die's probability of winning is 2/3. For rolling high number, B beats A, C beats B, D beats C, A beats D. A: 1, 2, 16, 17, 18, 19 B: 3, 4, 5, 20, 21, 22 C: 6, 7, 8, 9, 23, 24 D: 10, 11, 12, 13, 14, 15 Relation to Efron's dice These dice are basically the same as Efron's dice, as each number of a series of successive numbers on a single die can all be replaced by the lowest number of the series and afterwards renumbering them. A: → → B: → → C: → → D: → → Miwin's dice Miwin's Dice were invented in 1975 by the physicist Michael Winkelmann. Consider a set of three dice, III, IV and V such that die III has sides 1, 2, 5, 6, 7, 9 die IV has sides 1, 3, 4, 5, 8, 9 die V has sides 2, 3, 4, 6, 7, 8 Then: the probability that III rolls a higher number than IV is the probability that IV rolls a higher number than V is the probability that V rolls a higher number than III is Three-dice set with minimal alterations to standard dice The following intransitive dice have only a few differences compared to 1 through 6 standard dice: as with standard dice, the total number of pips is always 21 as with standard dice, the sides only carry pip numbers between 1 and 6 faces with the same number of pips occur a maximum of twice per dice only two sides on each die have numbers different from standard dice: A: 1, 1, 3, 5, 5, 6 B: 2, 3, 3, 4, 4, 5 C: 1, 2, 2, 4, 6, 6'Like Miwin’s set, the probability of A winning versus B (or B vs. C, C vs. A) is . The probability of a draw, however, is , so that only 15 out of 36 rolls lose. So the overall winning expectation is higher. Warren Buffett Warren Buffett is known to be a fan of intransitive dice. In the book Fortune's Formula: The Untold Story of the Scientific Betting System that Beat the Casinos and Wall Street, a discussion between him and Edward Thorp is described. Buffett and Thorp discussed their shared interest in intransitive dice. "These are a mathematical curiosity, a type of 'trick' dice that confound most people's ideas about probability."