All the Suckers's Bets Decks with, 4, decks, with deck sizes from 3 to, 4 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, 3 and there are, 6, denominations from 1(Ace) to, 6 Up to obvious cyclic symmetry, there are, 1, distinct such collection of decks where Deck , 1, beats deck, 2 Deck , 2, beats deck, 3 Deck , 3, beats deck, 4 but surprise, surprise Deck, 4, beats deck 1 Here there all are ------------------------------------------------------- Set Number, 1, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 --------------------------------------------------- --------------------------------------------------- This ends this chapter, that took, 0.166, seconds to generate. Chapter Number, 2 In this chapter we will consider the set whose deck sizes are, 3, 3, 3, 3 and there are, 7, denominations from 1(Ace) to, 7 Up to obvious cyclic symmetry, there are, 12, distinct such collection of decks where Deck , 1, beats deck, 2 Deck , 2, beats deck, 3 Deck , 3, beats deck, 4 but surprise, surprise Deck, 4, beats deck 1 Here there all are ------------------------------------------------------- Set Number, 1, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 6 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 2, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 7 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 7/9 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 3, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 7 Deck , 4, has denominations , 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 7/9 ------------------------------------------------------- Set Number, 4, is as follows Deck , 1, has denominations , 1, 5, 6 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 5, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 2, 5, 5 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 5, 5 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 7, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 5 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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 , 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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 , 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 10, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 3, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 11, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 12, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 --------------------------------------------------- --------------------------------------------------- This ends this chapter, that took, 0.741, seconds to generate. Chapter Number, 3 In this chapter we will consider the set whose deck sizes are, 3, 3, 3, 3 and there are, 8, denominations from 1(Ace) to, 8 Up to obvious cyclic symmetry, there are, 59, distinct such collection of decks where Deck , 1, beats deck, 2 Deck , 2, beats deck, 3 Deck , 3, beats deck, 4 but surprise, surprise Deck, 4, 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, 6, 6 Deck , 4, has denominations , 5, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 2, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 6, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 7/9 ------------------------------------------------------- Set Number, 3, is as follows Deck , 1, has denominations , 1, 5, 6 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 7 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 4, is as follows Deck , 1, has denominations , 1, 5, 6 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 7/9 yet Deck, 4, 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 , 3, 3, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 7/9 ------------------------------------------------------- Set Number, 6, is as follows Deck , 1, has denominations , 1, 5, 7 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 6 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 7, is as follows Deck , 1, has denominations , 1, 5, 7 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 8, is as follows Deck , 1, has denominations , 1, 5, 7 Deck , 2, has denominations , 4, 4, 6 Deck , 3, has denominations , 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 9, is as follows Deck , 1, has denominations , 1, 5, 8 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 7 Deck , 4, has denominations , 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, 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 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 5, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, 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 Deck , 3, has denominations , 3, 3, 7 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 4, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 7/9 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 13, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 7/9 ------------------------------------------------------- Set Number, 14, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 5, 5 Deck , 3, has denominations , 3, 3, 7 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 15, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 5, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 7/9 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 16, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 5, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 7/9 ------------------------------------------------------- Set Number, 17, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 2, 4, 8 Deck , 4, 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 , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 18, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, 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 , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 19, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 4, 7 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 20, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 4, 8 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 7/9 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 21, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 4, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 7/9 ------------------------------------------------------- Set Number, 22, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 4, 4, 7 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 23, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 4, 4, 8 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 7/9 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 24, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 2, 5, 5 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 25, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 3, 5, 5 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 26, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 5 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 27, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 4, 4, 5 Deck , 3, has denominations , 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 28, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 4, 5, 5 Deck , 3, has denominations , 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 29, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 3, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 30, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 31, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 32, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 2, 5, 6 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 33, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 2, 6, 6 Deck , 3, has denominations , 4, 4, 5 Deck , 4, 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 34, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 2, 6, 6 Deck , 3, has denominations , 4, 5, 5 Deck , 4, 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 35, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 2, 6, 6 Deck , 3, has denominations , 5, 5, 5 Deck , 4, 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 36, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 3, 5, 6 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 37, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 3, 6, 6 Deck , 3, has denominations , 4, 4, 5 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 38, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 3, 6, 6 Deck , 3, has denominations , 4, 5, 5 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 39, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 3, 6, 6 Deck , 3, has denominations , 5, 5, 5 Deck , 4, 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 40, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 5 Deck , 3, has denominations , 3, 3, 6 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 41, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 6 Deck , 3, has denominations , 3, 3, 5 Deck , 4, 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 , 7/9 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 42, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 6 Deck , 3, has denominations , 3, 5, 5 Deck , 4, 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 , 5/9 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 43, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 5, 5 Deck , 3, has denominations , 3, 3, 6 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 44, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 5, 6 Deck , 3, has denominations , 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 45, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 6, 6 Deck , 3, has denominations , 3, 3, 5 Deck , 4, 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 , 8/9 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 46, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 6, 6 Deck , 3, has denominations , 3, 5, 5 Deck , 4, 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 , 7/9 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 47, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 6, 6 Deck , 3, has denominations , 5, 5, 5 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 48, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 4, 6 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 49, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 4, 4, 6 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 50, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 6 Deck , 3, has denominations , 3, 3, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 51, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 6 Deck , 3, has denominations , 3, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 52, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 6 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 53, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 6, 6 Deck , 3, has denominations , 3, 3, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 54, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 6, 6 Deck , 3, has denominations , 3, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 55, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 6, 6 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 56, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6 Deck , 3, has denominations , 3, 4, 5 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 57, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6 Deck , 3, has denominations , 3, 5, 5 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 58, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6 Deck , 3, has denominations , 4, 4, 5 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 59, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6 Deck , 3, has denominations , 4, 5, 5 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 --------------------------------------------------- --------------------------------------------------- This ends this chapter, that took, 8.348, seconds to generate. Chapter Number, 4 In this chapter we will consider the set whose deck sizes are, 3, 3, 3, 4 and there are, 6, denominations from 1(Ace) to, 6 Up to obvious cyclic symmetry, there are, 2, distinct such collection of decks where Deck , 1, beats deck, 2 Deck , 2, beats deck, 3 Deck , 3, beats deck, 4 but surprise, surprise Deck, 4, beats deck 1 Here there all are ------------------------------------------------------- Set Number, 1, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 2, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 --------------------------------------------------- --------------------------------------------------- This ends this chapter, that took, 0.194, seconds to generate. Chapter Number, 5 In this chapter we will consider the set whose deck sizes are, 3, 3, 3, 4 and there are, 7, denominations from 1(Ace) to, 7 Up to obvious cyclic symmetry, there are, 27, distinct such collection of decks where Deck , 1, beats deck, 2 Deck , 2, beats deck, 3 Deck , 3, beats deck, 4 but surprise, surprise Deck, 4, beats deck 1 Here there all are ------------------------------------------------------- Set Number, 1, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 7 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 2, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 6 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 3, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, 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, 4 Deck , 3, has denominations , 3, 3, 6 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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 , 3, 3, 7 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 7/9 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 6, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 7 Deck , 4, has denominations , 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 7/9 ------------------------------------------------------- Set Number, 7, is as follows Deck , 1, has denominations , 1, 5, 6 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 8, is as follows Deck , 1, has denominations , 1, 5, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 9, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 2, 5, 5 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 10, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 3, 5, 5 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 4 Deck , 3, has denominations , 3, 3, 3, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 4, 5 Deck , 3, has denominations , 3, 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 13, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 14, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 3, 3, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 15, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 16, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 17, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 18, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 2, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 19, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 3, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 20, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 5 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 21, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 22, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 23, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 24, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 3, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 25, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 26, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 27, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 7 Deck , 4, has denominations , 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 3/4 --------------------------------------------------- --------------------------------------------------- This ends this chapter, that took, 1.397, seconds to generate. Chapter Number, 6 In this chapter we will consider the set whose deck sizes are, 3, 3, 3, 4 and there are, 8, denominations from 1(Ace) to, 8 Up to obvious cyclic symmetry, there are, 150, distinct such collection