Poker Hand Probability Calculator (Odds of Every Poker Hand)
Probability and odds of every poker hand — royal flush, straight flush, four of a kind, full house, flush, straight and more — in five-card poker and the best five of seven cards (Texas Hold'em).
How it works
Probability = number of hands of that type ÷ total hands · 5 cards: total = C(52, 5) = 2,598,960; e.g. full house = 13 × C(4,3) × 12 × C(4,2) = 3,744 · 7 cards: total = C(52, 7) = 133,784,560, each 7-card set counted once under its best 5-card hand · odds against = (1 − p) ÷ p
Poker hands are ranked by how rare they are. Counting combinations exactly — choosing ranks and suits with binomial coefficients — gives the number of ways to make each hand from a 52-card deck: four of a kind can be made 624 ways in five cards, a full house 3,744 ways and a flush 5,108 ways (excluding straight flushes). With seven cards, as in Texas Hold'em at the river, each seven-card combination is classified by its best five-card hand, which makes pairs and two pair much more common and even makes "high card" rarer than one pair. These are the probabilities for the cards you are dealt, before any draws or folds.
Worked example
Five-card poker, full house: 13 ranks for the three of a kind × C(4,3) = 4 suit choices × 12 ranks for the pair × C(4,2) = 6 suit choices = 3,744 hands out of C(52,5) = 2,598,960. Probability = 3,744 ÷ 2,598,960 = 0.1441%, or 1 in 694 (693.17 to 1 against). A full house or better comes up 0.1696% of the time.
Sources: Wikipedia — Poker probability (combinatorial derivations) · Wolfram MathWorld — Poker
Frequently asked questions
What are the odds of a royal flush?
In five cards, 4 in 2,598,960 — 1 in 649,740 (0.000154%). With the best five of seven cards, as in Texas Hold'em by the river, it is 4,324 in 133,784,560 — about 1 in 30,940.
Which is more likely, a flush or a straight?
A straight. In five cards there are 10,200 straights and 5,108 flushes, which is why a flush beats a straight. With seven cards the straight is still more common (4.62% versus 3.03%).
What is the chance of being dealt a pair?
Exactly one pair in five cards: 42.26%. In seven cards it is 43.82%, and having at least a pair is 82.6%.
Do these odds apply to Texas Hold'em starting hands?
No. They are for complete hands. For your two hole cards, the chance of a pocket pair is 5.88% (1 in 17) and of pocket aces 0.45% (1 in 221).
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Probabilities describe the long run, not the next bet. Every casino and lottery game has a negative expected value for the player; gamble only with money you can afford to lose, and seek help if gambling stops being fun.