 2, has denominations , 3, 3, 3, 6, 6
Deck , 3, has denominations , 2, 5, 5
It is readily seen that
14
Deck , 1, beats deck , 2, with probability , --
25
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 241, is as follows
Deck , 1, has denominations , 1, 4, 4, 5, 5
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 242, is as follows
Deck , 1, has denominations , 1, 4, 4, 5, 5
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 243, is as follows
Deck , 1, has denominations , 1, 4, 4, 5, 5
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 244, is as follows
Deck , 1, has denominations , 1, 4, 4, 5, 5
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 6, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
17
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 245, is as follows
Deck , 1, has denominations , 1, 4, 4, 5, 6
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 246, is as follows
Deck , 1, has denominations , 1, 4, 4, 6, 6
Deck , 2, has denominations , 3, 3, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 247, is as follows
Deck , 1, has denominations , 1, 4, 4, 6, 6
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 248, is as follows
Deck , 1, has denominations , 1, 4, 4, 7, 7
Deck , 2, has denominations , 2, 6, 6
Deck , 3, has denominations , 3, 5, 5, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 2/3
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 249, is as follows
Deck , 1, has denominations , 1, 4, 4, 7, 7
Deck , 2, has denominations , 3, 6, 6
Deck , 3, has denominations , 2, 5, 5, 5, 5
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 250, is as follows
Deck , 1, has denominations , 1, 4, 4, 7, 7
Deck , 2, has denominations , 2, 3, 6, 6, 6
Deck , 3, has denominations , 5, 5, 5
It is readily seen that
14
Deck , 1, beats deck , 2, with probability , --
25
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 251, is as follows
Deck , 1, has denominations , 1, 4, 5, 5, 5
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 252, is as follows
Deck , 1, has denominations , 1, 4, 5, 5, 5
Deck , 2, has denominations , 3, 3, 6
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 253, is as follows
Deck , 1, has denominations , 1, 4, 5, 5, 5
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 254, is as follows
Deck , 1, has denominations , 1, 4, 5, 5, 5
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 6, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
17
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 255, is as follows
Deck , 1, has denominations , 1, 4, 5, 5, 6
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 256, is as follows
Deck , 1, has denominations , 1, 4, 5, 6, 6
Deck , 2, has denominations , 3, 3, 3
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 257, is as follows
Deck , 1, has denominations , 1, 4, 6, 6, 6
Deck , 2, has denominations , 3, 3, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
11
Deck , 1, beats deck , 2, with probability , --
15
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 258, is as follows
Deck , 1, has denominations , 1, 4, 6, 6, 6
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 2/3
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 259, is as follows
Deck , 1, has denominations , 1, 4, 6, 6, 6
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 260, is as follows
Deck , 1, has denominations , 1, 4, 6, 6, 6
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 261, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 5
Deck , 2, has denominations , 2, 4, 7
Deck , 3, has denominations , 3, 3, 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 8/15
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 262, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 5
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 263, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 5
Deck , 2, has denominations , 3, 3, 7
Deck , 3, has denominations , 2, 2, 4, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 264, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 5
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 265, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 5
Deck , 2, has denominations , 3, 4, 6
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 266, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 5
Deck , 2, has denominations , 3, 4, 7
Deck , 3, has denominations , 2, 2, 2, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 267, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 5
Deck , 2, has denominations , 3, 4, 7
Deck , 3, has denominations , 2, 2, 6, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
17
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 268, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 269, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 5
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 270, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 5
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 271, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 5
Deck , 2, has denominations , 4, 4, 6
