M. Tismenetsky
International Journal of Computer Mathematics
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≥5. In particular, we derive closed expressions for the probabilities of flush, straight and full house and show that the probability of a flush is less than a straight when n≤11, and is more than a straight when n>11. Similarly, we show that the probability of a full house is less than a straight when n≤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 rank ordering does not follow the occurrence probability ordering, contrary to what intuition suggests.
M. Tismenetsky
International Journal of Computer Mathematics
Satoshi Hada
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Igor Devetak, Andreas Winter
ISIT 2003
Shashanka Ubaru, Lior Horesh, et al.
Journal of Biomedical Informatics