All the Suckers's Bets Decks with, 4, decks, with deck sizes, 6, 6, 6, 6, using , 6, denominations labelled from 1 to, 6 Where No denomination appears in more than one deck (hence there is never a \ tie) By Shalosh B. Ekhad 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, 1, 5, 5, 5, 5 Deck , 2, has denominations , 4, 4, 4, 4, 4, 4 Deck , 3, has denominations , 3, 3, 3, 3, 3, 3 Deck , 4, has denominations , 2, 2, 2, 2, 6, 6 It is readily seen that Deck , 1, beats deck , 2, with probability , 2/3 Deck , 2, beats deck , 3, with probability , 1 Deck , 3, beats deck , 4, with probability , 2/3 yet Deck, 4, beats deck 1, with probability , 5/9 --------------------------------------------------- --------------------------------------------------- This ends this article, that took, 2.293, seconds to generate.