Miwin's dice its 2 lowest numbers. The dots on each die are colored blue, red or black. Each die has the following numbers: Numbers 1 and 9, 2 and 7, and 3 and 8 are on opposite sides on all three dice. Additional numbers are 5 and 6 on die III, 4 and 5 on die IV, and 4 and 6 on die V. The dice are designed in such a way that, for every die, another will usually win against it. The probability that a given die in the sequence (III, IV, V, III) will roll a higher number than the
Nontransitive dice in favor of the second player, because the second player can always find a die that will beat the first player's die with probability . The following tables show all possible outcomes for all 3 pairs of dice. Though the three nontransitive dice A, B, C (first set of dice) P(A > B) = P(B > C) = P(C > A) = and the three nontransitive dice A′, B′, C′ (second set of dice) P(A′ > B′) = P(B′ > C′) = P(C′ > A′) = win against each other with equal probability they are not equivalent. While the first