of decks where Deck , 1, beats deck, 2 Deck , 2, beats deck, 3 Deck , 3, beats deck, 4 but surprise, surprise Deck, 4, 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, 6, 6 Deck , 4, has denominations , 5, 5, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 2, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 7 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 7/12 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 3, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 4, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 6, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 7/9 ------------------------------------------------------- Set Number, 5, is as follows Deck , 1, has denominations , 1, 5, 6 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 6, is as follows Deck , 1, has denominations , 1, 5, 6 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 7, is as follows Deck , 1, has denominations , 1, 5, 6 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 8, is as follows Deck , 1, has denominations , 1, 5, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 7 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 9, is as follows Deck , 1, has denominations , 1, 5, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 7/9 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 10, is as follows Deck , 1, has denominations , 1, 5, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 7/9 ------------------------------------------------------- Set Number, 11, is as follows Deck , 1, has denominations , 1, 5, 7 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 6 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 12, is as follows Deck , 1, has denominations , 1, 5, 7 Deck , 2, has denominations , 4, 4, 6 Deck , 3, has denominations , 3, 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 13, is as follows Deck , 1, has denominations , 1, 5, 7 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 6 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 14, is as follows Deck , 1, has denominations , 1, 5, 7 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 15, is as follows Deck , 1, has denominations , 1, 5, 7 Deck , 2, has denominations , 4, 4, 4, 6 Deck , 3, has denominations , 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 16, is as follows Deck , 1, has denominations , 1, 5, 8 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 7 Deck , 4, has denominations , 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 17, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 18, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 5 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 19, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 5 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 20, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 5, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 21, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 22, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 23, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 4, 8 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 24, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 4, 4, 8 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 25, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 2, 4, 4, 8 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 7/12 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 26, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 7 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 27, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 8 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 28, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 7 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 29, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 8 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 30, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 7 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 31, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 8 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 32, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 5, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 33, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 7 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 34, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 7/9 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 35, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 7/9 ------------------------------------------------------- Set Number, 36, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 7 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 37, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 7/9 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 38, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 7/9 ------------------------------------------------------- Set Number, 39, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 7 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 40, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 7/9 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 41, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 7/9 ------------------------------------------------------- Set Number, 42, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 2, 4, 8 Deck , 4, 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 , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 43, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, 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 , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 44, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 7 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 45, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 8 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 7/9 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 46, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 7/9 ------------------------------------------------------- Set Number, 47, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 7 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 48, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 8 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 7/9 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 49, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 2, 5, 5 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 5, 5 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 51, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 52, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 4, 4, 5 Deck , 3, has denominations , 3, 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 53, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 54, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 3, 3, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 55, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 56, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 57, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 58, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 2, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 59, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 3, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 4, 4 Deck , 3, has denominations , 3, 3, 5 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 4, 5 Deck , 3, has denominations , 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 4, 5, 5 Deck , 3, has denominations , 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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 Deck , 3, has denominations , 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 64, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 3, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 65, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 66, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 67, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 2, 5, 6 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 68, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 2, 6, 6 Deck , 3, has denominations , 4, 4, 4, 5 Deck , 4, 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 69, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 2, 6, 6 Deck , 3, has denominations , 4, 4, 5, 5 Deck , 4, 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 70, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 2, 6, 6 Deck , 3, has denominations , 4, 5, 5, 5 Deck , 4, 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 71, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 2, 6, 6 Deck , 3, has denominations , 5, 5, 5, 5 Deck , 4, 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 72, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 3, 5, 6 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 73, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 3, 6, 6 Deck , 3, has denominations , 4, 4, 4, 5 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 74, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 3, 6, 6 Deck , 3, has denominations , 4, 4, 5, 5 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 75, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 3, 6, 6 Deck , 3, has denominations , 4, 5, 5, 5 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 76, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 3, 6, 6 Deck , 3, has denominations , 5, 5, 5, 5 Deck , 4, 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 77, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 5 Deck , 3, has denominations , 3, 3, 3, 6 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 78, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 6 Deck , 3, has denominations , 3, 3, 3, 5 Deck , 4, 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 , 5/6 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 79, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 6 Deck , 3, has denominations , 3, 3, 5, 5 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 80, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 6 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 81, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 5, 6 Deck , 3, has denominations , 3, 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 82, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 6, 6 Deck , 3, has denominations , 3, 3, 3, 5 Deck , 4, has denominations , 2, 2, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 11 Deck , 2, beats deck , 3, with probability , -- 12 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 83, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 6, 6 Deck , 3, has denominations , 3, 3, 5, 5 Deck , 4, 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 , 5/6 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 84, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 6, 6 Deck , 3, has denominations , 3, 5, 5, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 85, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 6, 6 Deck , 3, has denominations , 5, 5, 5, 5 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 86, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 6 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 87, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 6 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 88, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 6 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 89, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 6 Deck , 3, has denominations , 3, 3, 3, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 90, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 6 Deck , 3, has denominations , 3, 3, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 91, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 6 Deck , 3, has denominations , 3, 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 92, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 6 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 93, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 6, 6 Deck , 3, has denominations , 3, 3, 3, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 94, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 6, 6 Deck , 3, has denominations , 3, 3, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 95, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 6, 6 Deck , 3, has denominations , 3, 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 96, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 6, 6 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 97, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6 Deck , 3, has denominations , 3, 3, 4, 5 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 98, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6 Deck , 3, has denominations , 3, 4, 4, 5 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 99, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6 Deck , 3, has denominations , 3, 4, 5, 5 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 100, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6 Deck , 3, has denominations , 3, 5, 5, 5 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 7/12 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 101, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6 Deck , 3, has denominations , 4, 4, 4, 5 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 102, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6 Deck , 3, has denominations , 4, 4, 5, 5 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 103, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6 Deck , 3, has denominations , 4, 5, 5, 5 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 5, 5, 6 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 5, 6, 6 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 6, 6, 6 Deck , 3, has denominations , 4, 4, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 6, 6, 6 Deck , 3, has denominations , 4, 5, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 109, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 3, 5, 5, 6 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 5, 6, 6 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 6, 6, 6 Deck , 3, has denominations , 4, 4, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 6, 6, 6 Deck , 3, has denominations , 4, 5, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 114, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 6 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 115, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 4, 6 Deck , 3, has denominations , 3, 3, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 116, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 6 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 117, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 5, 6 Deck , 3, has denominations , 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 118, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 6, 6 Deck , 3, has denominations , 3, 3, 5 Deck , 4, 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 , 5/6 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 119, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 6, 6 Deck , 3, has denominations , 3, 5, 5 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 120, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 6 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 5, 5, 6 Deck , 3, has denominations , 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 5, 6, 6 Deck , 3, has denominations , 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 6, 6, 6 Deck , 3, has denominations , 3, 3, 5 Deck , 4, has denominations , 2, 2, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 11 Deck , 2, beats deck , 3, with probability , -- 12 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 6, 6, 6 Deck , 3, has denominations , 3, 5, 5 Deck , 4, 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 , 5/6 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 126, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 6 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 127, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 