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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| Format: | Article |
| Language: | English |
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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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| author | Injo Hur Yeansu Kim |
| author_facet | Injo Hur Yeansu Kim |
| author_sort | Injo Hur |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a845bf1d0b2a41f6b0bbea0a2fdf5258 |
| institution | OA Journals |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-a845bf1d0b2a41f6b0bbea0a2fdf52582025-08-20T02:20:44ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66482486648248Possible Probability and Irreducibility of Balanced Nontransitive DiceInjo Hur0Yeansu Kim1Department of Mathematics Education, Chonnam National University, Gwangju City, Republic of KoreaDepartment of Mathematics Education, Chonnam National University, Gwangju City, Republic of KoreaWe 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.http://dx.doi.org/10.1155/2021/6648248 |
| spellingShingle | Injo Hur Yeansu Kim Possible Probability and Irreducibility of Balanced Nontransitive Dice Journal of Mathematics |
| title | Possible Probability and Irreducibility of Balanced Nontransitive Dice |
| title_full | Possible Probability and Irreducibility of Balanced Nontransitive Dice |
| title_fullStr | Possible Probability and Irreducibility of Balanced Nontransitive Dice |
| title_full_unstemmed | Possible Probability and Irreducibility of Balanced Nontransitive Dice |
| title_short | Possible Probability and Irreducibility of Balanced Nontransitive Dice |
| title_sort | possible probability and irreducibility of balanced nontransitive dice |
| url | http://dx.doi.org/10.1155/2021/6648248 |
| work_keys_str_mv | AT injohur possibleprobabilityandirreducibilityofbalancednontransitivedice AT yeansukim possibleprobabilityandirreducibilityofbalancednontransitivedice |