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 the same average roll. For example, These variant dice are useful, e.g., to introduce students to different ways of comparing random variables (and how only comparing averages may overlook essential details). A set of four dice using all of the numbers 1 through 24 can be made to be nontransitive. With adjacent pairs, one die's probability of winning is 2/3. For rolling high number, B beats A, C beats B, D beats C, A beats D. 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