Big Two and n-card poker probabilities
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914833198219264 |
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| author | Wu, Brian Wu, Chai Wah |
| author_facet | Wu, Brian Wu, Chai Wah |
| contents | Between the poker hands of straight, flush, and full house, which hand is more common? In standard 5-card poker, the order from most common to least common is straight, flush, full house. The same order is true for 7-card poker such as Texas hold'em. However, is the same true for n-card poker for larger n? We study the probability of obtaining these various hands for n-card poker for various values of $n\geq 5$. In particular, we derive equations for the probability of flush, straight and full house and show that the probability of flush is less than a straight when $n\leq 11$, and is more than a straight when n>11. Similarly, we show that the probability of full house is less than a straight when $n\leq 19$, and is more than a straight when n>19. This means that for games such as Big Two where the ordering of 13-card hands depends on the ordering in 5-card poker, the ranking ordering does not follow the occurrence probability ordering, contrary to what intuition suggests. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_00011 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Big Two and n-card poker probabilities Wu, Brian Wu, Chai Wah History and Overview 05Axx Between the poker hands of straight, flush, and full house, which hand is more common? In standard 5-card poker, the order from most common to least common is straight, flush, full house. The same order is true for 7-card poker such as Texas hold'em. However, is the same true for n-card poker for larger n? We study the probability of obtaining these various hands for n-card poker for various values of $n\geq 5$. In particular, we derive equations for the probability of flush, straight and full house and show that the probability of flush is less than a straight when $n\leq 11$, and is more than a straight when n>11. Similarly, we show that the probability of full house is less than a straight when $n\leq 19$, and is more than a straight when n>19. This means that for games such as Big Two where the ordering of 13-card hands depends on the ordering in 5-card poker, the ranking ordering does not follow the occurrence probability ordering, contrary to what intuition suggests. |
| title | Big Two and n-card poker probabilities |
| topic | History and Overview 05Axx |
| url | https://arxiv.org/abs/2309.00011 |