A 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 2:1. A set in which ties may occur, in which case the Dice are rolled again, which gives Odds of 11:6 is

**References**

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.

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1999-05-25