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 272, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 5
Deck , 2, has denominations , 4, 4, 7
Deck , 3, has denominations , 2, 2, 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 273, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 5
Deck , 2, has denominations , 4, 4, 7
Deck , 3, has denominations , 2, 3, 3, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
11
Deck , 2, beats deck , 3, with probability , --
15
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 274, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 5
Deck , 2, has denominations , 4, 4, 7
Deck , 3, has denominations , 2, 3, 6, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
17
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 275, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 6
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 276, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 6
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 277, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 278, is as follows
Deck , 1, has denominations , 1, 5, 5, 5, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 279, is as follows
Deck , 1, has denominations , 1, 5, 5, 6, 6
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 280, is as follows
Deck , 1, has denominations , 1, 5, 5, 6, 6
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 281, is as follows
Deck , 1, has denominations , 1, 5, 5, 6, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 282, is as follows
Deck , 1, has denominations , 1, 5, 5, 6, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 283, is as follows
Deck , 1, has denominations , 1, 5, 6, 6, 6
Deck , 2, has denominations , 3, 3, 4
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 284, is as follows
Deck , 1, has denominations , 1, 5, 6, 6, 6
Deck , 2, has denominations , 3, 4, 4
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 285, is as follows
Deck , 1, has denominations , 1, 5, 6, 6, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 286, is as follows
Deck , 1, has denominations , 1, 5, 6, 6, 6
Deck , 2, has denominations , 4, 4, 4
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 287, is as follows
Deck , 1, has denominations , 1, 6, 6, 6, 6
Deck , 2, has denominations , 3, 4, 5
Deck , 3, has denominations , 2, 2, 2, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 288, is as follows
Deck , 1, has denominations , 1, 6, 6, 6, 6
Deck , 2, has denominations , 3, 5, 5
Deck , 3, has denominations , 2, 2, 4, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 8/15
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 289, is as follows
Deck , 1, has denominations , 1, 6, 6, 6, 6
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 290, is as follows
Deck , 1, has denominations , 1, 6, 6, 6, 6
Deck , 2, has denominations , 4, 4, 5
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 291, is as follows
Deck , 1, has denominations , 1, 6, 6, 6, 6
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 2, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 292, is as follows
Deck , 1, has denominations , 1, 6, 6, 6, 6
Deck , 2, has denominations , 4, 5, 5
Deck , 3, has denominations , 2, 3, 3, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
-------------------------------------------------------
Set Number, 293, is as follows
Deck , 1, has denominations , 1, 6, 6, 6, 6
Deck , 2, has denominations , 5, 5, 5
Deck , 3, has denominations , 2, 3, 4, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 4/5
Deck , 2, beats deck , 3, with probability , 3/5
13
yet Deck, 3, beats deck 1, with probability , --
25
---------------------------------------------------
---------------------------------------------------
This ends this chapter, that took, 1.876, seconds to generate.
Chapter Number, 29
In this chapter we will consider the set whose deck sizes are, 3, 5, 5
and there are, 8, denominations from 1(Ace) to, 8
Up to obvious cyclic symmetry, there are, 996,
distinct such collection of decks where
Deck , 1, beats deck, 2
Deck , 2, beats deck, 3
but surprise, surprise Deck, 3, beats deck 1
Here there all are
-------------------------------------------------------
Set Number, 1, is as follows
Deck , 1, has denominations , 1, 4, 4
Deck , 2, has denominations , 3, 3, 3, 3, 8
Deck , 3, has denominations , 2, 2, 5, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
13
Deck , 2, beats deck , 3, with probability , --
25
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 2, is as follows
Deck , 1, has denominations , 1, 4, 5
Deck , 2, has denominations , 3, 3, 3, 3, 6
Deck , 3, has denominations , 2, 2, 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 3, is as follows
Deck , 1, has denominations , 1, 4, 5
Deck , 2, has denominations , 3, 3, 3, 3, 7
Deck , 3, has denominations , 2, 2, 2, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
16
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 4, is as follows
Deck , 1, has denominations , 1, 4, 5
Deck , 2, has denominations , 3, 3, 3, 3, 8
Deck , 3, has denominations , 2, 2, 2, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
17
