Big Two and n-card poker probabilities

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Wu, Brian, Wu, Chai Wah
Format: Preprint
Published: 2023
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866914833198219264
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