May the Best One Win

The main mathematical news

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.

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Additional Theorems / conjectures / Open questions
  • 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
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The main mathematical concepts / Principles

Game theory (MSC2010#97K99)

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