Poker Hand Probabilities: How Combinations Rank the Hands
October 21, 2026
A five-card poker hand is a combination of 5 cards from 52, so there are C(52,5) = 2,598,960 possible hands. Poker rankings follow rarity: the fewer ways to make a hand, the higher it ranks. There are only 4 royal flushes, 624 four-of-a-kind hands, and 3,744 full houses, compared with 1,098,240 hands containing exactly one pair.
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Four of a kind: choose the rank (13 ways), take all four cards of that rank, and add any of the remaining 48 cards: 13 × 48 = 624. Full house: choose the rank for three cards (13), choose 3 of 4 suits (4), choose a different rank for the pair (12), and choose 2 of 4 suits (6): 13 × 4 × 12 × 6 = 3,744.
A flush needs five cards of one suit, which can happen in 4 × C(13,5) = 5,148 ways, but 40 of them are straight flushes, leaving 5,108 ordinary flushes.
| Hand | Number of hands | Probability | Odds (1 in ...) |
|---|---|---|---|
| Royal flush | 4 | 0.00015% | 649,740 |
| Four of a kind | 624 | 0.024% | 4,165 |
| Full house | 3,744 | 0.144% | 694 |
| Flush | 5,108 | 0.197% | 509 |
| Straight | 10,200 | 0.392% | 255 |
| One pair | 1,098,240 | 42.3% | 2.4 |
Why Rank Follows Rarity
Early poker players learned by experience which hands were rarer. A flush ranks above a straight because it is rarer in a standard 52-card deck, even though intuition might say a run of consecutive numbers is harder.
Rules change in variants. With wild cards, a joker, or fewer cards in the deck, the ranking of hands by probability changes, and some games use different hierarchies for that reason.
Practical Takeaways
Knowing the frequencies helps with decisions. If you hold four cards to a flush before the draw, you have 9 remaining cards of that suit among 47 unseen cards, about a 19% chance of completing it on a single draw.
Probabilities describe long-run frequencies. Over a few hours, luck dominates, which is why even well-played hands lose often.
Frequently Asked Questions
How many five-card poker hands are there?
2,598,960, which is C(52,5).
Why does a flush beat a straight?
A flush is less likely: 5,108 hands versus 10,200 for a straight.
What are the odds of a royal flush?
1 in 649,740 in a five-card deal.
Do the odds change in Texas Hold'em?
Yes. With seven cards available, the chance of making a given hand is higher than with five.