May the Best One Win

1970: Martin Gardner described Bradley Efron’s invention of a set of 4 nontransitive dice.

2017: Heilman and Pasciuto created several sets of nontransitive Octahedral dice, one is an extension of Tiggerman’s tetrahedral ones.

2017: Heilman and Pasciuto created a set of 5 nontransitive dodecahedral dice.

2017: Heilman and Pasciuto designed a set of three nontransitive icosahedral dice.

• Transitivity is a key property of an order relation
• A set of nontransitive dice with a 3:1 probability (or higher) of winning does not exist

Game theory (MSC2010#97K99)

• Fair game
• Probability
• The transitive law
• Cyclic preferences
• Voting Paradox