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 5, is as follows
Deck , 1, has denominations , 1, 4, 5
Deck , 2, has denominations , 3, 3, 3, 3, 8
Deck , 3, has denominations , 2, 2, 6, 6, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
13
Deck , 2, beats deck , 3, with probability , --
25
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 6, is as follows
Deck , 1, has denominations , 1, 4, 5
Deck , 2, has denominations , 3, 3, 3, 3, 8
Deck , 3, has denominations , 2, 2, 6, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
13
Deck , 2, beats deck , 3, with probability , --
25
11
yet Deck, 3, beats deck 1, with probability , --
15
-------------------------------------------------------
Set Number, 7, is as follows
Deck , 1, has denominations , 1, 4, 6
Deck , 2, has denominations , 3, 3, 3, 3, 5
Deck , 3, has denominations , 2, 2, 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 8, is as follows
Deck , 1, has denominations , 1, 4, 6
Deck , 2, has denominations , 3, 3, 3, 3, 7
Deck , 3, has denominations , 2, 2, 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
16
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 9, is as follows
Deck , 1, has denominations , 1, 4, 6
Deck , 2, has denominations , 3, 3, 3, 3, 8
Deck , 3, has denominations , 2, 2, 2, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
17
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 10, is as follows
Deck , 1, has denominations , 1, 4, 6
Deck , 2, has denominations , 3, 3, 3, 3, 8
Deck , 3, has denominations , 2, 2, 5, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
13
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 11, is as follows
Deck , 1, has denominations , 1, 4, 6
Deck , 2, has denominations , 3, 3, 3, 3, 8
Deck , 3, has denominations , 2, 2, 5, 7, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
13
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 2/3
-------------------------------------------------------
Set Number, 12, is as follows
Deck , 1, has denominations , 1, 4, 6
Deck , 2, has denominations , 3, 3, 3, 5, 5
Deck , 3, has denominations , 2, 2, 2, 7, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 13, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 3, 3, 5
Deck , 3, has denominations , 2, 2, 2, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 14, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 3, 3, 6
Deck , 3, has denominations , 2, 2, 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
16
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 15, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 3, 3, 8
Deck , 3, has denominations , 2, 2, 5, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
13
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 16, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 3, 3, 8
Deck , 3, has denominations , 2, 2, 5, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
13
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 17, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 3, 5, 5
Deck , 3, has denominations , 2, 2, 2, 6, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 18, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 3, 5, 6
Deck , 3, has denominations , 2, 2, 2, 8, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
Deck , 2, beats deck , 3, with probability , 3/5
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 19, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 3, 6, 6
Deck , 3, has denominations , 2, 2, 2, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
17
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 20, is as follows
Deck , 1, has denominations , 1, 4, 7
Deck , 2, has denominations , 3, 3, 3, 6, 6
Deck , 3, has denominations , 2, 2, 5, 5, 8
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
14
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 3/5
-------------------------------------------------------
Set Number, 21, is as follows
Deck , 1, has denominations , 1, 4, 8
Deck , 2, has denominations , 3, 3, 3, 3, 7
Deck , 3, has denominations , 2, 2, 5, 5, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
13
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 22, is as follows
Deck , 1, has denominations , 1, 4, 8
Deck , 2, has denominations , 3, 3, 3, 3, 7
Deck , 3, has denominations , 2, 2, 5, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 3/5
13
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 23, is as follows
Deck , 1, has denominations , 1, 4, 8
Deck , 2, has denominations , 3, 3, 3, 5, 7
Deck , 3, has denominations , 2, 2, 6, 6, 6
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
13
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 24, is as follows
Deck , 1, has denominations , 1, 4, 8
Deck , 2, has denominations , 3, 3, 3, 6, 6
Deck , 3, has denominations , 2, 2, 5, 5, 7
It is readily seen that
Deck , 1, beats deck , 2, with probability , 8/15
14
Deck , 2, beats deck , 3, with probability , --
25
yet Deck, 3, beats deck 1, with probability , 8/15
-------------------------------------------------------
Set Number, 25, is as follows
Deck , 1, has denominations , 1, 4, 8
Deck , 2, has denominations , 3, 3, 3, 6, 7