6 Deck , 4, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 128, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 5, 6 Deck , 3, has denominations , 3, 3, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 129, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 5, 6 Deck , 3, has denominations , 3, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 130, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 5, 6 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 131, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 6, 6 Deck , 3, has denominations , 3, 3, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 132, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 6, 6 Deck , 3, has denominations , 3, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 133, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 6, 6 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 134, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 6, 6, 6 Deck , 3, has denominations , 3, 3, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 135, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 6, 6, 6 Deck , 3, has denominations , 3, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 136, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 6, 6, 6 Deck , 3, has denominations , 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 137, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6, 6 Deck , 3, has denominations , 3, 4, 5 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 138, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6, 6 Deck , 3, has denominations , 3, 5, 5 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 139, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6, 6 Deck , 3, has denominations , 4, 4, 5 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 140, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6, 6 Deck , 3, has denominations , 4, 5, 5 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 141, is as follows Deck , 1, has denominations , 1, 3, 7, 7 Deck , 2, has denominations , 2, 6, 6 Deck , 3, has denominations , 5, 5, 5 Deck , 4, has denominations , 4, 4, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 7/12 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 142, is as follows Deck , 1, has denominations , 1, 4, 4, 8 Deck , 2, has denominations , 3, 3, 7 Deck , 3, has denominations , 2, 6, 6 Deck , 4, has denominations , 5, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 143, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 6, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 144, is as follows Deck , 1, has denominations , 1, 5, 5, 6 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 145, is as follows Deck , 1, has denominations , 1, 5, 5, 7 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 7/12 ------------------------------------------------------- Set Number, 146, is as follows Deck , 1, has denominations , 1, 5, 5, 8 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 7 Deck , 4, has denominations , 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 7/12 ------------------------------------------------------- Set Number, 147, is as follows Deck , 1, has denominations , 1, 5, 6, 6 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 148, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 149, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 5, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 150, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 4, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 3/4 --------------------------------------------------- --------------------------------------------------- This ends this chapter, that took, 6.737, seconds to generate. Chapter Number, 7 In this chapter we will consider the set whose deck sizes are, 3, 3, 4, 4 and there are, 6, denominations from 1(Ace) to, 6 Up to obvious cyclic symmetry, there are, 1, distinct such collection of decks where Deck , 1, beats deck, 2 Deck , 2, beats deck, 3 Deck , 3, beats deck, 4 but surprise, surprise Deck, 4, beats deck 1 Here there all are ------------------------------------------------------- Set Number, 1, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 --------------------------------------------------- --------------------------------------------------- This ends this chapter, that took, 1.474, seconds to generate. Chapter Number, 8 In this chapter we will consider the set whose deck sizes are, 3, 3, 4, 4 and there are, 7, denominations from 1(Ace) to, 7 Up to obvious cyclic symmetry, there are, 16, distinct such collection of decks where Deck , 1, beats deck, 2 Deck , 2, beats deck, 3 Deck , 3, beats deck, 4 but surprise, surprise Deck, 4, beats deck 1 Here there all are ------------------------------------------------------- Set Number, 1, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 2, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 6 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 3, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 4, is as follows Deck , 1, has denominations , 1, 5, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 5, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 2, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 7, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 4, 5 Deck , 3, has denominations , 3, 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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, 5, 5, 5 Deck , 3, has denominations , 3, 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 11, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 3, 3, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 12, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 13, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 14, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 15, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 7 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 16, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 7 Deck , 4, has denominations , 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 3/4 --------------------------------------------------- --------------------------------------------------- This ends this chapter, that took, 1.314, seconds to generate. Chapter Number, 9 In this chapter we will consider the set whose deck sizes are, 3, 3, 4, 4 and there are, 8, denominations from 1(Ace) to, 8 Up to obvious cyclic symmetry, there are, 113, distinct such collection of decks where Deck , 1, beats deck, 2 Deck , 2, beats deck, 3 Deck , 3, beats deck, 4 but surprise, surprise Deck, 4, beats deck 1 Here there all are ------------------------------------------------------- Set Number, 1, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 2, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 3, is as follows Deck , 1, has denominations , 1, 5, 6 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 4, is as follows Deck , 1, has denominations , 1, 5, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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 , 3, 3, 3, 8 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 6, is as follows Deck , 1, has denominations , 1, 5, 7 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 6 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 7, is as follows Deck , 1, has denominations , 1, 5, 7 Deck , 2, has denominations , 4, 4, 4, 6 Deck , 3, has denominations , 3, 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, 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 , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 9, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 10, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 11, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 12, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 13, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 2, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 7 Deck , 4, 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 , 9/16 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 14, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 2, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 8 Deck , 4, 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 , 9/16 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 15, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 3, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 7 Deck , 4, 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 , 9/16 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 16, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 3, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 8 Deck , 4, 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 , 9/16 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 17, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 18, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 19, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 20, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 21, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 22, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 23, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 2, 4, 4, 8 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 7/12 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 24, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 7 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 25, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 8 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 26, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 7 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 27, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 8 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 28, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 7 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 29, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 8 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 30, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 2, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 31, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 3, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 32, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 33, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 34, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 35, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 36, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 3, 3, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 37, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 38, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 39, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 40, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 2, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 6 Deck , 4, 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 , 9/16 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 41, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 2, 5, 5, 6 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 42, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 2, 5, 6, 6 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 43, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 4, 4, 4, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 44, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 4, 4, 5, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 45, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 4, 5, 5, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 46, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 47, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 3, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 6 Deck , 4, 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 , 9/16 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 48, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 3, 5, 5, 6 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 49, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 3, 5, 6, 6 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 50, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 3, 6, 6, 6 Deck , 3, has denominations , 4, 4, 4, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 51, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 3, 6, 6, 6 Deck , 3, has denominations , 4, 4, 5, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 52, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 3, 6, 6, 6 Deck , 3, has denominations , 4, 5, 5, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 53, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 3, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 54, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 3, 6 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 55, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 4, 6 Deck , 3, has denominations , 3, 3, 3, 5 Deck , 4, has denominations , 2, 2, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 13 Deck , 2, beats deck , 3, with probability , -- 16 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 56, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 4, 6 Deck , 3, has denominations , 3, 3, 5, 5 Deck , 4, 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 , 5/8 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 57, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 6 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 58, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 5, 6 Deck , 3, has denominations , 3, 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 59, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 6, 6 Deck , 3, has denominations , 3, 3, 3, 5 Deck , 4, 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 , 7/8 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 60, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 6, 6 Deck , 3, has denominations , 3, 3, 5, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 61, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 6, 6 Deck , 3, has denominations , 3, 5, 5, 5 Deck , 4, 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 , 5/8 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 62, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 3, 6 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 63, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 5, 5, 6 Deck , 3, has denominations , 3, 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 64, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 5, 6, 6 Deck , 3, has denominations , 3, 3, 3, 3 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 65, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 6, 6, 6 Deck , 3, has denominations , 3, 3, 3, 5 Deck , 4, has denominations , 2, 2, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 15 Deck , 2, beats deck , 3, with probability , -- 16 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 66, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 6, 6, 6 Deck , 3, has denominations , 3, 3, 5, 5 Deck , 4, 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 , 7/8 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 67, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 6, 6, 6 Deck , 3, has denominations , 3, 5, 5, 5 Deck , 4, has denominations , 2, 2, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 13 Deck , 2, beats deck , 3, with probability , -- 16 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 68, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 5 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 69, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 6 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 70, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 6 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 71, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 6 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 72, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 5, 6 Deck , 3, has denominations , 3, 3, 3, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 73, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 5, 6 Deck , 3, has denominations , 3, 3, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 74, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 5, 6 Deck , 3, has denominations , 3, 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 75, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 5, 6 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 76, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 6, 6 Deck , 3, has denominations , 3, 3, 3, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 77, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 6, 6 Deck , 3, has denominations , 3, 3, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 78, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 6, 6 Deck , 3, has denominations , 3, 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 79, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 6, 6 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 80, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 6, 6, 6 Deck , 3, has denominations , 3, 3, 3, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 81, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 6, 6, 6 Deck , 3, has denominations , 3, 3, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 82, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 6, 6, 6 Deck , 3, has denominations , 3, 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 83, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 6, 6, 6 Deck , 3, has denominations , 4, 4, 4, 4 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 84, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6, 6 Deck , 3, has denominations , 3, 3, 4, 5 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 85, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6, 6 Deck , 3, has denominations , 3, 4, 4, 5 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 86, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6, 6 Deck , 3, has denominations , 3, 4, 5, 5 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 87, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6, 6 Deck , 3, has denominations , 3, 5, 5, 5 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 7/12 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 88, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6, 6 Deck , 3, has denominations , 4, 4, 4, 5 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 89, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6, 6 Deck , 3, has denominations , 4, 4, 5, 5 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 90, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6, 6 Deck , 3, has denominations , 4, 5, 5, 5 Deck , 4, 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 , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 ------------------------------------------------------- Set Number, 91, is as follows Deck , 1, has denominations , 1, 3, 7, 7 Deck , 2, has denominations , 2, 6, 6 Deck , 3, has denominations , 5, 5, 5 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 92, is as follows Deck , 1, has denominations , 1, 3, 7, 7 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5 Deck , 4, has denominations , 4, 4, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 93, is as follows Deck , 1, has denominations , 1, 4, 4, 8 Deck , 2, has denominations , 3, 3, 7 Deck , 3, has denominations , 2, 6, 6 Deck , 4, has denominations , 5, 5, 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 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 94, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 7 Deck , 4, has denominations , 2, 2, 6, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 7/12 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 95, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 96, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 6, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 97, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 6 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 98, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 7 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 99, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 7 Deck , 4, has denominations , 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 100, is as follows Deck , 1, has denominations , 1, 5, 5, 6 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 101, is as follows Deck , 1, has denominations , 1, 5, 5, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 102, is as follows Deck , 1, has denominations , 1, 5, 5, 7 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 7/12 ------------------------------------------------------- Set Number, 103, is as follows Deck , 1, has denominations , 1, 5, 5, 8 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 7 Deck , 4, has denominations , 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 7/12 ------------------------------------------------------- Set Number, 104, is as follows Deck , 1, has denominations , 1, 5, 6, 6 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 105, is as follows Deck , 1, has denominations , 1, 5, 6, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 106, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 107, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 5, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 108, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 4, 8 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 109, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 4, 4, 8 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 110, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 111, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 112, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 113, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 5/9 yet Deck, 4, beats deck 1, with probability , 3/4 --------------------------------------------------- --------------------------------------------------- This ends this chapter, that took, 31.716, seconds to generate. Chapter Number, 10 In this chapter we will consider the set whose deck sizes are, 3, 4, 4, 4 and there are, 7, denominations from 1(Ace) to, 7 Up to obvious cyclic symmetry, there are, 3, distinct such collection of decks where Deck , 1, beats deck, 2 Deck , 2, beats deck, 3 Deck , 3, beats deck, 4 but surprise, surprise Deck, 4, beats deck 1 Here there all are ------------------------------------------------------- Set Number, 1, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 2, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 3, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 7 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 --------------------------------------------------- --------------------------------------------------- This ends this chapter, that took, 1.904, seconds to generate. Chapter Number, 11 In this chapter we will consider the set whose deck sizes are, 3, 4, 4, 4 and there are, 8, denominations from 1(Ace) to, 8 Up to obvious cyclic symmetry, there are, 36, distinct such collection of decks where Deck , 1, beats deck, 2 Deck , 2, beats deck, 3 Deck , 3, beats deck, 4 but surprise, surprise Deck, 4, beats deck 1 Here there all are ------------------------------------------------------- Set Number, 1, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 2, is as follows Deck , 1, has denominations , 1, 5, 5 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 3, is as follows Deck , 1, has denominations , 1, 5, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 4, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 2, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 8 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 5, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 3, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 8 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 6, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 7, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 8, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 9, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 10, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 11, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 12, is as follows Deck , 1, has denominations , 1, 3, 7, 7 Deck , 2, has denominations , 2, 6, 6 Deck , 3, has denominations , 5, 5, 5, 5 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 13, is as follows Deck , 1, has denominations , 1, 3, 7, 7 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5 Deck , 4, has denominations , 4, 4, 4, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 14, is as follows Deck , 1, has denominations , 1, 3, 7, 7 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 5 Deck , 4, has denominations , 4, 4, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 15, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, has denominations , 2, 2, 6, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 16, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 17, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 7 Deck , 4, has denominations , 2, 2, 6, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 7/12 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 18, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 19, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 6 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 20, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 7 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 21, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 7 Deck , 4, has denominations , 2, 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 22, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 7, 7 Deck , 4, has denominations , 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- 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 , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 24, is as follows Deck , 1, has denominations , 1, 5, 5, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 25, is as follows Deck , 1, has denominations , 1, 5, 6, 6 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 26, is as follows Deck , 1, has denominations , 1, 5, 6, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 27, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 5 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 28, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 29, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 30, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 31, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 32, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 33, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 34, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 35, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 8 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 36, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 8 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 --------------------------------------------------- --------------------------------------------------- This ends this chapter, that took, 81.471, seconds to generate. Chapter Number, 12 In this chapter we will consider the set whose deck sizes are, 3, 4, 4, 4 and there are, 9, denominations from 1(Ace) to, 9 Up to obvious cyclic symmetry, there are, 228, distinct such collection of decks where Deck , 1, beats deck, 2 Deck , 2, beats deck, 3 Deck , 3, beats deck, 4 but surprise, surprise Deck, 4, beats deck 1 Here there all are ------------------------------------------------------- Set Number, 1, is as follows Deck , 1, has denominations , 1, 5, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 2, is as follows Deck , 1, has denominations , 1, 5, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 3, is as follows Deck , 1, has denominations , 1, 5, 7 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 2, 2, 6, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 7/12 ------------------------------------------------------- Set Number, 4, is as follows Deck , 1, has denominations , 1, 5, 7 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 7/12 ------------------------------------------------------- Set Number, 5, is as follows Deck , 1, has denominations , 1, 5, 7 Deck , 2, has denominations , 4, 4, 4, 6 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 6, is as follows Deck , 1, has denominations , 1, 5, 8 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, has denominations , 2, 2, 6, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 7/12 ------------------------------------------------------- Set Number, 7, is as follows Deck , 1, has denominations , 1, 5, 9 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 7, 7 Deck , 4, has denominations , 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 , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 7/12 ------------------------------------------------------- Set Number, 8, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 2, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 8 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 9, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 2, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 10, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 3, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 8 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 11, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 3, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 12, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 13, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 14, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 15, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 16, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 17, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 18, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 19, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 20, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 21, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 22, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 23, is as follows Deck , 1, has denominations , 1, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 24, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 2, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 25, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 3, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 26, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 27, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 28, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 29, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 30, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 31, is as follows Deck , 1, has denominations , 1, 6, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 32, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 2, 5, 5, 6 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 33, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 2, 5, 6, 6 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 34, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 4, 4, 5, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 35, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 4, 5, 5, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 36, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 37, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 3, 5, 5, 6 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 38, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 3, 5, 6, 6 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 39, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 3, 6, 6, 6 Deck , 3, has denominations , 4, 4, 5, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 40, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 3, 6, 6, 6 Deck , 3, has denominations , 4, 5, 5, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 41, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 3, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 42, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 4, 6 Deck , 3, has denominations , 3, 3, 5, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 43, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 5, 6 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 44, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 4, 6, 6 Deck , 3, has denominations , 3, 3, 5, 9 Deck , 4, has denominations , 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 , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 45, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 5, 5, 6 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 46, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 5, 6, 6 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 47, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 6, 6, 6 Deck , 3, has denominations , 3, 3, 5, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 11 Deck , 2, beats deck , 3, with probability , -- 16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 48, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 6, 6, 6 Deck , 3, has denominations , 3, 5, 5, 9 Deck , 4, has denominations , 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 , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 49, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 4, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 50, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 5, 6 Deck , 3, has denominations , 3, 3, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 51, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 5, 6 Deck , 3, has denominations , 3, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 52, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 5, 6 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 53, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 6, 6 Deck , 3, has denominations , 3, 3, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 54, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 6, 6 Deck , 3, has denominations , 3, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 55, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 5, 6, 6 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 56, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 6, 6, 6 Deck , 3, has denominations , 3, 3, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 57, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 6, 6, 6 Deck , 3, has denominations , 3, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 58, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 5, 6, 6, 6 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 59, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6, 6 Deck , 3, has denominations , 3, 4, 5, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 60, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6, 6 Deck , 3, has denominations , 3, 5, 5, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 61, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6, 6 Deck , 3, has denominations , 4, 4, 5, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 62, is as follows Deck , 1, has denominations , 1, 7, 7 Deck , 2, has denominations , 6, 6, 6, 6 Deck , 3, has denominations , 4, 5, 5, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 63, is as follows Deck , 1, has denominations , 1, 3, 7, 7 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 8 Deck , 4, has denominations , 4, 4, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 64, is as follows Deck , 1, has denominations , 1, 3, 7, 7 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 9 Deck , 4, has denominations , 4, 4, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- 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 , 5, 5, 5, 5 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 66, is as follows Deck , 1, has denominations , 1, 3, 7, 8 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5 Deck , 4, has denominations , 4, 4, 4, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 67, is as follows Deck , 1, has denominations , 1, 3, 7, 8 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 5 Deck , 4, has denominations , 4, 4, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- 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 , 5, 5, 5, 5 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 9/16 ------------------------------------------------------- Set Number, 69, is as follows Deck , 1, has denominations , 1, 3, 7, 9 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5 Deck , 4, has denominations , 4, 4, 4, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 9/16 ------------------------------------------------------- Set Number, 70, is as follows Deck , 1, has denominations , 1, 3, 7, 9 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 5 Deck , 4, has denominations , 4, 4, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 7/12 ------------------------------------------------------- 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 , 5, 5, 5, 5 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 72, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 7, 7 Deck , 3, has denominations , 4, 6, 6, 6 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- 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 , 5, 5, 5, 6 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- 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 , 5, 5, 6, 6 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- 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 , 5, 6, 6, 6 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 76, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 7, 7 Deck , 3, has denominations , 6, 6, 6, 6 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 77, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 7, 7 Deck , 3, has denominations , 6, 6, 6, 6 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 78, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 7 Deck , 4, has denominations , 4, 4, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 79, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 6, 6, 7 Deck , 3, has denominations , 5, 5, 5 Deck , 4, has denominations , 4, 4, 4, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 80, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 6, 6, 7 Deck , 3, has denominations , 5, 5, 5, 5 Deck , 4, has denominations , 4, 4, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 81, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 6, 7, 7 Deck , 3, has denominations , 5, 5, 5 Deck , 4, has denominations , 4, 4, 4, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 82, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 6, 7, 7 Deck , 3, has denominations , 5, 5, 5, 5 Deck , 4, has denominations , 4, 4, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 83, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 7, 7, 7 Deck , 3, has denominations , 5, 5, 6 Deck , 4, has denominations , 4, 4, 4, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 84, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 7, 7, 7 Deck , 3, has denominations , 5, 6, 6 Deck , 4, has denominations , 4, 4, 4, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 85, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 7, 7, 7 Deck , 3, has denominations , 6, 6, 6 Deck , 4, has denominations , 4, 4, 5, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 86, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 7, 7, 7 Deck , 3, has denominations , 6, 6, 6 Deck , 4, has denominations , 4, 5, 5, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 87, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 7, 7, 7 Deck , 3, has denominations , 5, 5, 5, 6 Deck , 4, has denominations , 4, 4, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 88, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 7, 7, 7 Deck , 3, has denominations , 5, 5, 6, 6 Deck , 4, has denominations , 4, 4, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 89, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 7, 7, 7 Deck , 3, has denominations , 5, 6, 6, 6 Deck , 4, has denominations , 4, 4, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 90, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 7, 7, 7 Deck , 3, has denominations , 6, 6, 6, 6 Deck , 4, has denominations , 4, 5, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 2/3 ------------------------------------------------------- Set Number, 91, is as follows Deck , 1, has denominations , 1, 4, 8, 8 Deck , 2, has denominations , 2, 7, 7 Deck , 3, has denominations , 3, 6, 6, 6 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 92, is as follows Deck , 1, has denominations , 1, 4, 8, 8 Deck , 2, has denominations , 2, 7, 7 Deck , 3, has denominations , 6, 6, 6, 6 Deck , 4, has denominations , 3, 5, 5, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 7/12 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 9/16 ------------------------------------------------------- Set Number, 93, is as follows Deck , 1, has denominations , 1, 4, 8, 8 Deck , 2, has denominations , 3, 7, 7 Deck , 3, has denominations , 2, 6, 6, 6 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 94, is as follows Deck , 1, has denominations , 1, 4, 8, 8 Deck , 2, has denominations , 3, 7, 7 Deck , 3, has denominations , 6, 6, 6, 6 Deck , 4, 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 , 2/3 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 9/16 ------------------------------------------------------- Set Number, 95, is as follows Deck , 1, has denominations , 1, 4, 8, 8 Deck , 2, has denominations , 2, 7, 7, 7 Deck , 3, has denominations , 6, 6, 6 Deck , 4, has denominations , 3, 5, 5, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 9/16 ------------------------------------------------------- Set Number, 96, is as follows Deck , 1, has denominations , 1, 4, 8, 8 Deck , 2, has denominations , 2, 7, 7, 7 Deck , 3, has denominations , 6, 6, 6, 6 Deck , 4, has denominations , 3, 5, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 7/12 ------------------------------------------------------- Set Number, 97, is as follows Deck , 1, has denominations , 1, 4, 8, 8 Deck , 2, has denominations , 3, 7, 7, 7 Deck , 3, has denominations , 6, 6, 6 Deck , 4, has denominations , 2, 5, 5, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 9/16 ------------------------------------------------------- Set Number, 98, is as follows Deck , 1, has denominations , 1, 4, 8, 8 Deck , 2, has denominations , 3, 7, 7, 7 Deck , 3, has denominations , 6, 6, 6, 6 Deck , 4, 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 , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 7/12 ------------------------------------------------------- Set Number, 99, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 6 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 7/12 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 100, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 6 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 2, 2, 7, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 101, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 7 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 2, 6, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 7/12 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 102, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 7 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 2, 2, 6, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 103, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 7 Deck , 4, has denominations , 2, 2, 6, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 7/12 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 104, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 2, 2, 6, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 105, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 7, 9 Deck , 4, has denominations , 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 106, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 7 Deck , 4, has denominations , 2, 2, 6, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 7/12 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 107, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 2, 6, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 108, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 7, 8 Deck , 4, has denominations , 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 109, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 8, 8 Deck , 4, has denominations , 2, 6, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 110, is as follows Deck , 1, has denominations , 1, 5, 5, 6 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 111, is as follows Deck , 1, has denominations , 1, 5, 5, 6 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 112, is as follows Deck , 1, has denominations , 1, 5, 5, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 7/12 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 113, is as follows Deck , 1, has denominations , 1, 5, 5, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 114, is as follows Deck , 1, has denominations , 1, 5, 5, 6 Deck , 2, has denominations , 4, 4, 4, 7 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 115, is as follows Deck , 1, has denominations , 1, 5, 5, 6 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 116, is as follows Deck , 1, has denominations , 1, 5, 5, 6 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 117, is as follows Deck , 1, has denominations , 1, 5, 5, 6 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 8, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 118, is as follows Deck , 1, has denominations , 1, 5, 5, 7 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 2, 2, 6, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 9/16 ------------------------------------------------------- Set Number, 119, is as follows Deck , 1, has denominations , 1, 5, 5, 7 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 2, 2, 6, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 9/16 ------------------------------------------------------- Set Number, 120, is as follows Deck , 1, has denominations , 1, 5, 5, 7 Deck , 2, has denominations , 4, 4, 6 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 121, is as follows Deck , 1, has denominations , 1, 5, 5, 7 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 2, 6, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 7/12 yet Deck, 4, beats deck 1, with probability , 9/16 ------------------------------------------------------- Set Number, 122, is as follows Deck , 1, has denominations , 1, 5, 5, 7 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 2, 2, 6, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 9/16 ------------------------------------------------------- Set Number, 123, is as follows Deck , 1, has denominations , 1, 5, 5, 7 Deck , 2, has denominations , 4, 4, 4, 6 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 5/8 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 124, is as follows Deck , 1, has denominations , 1, 5, 5, 7 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 8, 8 Deck , 4, has denominations , 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 7/12 ------------------------------------------------------- Set Number, 125, is as follows Deck , 1, has denominations , 1, 5, 5, 8 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, has denominations , 2, 2, 6, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 9/16 ------------------------------------------------------- Set Number, 126, is as follows Deck , 1, has denominations , 1, 5, 5, 8 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 7 Deck , 4, has denominations , 2, 2, 6, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 7/12 yet Deck, 4, beats deck 1, with probability , 9/16 ------------------------------------------------------- Set Number, 127, is as follows Deck , 1, has denominations , 1, 5, 5, 8 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 7, 7 Deck , 4, has denominations , 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 7/12 ------------------------------------------------------- Set Number, 128, is as follows Deck , 1, has denominations , 1, 5, 5, 9 Deck , 2, has denominations , 4, 4, 8 Deck , 3, has