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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
Notes:
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.