Efron's dice are set of four nontransitive dice such that the probabilities of A winning against B, B against C, C against D, and D against
A are all the same.
The images above depict two different sets of Efron's dice having 2:1 odds for winning pairs.
Another set of dice in which ties may occur (in which case the dice are rolled again) and which gives odds of 11:6 for winning
pairs is illustrated above.
Gardner, M. "Mathematical Games: The Paradox of the Nontransitive Dice and the Elusive Principle of Indifference." Sci. Amer.223,
110-114, Dec. 1970.Honsberger, R. "Some Surprises in Probability."
Ch. 5 in Mathematical
Plums (Ed. R. Honsberger). Washington, DC: Math. Assoc. Amer., pp. 94-97,
1979.