denominations , 3, 3, 7, 7 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 129, is as follows Deck , 1, has denominations , 1, 5, 5, 9 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 7, 7 Deck , 4, has denominations , 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 5/8 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 7/12 ------------------------------------------------------- Set Number, 130, is as follows Deck , 1, has denominations , 1, 5, 6, 6 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 131, is as follows Deck , 1, has denominations , 1, 5, 6, 6 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 132, is as follows Deck , 1, has denominations , 1, 5, 6, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 7/12 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 133, is as follows Deck , 1, has denominations , 1, 5, 6, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 134, is as follows Deck , 1, has denominations , 1, 5, 6, 6 Deck , 2, has denominations , 4, 4, 4, 7 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 135, is as follows Deck , 1, has denominations , 1, 5, 6, 6 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 136, is as follows Deck , 1, has denominations , 1, 5, 6, 6 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 137, is as follows Deck , 1, has denominations , 1, 5, 6, 6 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 8, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 138, is as follows Deck , 1, has denominations , 1, 5, 6, 7 Deck , 2, has denominations , 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 139, is as follows Deck , 1, has denominations , 1, 5, 6, 7 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 140, is as follows Deck , 1, has denominations , 1, 5, 7, 7 Deck , 2, has denominations , 4, 4, 6 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 141, is as follows Deck , 1, has denominations , 1, 5, 7, 7 Deck , 2, has denominations , 4, 6, 6 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 142, is as follows Deck , 1, has denominations , 1, 5, 7, 7 Deck , 2, has denominations , 4, 4, 4, 6 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that 11 Deck , 1, beats deck , 2, with probability , -- 16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 143, is as follows Deck , 1, has denominations , 1, 5, 7, 7 Deck , 2, has denominations , 4, 4, 6, 6 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 5/8 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 144, is as follows Deck , 1, has denominations , 1, 5, 7, 7 Deck , 2, has denominations , 4, 6, 6, 6 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 145, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 5 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 146, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 5 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 147, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 148, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 149, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 8 Deck , 4, has denominations , 2, 2, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 150, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 151, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 8 Deck , 4, has denominations , 2, 2, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 152, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 153, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 8 Deck , 4, has denominations , 2, 3, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 154, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 155, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 2, 5, 5, 9 Deck , 3, has denominations , 4, 4, 8 Deck , 4, has denominations , 3, 3, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 7/12 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 156, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 3, 5, 5, 9 Deck , 3, has denominations , 4, 4, 8 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 7/12 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 157, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 7/12 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 158, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 159, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 7/12 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 160, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 161, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 5, 7 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 162, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 5, 8 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 163, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 5, 9 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 164, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 5, 9 Deck , 3, has denominations , 3, 3, 8, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 165, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 7/12 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 166, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 167, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 5, 5, 7 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 168, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 5, 5, 8 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 169, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 5, 5, 9 Deck , 3, has denominations , 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 170, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 5, 5, 9 Deck , 3, has denominations , 3, 3, 8, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 171, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 8 Deck , 4, has denominations , 2, 2, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 7/12 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 172, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 173, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 8 Deck , 4, has denominations , 2, 3, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 7/12 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 174, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 175, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 7 Deck , 3, has denominations , 3, 4, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 176, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 7 Deck , 3, has denominations , 4, 4, 9 Deck , 4, has denominations , 2, 3, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 177, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 8 Deck , 3, has denominations , 3, 4, 9 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 178, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 8 Deck , 3, has denominations , 4, 4, 9 Deck , 4, has denominations , 2, 3, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 179, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 9 Deck , 3, has denominations , 3, 4, 8 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 180, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 9 Deck , 3, has denominations , 4, 4, 8 Deck , 4, has denominations , 2, 3, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 181, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 9 Deck , 3, has denominations , 2, 4, 8, 8 Deck , 4, has denominations , 3, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 7/12 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 182, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 9 Deck , 3, has denominations , 3, 4, 8, 8 Deck , 4, has denominations , 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 183, is as follows Deck , 1, has denominations , 1, 6, 6, 7 Deck , 2, has denominations , 4, 4, 5 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 184, is as follows Deck , 1, has denominations , 1, 6, 6, 7 Deck , 2, has denominations , 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 185, is as follows Deck , 1, has denominations , 1, 6, 6, 7 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 186, is as follows Deck , 1, has denominations , 1, 6, 6, 7 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 187, is as follows Deck , 1, has denominations , 1, 6, 6, 7 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 188, is as follows Deck , 1, has denominations , 1, 6, 6, 7 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 189, is as follows Deck , 1, has denominations , 1, 6, 6, 7 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 190, is as follows Deck , 1, has denominations , 1, 6, 6, 7 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 191, is as follows Deck , 1, has denominations , 1, 6, 6, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 192, is as follows Deck , 1, has denominations , 1, 6, 6, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 193, is as follows Deck , 1, has denominations , 1, 6, 7, 7 Deck , 2, has denominations , 4, 4, 5 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 194, is as follows Deck , 1, has denominations , 1, 6, 7, 7 Deck , 2, has denominations , 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 195, is as follows Deck , 1, has denominations , 1, 6, 7, 7 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 196, is as follows Deck , 1, has denominations , 1, 6, 7, 7 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 197, is as follows Deck , 1, has denominations , 1, 6, 7, 7 Deck , 2, has denominations , 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 198, is as follows Deck , 1, has denominations , 1, 6, 7, 7 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 199, is as follows Deck , 1, has denominations , 1, 6, 7, 7 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 200, is as follows Deck , 1, has denominations , 1, 6, 7, 7 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 201, is as follows Deck , 1, has denominations , 1, 6, 7, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 202, is as follows Deck , 1, has denominations , 1, 6, 7, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 203, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 4, 4, 6 Deck , 3, has denominations , 3, 3, 5, 9 Deck , 4, has denominations , 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 , 7/12 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 204, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 4, 5, 6 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 205, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 4, 6, 6 Deck , 3, has denominations , 3, 3, 5, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 206, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 4, 6, 6 Deck , 3, has denominations , 3, 5, 5, 9 Deck , 4, has denominations , 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 , 7/12 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 207, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 5, 5, 6 Deck , 3, has denominations , 3, 3, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 208, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 5, 5, 6 Deck , 3, has denominations , 3, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 209, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 5, 5, 6 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 210, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 5, 6, 6 Deck , 3, has denominations , 3, 3, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 211, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 5, 6, 6 Deck , 3, has denominations , 3, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 212, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 5, 6, 6 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 213, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 6, 6, 6 Deck , 3, has denominations , 3, 4, 5, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 214, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 6, 6, 6 Deck , 3, has denominations , 3, 5, 5, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 215, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 6, 6, 6 Deck , 3, has denominations , 4, 4, 5, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 216, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 6, 6, 6 Deck , 3, has denominations , 4, 5, 5, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 217, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 4, 4, 5, 6 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 218, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 4, 5, 5, 6 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 219, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 4, 5, 6, 6 Deck , 3, has denominations , 3, 3, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 220, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 4, 6, 6, 6 Deck , 3, has denominations , 3, 5, 9 Deck , 4, has denominations , 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 , 7/12 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 221, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 5, 5, 5, 6 Deck , 3, has denominations , 3, 4, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 222, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 5, 5, 5, 6 Deck , 3, has denominations , 4, 4, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 223, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 5, 5, 6, 6 Deck , 3, has denominations , 3, 4, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 224, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 5, 5, 6, 6 Deck , 3, has denominations , 4, 4, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 225, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 5, 6, 6, 6 Deck , 3, has denominations , 3, 4, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 226, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 5, 6, 6, 6 Deck , 3, has denominations , 4, 4, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 227, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 6, 6, 6, 6 Deck , 3, has denominations , 3, 5, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 7/12 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 228, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 6, 6, 6, 6 Deck , 3, has denominations , 4, 5, 9 Deck , 4, has denominations , 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 , 2/3 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/8 --------------------------------------------------- --------------------------------------------------- This ends this chapter, that took, 966.670, seconds to generate. Chapter Number, 13 In this chapter we will consider the set whose deck sizes are, 4, 4, 4, 4 and there are, 7, denominations from 1(Ace) to, 7 Up to obvious cyclic symmetry, there are, 1, distinct such collection of decks where Deck , 1, beats deck, 2 Deck , 2, beats deck, 3 Deck , 3, beats deck, 4 but surprise, surprise Deck, 4, beats deck 1 Here there all are ------------------------------------------------------- Set Number, 1, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 --------------------------------------------------- --------------------------------------------------- This ends this chapter, that took, 2.929, seconds to generate. Chapter Number, 14 In this chapter we will consider the set whose deck sizes are, 4, 4, 4, 4 and there are, 8, denominations from 1(Ace) to, 8 Up to obvious cyclic symmetry, there are, 18, distinct such collection of decks where Deck , 1, beats deck, 2 Deck , 2, beats deck, 3 Deck , 3, beats deck, 4 but surprise, surprise Deck, 4, beats deck 1 Here there all are ------------------------------------------------------- Set Number, 1, is as follows Deck , 1, has denominations , 1, 3, 7, 7 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 5 Deck , 4, has denominations , 4, 4, 4, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 2, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, has denominations , 2, 2, 6, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 3, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 4, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 6 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 5, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 7 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 2, 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 6, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, has denominations , 2, 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 13 Deck , 2, beats deck , 3, with probability , -- 16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 7, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 7, 7 Deck , 4, has denominations , 2, 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 8, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 7, 7 Deck , 4, has denominations , 2, 6, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 13 yet Deck, 4, beats deck 1, with probability , -- 16 ------------------------------------------------------- Set Number, 9, is as follows Deck , 1, has denominations , 1, 5, 5, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 10, is as follows Deck , 1, has denominations , 1, 5, 6, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 11, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 2, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 8 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 12, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 3, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 8 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 13, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 14, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 15, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 16, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 17, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 18, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 8 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 --------------------------------------------------- --------------------------------------------------- This ends this chapter, that took, 536.269, seconds to generate. Chapter Number, 15 In this chapter we will consider the set whose deck sizes are, 4, 4, 4, 4 and there are, 9, denominations from 1(Ace) to, 9 Up to obvious cyclic symmetry, there are, 166, distinct such collection of decks where Deck , 1, beats deck, 2 Deck , 2, beats deck, 3 Deck , 3, beats deck, 4 but surprise, surprise Deck, 4, beats deck 1 Here there all are ------------------------------------------------------- Set Number, 1, is as follows Deck , 1, has denominations , 1, 3, 7, 7 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 8 Deck , 4, has denominations , 4, 4, 4, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 2, is as follows Deck , 1, has denominations , 1, 3, 7, 7 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 9 Deck , 4, has denominations , 4, 4, 4, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 9/16 13 Deck , 3, beats deck , 4, with probability , -- 16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 3, is as follows Deck , 1, has denominations , 1, 3, 7, 7 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 9 Deck , 4, has denominations , 4, 4, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 3/4 ------------------------------------------------------- Set Number, 4, is as follows Deck , 1, has denominations , 1, 3, 7, 8 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 5 Deck , 4, has denominations , 4, 4, 4, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 5, is as follows Deck , 1, has denominations , 1, 3, 7, 9 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 5 Deck , 4, has denominations , 4, 4, 4, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 9/16 ------------------------------------------------------- Set Number, 6, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 7 Deck , 4, has denominations , 4, 4, 4, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 7, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 6, 6, 7 Deck , 3, has denominations , 5, 5, 5, 5 Deck , 4, has denominations , 4, 4, 4, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 8, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 6, 7, 7 Deck , 3, has denominations , 5, 5, 5, 5 Deck , 4, has denominations , 4, 4, 4, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 9, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 7, 7, 7 Deck , 3, has denominations , 4, 6, 6, 6 Deck , 4, has denominations , 5, 5, 5, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 10, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 7, 7, 7 Deck , 3, has denominations , 5, 5, 5, 6 Deck , 4, has denominations , 4, 4, 4, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 11, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 7, 7, 7 Deck , 3, has denominations , 5, 5, 6, 6 Deck , 4, has denominations , 4, 4, 4, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 12, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 7, 7, 7 Deck , 3, has denominations , 5, 6, 6, 6 Deck , 4, has denominations , 4, 4, 4, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 13, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 7, 7, 7 Deck , 3, has denominations , 6, 6, 6, 6 Deck , 4, has denominations , 4, 4, 5, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 14, is as follows Deck , 1, has denominations , 1, 3, 8, 8 Deck , 2, has denominations , 2, 7, 7, 7 Deck , 3, has denominations , 6, 6, 6, 6 Deck , 4, has denominations , 4, 5, 5, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 15, is as follows Deck , 1, has denominations , 1, 4, 7, 7 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 9 Deck , 4, has denominations , 3, 3, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 16, is as follows Deck , 1, has denominations , 1, 4, 7, 7 Deck , 2, has denominations , 3, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 17, is as follows Deck , 1, has denominations , 1, 4, 8, 8 Deck , 2, has denominations , 2, 7, 7, 7 Deck , 3, has denominations , 3, 6, 6, 6 Deck , 4, has denominations , 5, 5, 5, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 18, is as follows Deck , 1, has denominations , 1, 4, 8, 8 Deck , 2, has denominations , 2, 7, 7, 7 Deck , 3, has denominations , 6, 6, 6, 6 Deck , 4, has denominations , 3, 5, 5, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 9/16 ------------------------------------------------------- Set Number, 19, is as follows Deck , 1, has denominations , 1, 4, 8, 8 Deck , 2, has denominations , 3, 3, 7, 7 Deck , 3, has denominations , 2, 6, 6, 6 Deck , 4, has denominations , 5, 5, 5, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 5/8 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 20, is as follows Deck , 1, has denominations , 1, 4, 8, 8 Deck , 2, has denominations , 3, 7, 7, 7 Deck , 3, has denominations , 2, 6, 6, 6 Deck , 4, has denominations , 5, 5, 5, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 13 Deck , 2, beats deck , 3, with probability , -- 16 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 21, is as follows Deck , 1, has denominations , 1, 4, 8, 8 Deck , 2, has denominations , 3, 7, 7, 7 Deck , 3, has denominations , 6, 6, 6, 6 Deck , 4, has denominations , 2, 5, 5, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 9/16 ------------------------------------------------------- Set Number, 22, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 6 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 23, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 6 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 2, 2, 7, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 24, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 7 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 2, 2, 6, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 25, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 7 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 2, 2, 6, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 26, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 7 Deck , 3, has denominations , 3, 3, 6, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 27, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, has denominations , 2, 2, 6, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 13 Deck , 2, beats deck , 3, with probability , -- 16 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 28, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 2, 2, 6, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 29, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 6, 9 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 30, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 7, 7 Deck , 4, has denominations , 2, 2, 6, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 31, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 7, 9 Deck , 4, has denominations , 2, 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 32, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 7, 9 Deck , 4, has denominations , 2, 6, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 13 yet Deck, 4, beats deck 1, with probability , -- 16 ------------------------------------------------------- Set Number, 33, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, has denominations , 2, 2, 6, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 13 Deck , 2, beats deck , 3, with probability , -- 16 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 34, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 2, 2, 6, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 13 Deck , 2, beats deck , 3, with probability , -- 16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 35, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 6, 8 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 36, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 7, 7 Deck , 4, has denominations , 2, 2, 6, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 37, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 7, 8 Deck , 4, has denominations , 2, 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 38, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 7, 8 Deck , 4, has denominations , 2, 6, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 13 yet Deck, 4, beats deck 1, with probability , -- 16 ------------------------------------------------------- Set Number, 39, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 8, 8 Deck , 4, has denominations , 2, 2, 6, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 40, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 8, 8 Deck , 4, has denominations , 2, 6, 6, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 13 yet Deck, 4, beats deck 1, with probability , -- 16 ------------------------------------------------------- Set Number, 41, is as follows Deck , 1, has denominations , 1, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 8, 8 Deck , 4, has denominations , 2, 6, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 13 yet Deck, 4, beats deck 1, with probability , -- 16 ------------------------------------------------------- Set Number, 42, is as follows Deck , 1, has denominations , 1, 5, 5, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 43, is as follows Deck , 1, has denominations , 1, 5, 5, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 44, is as follows Deck , 1, has denominations , 1, 5, 5, 6 Deck , 2, has denominations , 4, 4, 4, 7 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 45, is as follows Deck , 1, has denominations , 1, 5, 5, 6 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 46, is as follows Deck , 1, has denominations , 1, 5, 5, 6 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 13 Deck , 2, beats deck , 3, with probability , -- 16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 47, is as follows Deck , 1, has denominations , 1, 5, 5, 6 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 8, 8 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 48, is as follows Deck , 1, has denominations , 1, 5, 5, 6 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 8, 8 Deck , 4, has denominations , 2, 7, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 13 yet Deck, 4, beats deck 1, with probability , -- 16 ------------------------------------------------------- Set Number, 49, is as follows Deck , 1, has denominations , 1, 5, 5, 7 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 2, 2, 6, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 9/16 ------------------------------------------------------- Set Number, 50, is as follows Deck , 1, has denominations , 1, 5, 5, 7 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 2, 2, 6, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 9/16 ------------------------------------------------------- Set Number, 51, is as follows Deck , 1, has denominations , 1, 5, 5, 7 Deck , 2, has denominations , 4, 4, 4, 6 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 5/8 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 52, is as follows Deck , 1, has denominations , 1, 5, 5, 7 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 8, 8 Deck , 4, has denominations , 2, 6, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 53, is as follows Deck , 1, has denominations , 1, 5, 5, 8 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 7 Deck , 4, has denominations , 2, 2, 6, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 9/16 ------------------------------------------------------- Set Number, 54, is as follows Deck , 1, has denominations , 1, 5, 5, 8 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 7, 7 Deck , 4, has denominations , 2, 6, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 55, is as follows Deck , 1, has denominations , 1, 5, 5, 9 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 7, 7 Deck , 4, has denominations , 2, 6, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 5/8 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 56, is as follows Deck , 1, has denominations , 1, 5, 6, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 57, is as follows Deck , 1, has denominations , 1, 5, 6, 6 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 58, is as follows Deck , 1, has denominations , 1, 5, 6, 6 Deck , 2, has denominations , 4, 4, 4, 7 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 59, is as follows Deck , 1, has denominations , 1, 5, 6, 6 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 60, is as follows Deck , 1, has denominations , 1, 5, 6, 6 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 13 Deck , 2, beats deck , 3, with probability , -- 16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 61, is as follows Deck , 1, has denominations , 1, 5, 6, 6 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 8, 8 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 62, is as follows Deck , 1, has denominations , 1, 5, 6, 6 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 8, 8 Deck , 4, has denominations , 2, 7, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 13 yet Deck, 4, beats deck 1, with probability , -- 16 ------------------------------------------------------- Set Number, 63, is as follows Deck , 1, has denominations , 1, 5, 6, 7 Deck , 2, has denominations , 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 64, is as follows Deck , 1, has denominations , 1, 5, 7, 7 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 3, 3, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 65, is as follows Deck , 1, has denominations , 1, 5, 7, 7 Deck , 2, has denominations , 3, 6, 6, 6 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 66, is as follows Deck , 1, has denominations , 1, 5, 7, 7 Deck , 2, has denominations , 4, 4, 4, 6 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that 11 Deck , 1, beats deck , 2, with probability , -- 16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 67, is as follows Deck , 1, has denominations , 1, 5, 7, 7 Deck , 2, has denominations , 4, 4, 6, 6 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 5/8 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 68, is as follows Deck , 1, has denominations , 1, 5, 7, 7 Deck , 2, has denominations , 4, 6, 6, 6 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 69, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 2, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 8 Deck , 4, has denominations , 3, 3, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 70, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 2, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 71, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 2, 5, 5, 7 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 3, 3, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 72, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 2, 5, 5, 8 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 3, 3, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 73, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 2, 5, 5, 9 Deck , 3, has denominations , 4, 4, 4, 8 Deck , 4, has denominations , 3, 3, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 74, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 3, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 8 Deck , 4, has denominations , 2, 2, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 75, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 3, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 76, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 3, 5, 5, 7 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 77, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 3, 5, 5, 8 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 78, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 3, 5, 5, 9 Deck , 3, has denominations , 4, 4, 4, 8 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 79, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 80, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 81, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 4, 7 Deck , 3, has denominations , 3, 3, 5, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 82, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 4, 8 Deck , 3, has denominations , 3, 3, 5, 9 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 83, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 5, 8 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 84, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 4, 9 Deck , 3, has denominations , 3, 3, 8, 8 Deck , 4, has denominations , 2, 5, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 85, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 86, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 87, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 5, 7 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 88, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 5, 8 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 89, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 5, 9 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 13 Deck , 2, beats deck , 3, with probability , -- 16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 90, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 5, 9 Deck , 3, has denominations , 3, 3, 8, 8 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 91, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 4, 5, 9 Deck , 3, has denominations , 3, 3, 8, 8 Deck , 4, has denominations , 2, 7, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 13 yet Deck, 4, beats deck 1, with probability , -- 16 ------------------------------------------------------- Set Number, 92, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 93, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 94, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 5, 5, 7 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 95, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 5, 5, 8 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 96, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 5, 5, 9 Deck , 3, has denominations , 3, 3, 3, 8 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 13 Deck , 2, beats deck , 3, with probability , -- 16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 97, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 5, 5, 9 Deck , 3, has denominations , 3, 3, 8, 8 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 98, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 4, 5, 5, 9 Deck , 3, has denominations , 3, 3, 8, 8 Deck , 4, has denominations , 2, 7, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 13 yet Deck, 4, beats deck 1, with probability , -- 16 ------------------------------------------------------- Set Number, 99, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 8 Deck , 4, has denominations , 2, 2, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 100, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 101, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 8 Deck , 4, has denominations , 2, 2, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 102, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 103, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 8 Deck , 4, has denominations , 2, 3, 7, 9 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 104, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 105, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 7 Deck , 3, has denominations , 3, 3, 4, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 106, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 7 Deck , 3, has denominations , 3, 4, 4, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 107, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 7 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 2, 3, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 108, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 8 Deck , 3, has denominations , 3, 3, 4, 9 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 109, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 8 Deck , 3, has denominations , 3, 4, 4, 9 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 110, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 8 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 2, 3, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 111, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 9 Deck , 3, has denominations , 2, 4, 8, 8 Deck , 4, has denominations , 3, 3, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 112, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 9 Deck , 3, has denominations , 2, 4, 8, 8 Deck , 4, has denominations , 3, 7, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 9/16 13 yet Deck, 4, beats deck 1, with probability , -- 16 ------------------------------------------------------- Set Number, 113, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 9 Deck , 3, has denominations , 3, 3, 4, 8 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 13 Deck , 2, beats deck , 3, with probability , -- 16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 114, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 9 Deck , 3, has denominations , 3, 3, 8, 8 Deck , 4, has denominations , 2, 4, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 115, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 9 Deck , 3, has denominations , 3, 4, 4, 8 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 13 Deck , 2, beats deck , 3, with probability , -- 16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 116, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 9 Deck , 3, has denominations , 3, 4, 8, 8 Deck , 4, has denominations , 2, 2, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 117, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 9 Deck , 3, has denominations , 3, 4, 8, 8 Deck , 4, has denominations , 2, 7, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 13 yet Deck, 4, beats deck 1, with probability , -- 16 ------------------------------------------------------- Set Number, 118, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 9 Deck , 3, has denominations , 4, 4, 4, 8 Deck , 4, has denominations , 2, 3, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 13 Deck , 2, beats deck , 3, with probability , -- 16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 119, is as follows Deck , 1, has denominations , 1, 6, 6, 6 Deck , 2, has denominations , 5, 5, 5, 9 Deck , 3, has denominations , 4, 4, 8, 8 Deck , 4, has denominations , 2, 3, 7, 7 It is readily seen that Deck , 1, beats deck , 2, with probability , 9/16 Deck , 2, beats deck , 3, with probability , 5/8 Deck , 3, beats deck , 4, with probability , 3/4 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 120, is as follows Deck , 1, has denominations , 1, 6, 6, 7 Deck , 2, has denominations , 2, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 121, is as follows Deck , 1, has denominations , 1, 6, 6, 7 Deck , 2, has denominations , 3, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 122, is as follows Deck , 1, has denominations , 1, 6, 6, 7 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 123, is as follows Deck , 1, has denominations , 1, 6, 6, 7 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 124, is as follows Deck , 1, has denominations , 1, 6, 6, 7 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 125, is as follows Deck , 1, has denominations , 1, 6, 6, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 126, is as follows Deck , 1, has denominations , 1, 6, 6, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 127, is as follows Deck , 1, has denominations , 1, 6, 6, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 128, is as follows Deck , 1, has denominations , 1, 6, 7, 7 Deck , 2, has denominations , 2, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 129, is as follows Deck , 1, has denominations , 1, 6, 7, 7 Deck , 2, has denominations , 3, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 130, is as follows Deck , 1, has denominations , 1, 6, 7, 7 Deck , 2, has denominations , 4, 4, 4, 5 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 131, is as follows Deck , 1, has denominations , 1, 6, 7, 7 Deck , 2, has denominations , 4, 4, 5, 5 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 132, is as follows Deck , 1, has denominations , 1, 6, 7, 7 Deck , 2, has denominations , 4, 5, 5, 5 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 133, is as follows Deck , 1, has denominations , 1, 6, 7, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 3, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 134, is as follows Deck , 1, has denominations , 1, 6, 7, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 3, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 135, is as follows Deck , 1, has denominations , 1, 6, 7, 7 Deck , 2, has denominations , 5, 5, 5, 5 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 136, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 2, 5, 5, 6 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 137, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 2, 5, 6, 6 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 138, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 4, 4, 5, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 139, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 4, 5, 5, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 140, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 2, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 141, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 3, 5, 5, 6 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 142, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 3, 5, 6, 6 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 143, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 3, 6, 6, 6 Deck , 3, has denominations , 4, 4, 5, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 144, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 3, 6, 6, 6 Deck , 3, has denominations , 4, 5, 5, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 145, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 3, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 146, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 4, 4, 4, 6 Deck , 3, has denominations , 3, 3, 5, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 147, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 4, 4, 5, 6 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 148, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 4, 4, 6, 6 Deck , 3, has denominations , 3, 3, 5, 9 Deck , 4, has denominations , 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 , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 149, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 4, 5, 5, 6 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 150, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 4, 5, 6, 6 Deck , 3, has denominations , 3, 3, 3, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 151, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 4, 6, 6, 6 Deck , 3, has denominations , 3, 3, 5, 9 Deck , 4, has denominations , 2, 2, 8, 8 It is readily seen that Deck , 1, beats deck , 2, with probability , 3/4 11 Deck , 2, beats deck , 3, with probability , -- 16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 152, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 4, 6, 6, 6 Deck , 3, has denominations , 3, 5, 5, 9 Deck , 4, has denominations , 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 , 5/8 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 153, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 4, 6, 6, 6 Deck , 3, has denominations , 5, 5, 5, 9 Deck , 4, has denominations , 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 , 9/16 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 154, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 5, 5, 5, 6 Deck , 3, has denominations , 3, 3, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 155, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 5, 5, 5, 6 Deck , 3, has denominations , 3, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 156, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 5, 5, 5, 6 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 157, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 5, 5, 6, 6 Deck , 3, has denominations , 3, 3, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 158, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 5, 5, 6, 6 Deck , 3, has denominations , 3, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 159, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 5, 5, 6, 6 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 160, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 5, 6, 6, 6 Deck , 3, has denominations , 3, 3, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 161, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 5, 6, 6, 6 Deck , 3, has denominations , 3, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 162, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 5, 6, 6, 6 Deck , 3, has denominations , 4, 4, 4, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 163, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 6, 6, 6, 6 Deck , 3, has denominations , 3, 4, 5, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 164, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 6, 6, 6, 6 Deck , 3, has denominations , 3, 5, 5, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 9/16 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 165, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 6, 6, 6, 6 Deck , 3, has denominations , 4, 4, 5, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 ------------------------------------------------------- Set Number, 166, is as follows Deck , 1, has denominations , 1, 7, 7, 7 Deck , 2, has denominations , 6, 6, 6, 6 Deck , 3, has denominations , 4, 5, 5, 9 Deck , 4, has denominations , 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 , 3/4 Deck , 3, beats deck , 4, with probability , 5/8 yet Deck, 4, beats deck 1, with probability , 5/8 --------------------------------------------------- --------------------------------------------------- This ends this chapter, that took, 8322.900, seconds to generate. ----------------------------------------------------------------------------\ -- This ends this book that took, 10051.392, seconds to generate.