Possible Probability and Irreducibility of Balanced Nontransitive Dice
We construct irreducible balanced nontransitive sets of n-sided dice for any positive integer n. One main tool of the construction is to study so-called fair sets of dice. Furthermore, we also study the distribution of the probabilities of balanced nontransitive sets of dice. For a lower bound, we s...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6648248 |
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| Summary: | We construct irreducible balanced nontransitive sets of n-sided dice for any positive integer n. One main tool of the construction is to study so-called fair sets of dice. Furthermore, we also study the distribution of the probabilities of balanced nontransitive sets of dice. For a lower bound, we show that the winning probability can be arbitrarily close to 1/2. We hypothesize that the winning probability cannot be more than 1/2+1/9, and we construct a balanced nontransitive set of dice whose probability is 1/2+13−153/24≈1/2+1/9.12. |
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| ISSN: | 2314-4629 2314-4785 |