For every n≥3, every rational p between 1/2 and the bound π_n is the common win probability of some balanced nontransitive n-tuple of dice.
The paradox of the nontransitive dice and the elusive principle of indifference
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Winning Probabilities of Balanced and Nontransitive n-tuples of Dice
For every n≥3, every rational p between 1/2 and the bound π_n is the common win probability of some balanced nontransitive n-tuple of dice.