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Index > Poker games and rules > Odds and probabilities

Why are poker hands ranked the way they are?

Author: Michael Maurer, Darse Billings, Roy Hashimoto
Last updated: 1995
Copyright © 2004 Michael Maurer, Darse Billings, Roy Hashimoto
The official and up-to-date version of this answer is here.

The standard poker hands are ranked based on the probability of their being dealt pat in 5 cards from a full 52-card deck. The following table lists the hands in order of increasing frequency, and shows how many ways each hand can be dealt in 3, 5, and 7 cards.

Hand                  3 cards           5 cards           7 cards
====                  =======           =======           =======
Straight Flush             48                40            41,584
Four of a Kind              0               624           224,848
Full House                  0             3,744         3,473,184
Flush                   1,096             5,108         4,047,644
Straight                  720            10,200         6,180,020
Three of a Kind            52            54,912         6,461,620
Two Pair                    0           123,552        31,433,400
One Pair                3,744         1,098,240        58,627,800
High Card              16,440         1,302,540        23,294,460
TOTALS                 22,100         2,598,960       133,784,560


1. The standard rankings are incorrect for 3-card hands, since it is easier to get a flush than a straight, and easier to get a straight than three of a kind. See the entry on three-card rankings.

2. For 7-card hands, the numbers reflect the best possible 5-card hand out of the 7 cards. For instance, a hand that contains both a straight and three of a kind is counted as a straight.

3. For 7-card hands, only five cards need be in sequence to make a straight, or of the same suit to make a flush. In a 3-card hand a sequence of three is considered a straight, and three of the same suit a flush. These rules reflect standard poker practice.

4. In a 7-card hand, it is easier for one's *best* 5 cards to have one or two pair than no pair. (Good bar bet opportunity!) However, if we changed the ranking to value no pairs above two pairs, all of the one pair hands and most of the two pair hands would be able to qualify for "no pair" by choosing a different set of five cards.

5. Within each type of hand (e.g., among all flushes) the hands are ranked according to an arbitrary scheme, unrelated to probability. See the explanation of flush and two-pair rankings.