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  • April 10, 2024
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An article by Y. L. Cheung [1] gives reasons why poker is usually played with five cards. The author gives several reasons, but here I’ll just look at one reason: pairs don’t act like you might expect if you have more than five cards.

In five-card poker, the more pairs the better. Better here means less likely. One pair is better than no pair, and two pairs is better than one pair. But in six-card or seven-card poker, a hand with no pair is less likely than a hand with one pair.

For a five-card hand, the probabilities of 0, 1, or 2 pair are 0.5012, 0.4226, and 0.0475 respectively.

For a six-card hand, the same probabilities are 0.3431, 0.4855, and 0.1214.

For a seven-card hand, the probabilities are 0.2091, 0.4728, and 0.2216.

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[1] Y. L. Cheung. Why Poker Is Played with Five Cards. The Mathematical Gazette, Dec., 1989, Vol. 73, No. 466 (Dec., 1989), pp. 313–315

The post Pairs in poker first appeared on John D. Cook.

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