Poker Odds

This section on poker odds borrows a chart from the rec.gambling.poker FAQ. The information is simply mathematical, and shows why we rank poker hands in the way that we do. The hands are ranked according to the odds of that hand being built when 5 cards are pulled from a 52-card deck. Poker hand ranks are based on the odds of that hand coming up, relative to the other hands.

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.
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.
Poker odds are fairly straightforward. Much like craps or blackjack, the possibilities are finite, and to some degree predictable. Poker odds change as cards are dealt from the deck. One of the most important aspects of developing a sense for evolving poker odds over the course of a hand is to study as much up-card information as possible in relation to your own hand.