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Non-transitive sets of dice

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It is well-known that there is a trio of “three-sided dice” A, B and C, with the following property. Â If A and B are rolled, then the probability that the number showing on die A is greater than that on die B is strictly greater than 1/2 – A beats B – while similarly B beats C and C beats A. This observation may seem to lie purely within the realm of recreational mathematics; my aim in this talk is to explain how examples of such “non-transitivity” lead to some interesting mathematics.

This talk is part of the The Archimedeans (CU Mathematical Society) series.

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