Poker
Poker hands probability
Poker hands probability measures how often a particular hand type appears in a deal, calculated by dividing the number of ways that hand can occur by the total number of possible hands.
- Sample space
- 52-card deck yields 2,598,960 possible five-card hands1
- Rarest hand
- Royal flush occurs 4 ways; probability is about 1 in 649,740 (0.000154%)1
- Calculation method
- Count combinations producing the target hand, then divide by total possible hands12
- Also called
- Hand probability, poker hand odds, hand frequencies12
Key points
- The probability of any five-card hand type equals its combination count divided by 2,598,960.1
- In Texas hold ’em, hand strength is estimated by counting outs — unseen cards that improve the hand.3
- Hand rankings are related to rarity but are not the same as probability; rankings order hand types, while probability measures their frequency.45
Five-card hand probabilities
| Hand type | Combinations | Probability |
|---|---|---|
| Royal flush | 4 | 1 in 649,740 |
| Straight flush (excl. royal) | 36 | 1 in 72,193 |
| Four of a kind | 624 | 1 in 4,165 |
| Full house | 3,744 | 1 in 694 |
| Flush | 5,108 | 1 in 508 |
| Straight | 10,200 | 1 in 255 |
| Three of a kind | 54,912 | 1 in 47 |
| Two pair | 123,552 | 1 in 21 |
| One pair | 1,098,240 | 1 in 2.37 |
| High card | 1,302,540 | 1 in 2.00 |
Where this term is used
Not the same as
- Poker probability — a broader term covering all chance calculations in poker, not just hand outcomes
- Poker hand rankings — the ordered strength of hand types, which is related to rarity but is not the probability itself
Related terms
Poker
Boat (poker hands)
Explains the full house hand type and its frequency.
Poker
Poker hand rankings probability
Covers the probability behind each hand ranking.
Poker
Poker probability
Broader topic of chance calculations in poker, including pot odds and expected value.
Poker
Poker hand rankings
Lists hand types in order of strength, from high card to royal flush.
Poker
Poker hands quads
Details four of a kind, its combinations and probability.
Poker
Omaha poker hands
Explains hand probabilities specific to Omaha, where players use two of four hole cards.
Sources
- Poker probability en.wikipedia.org Provides the sample space size, royal flush count, and calculation method for five-card hand probabilities.
- Rules of Card Games: Poker Hand Probabilities pagat.com Confirms the calculation method and alternative names for hand probability.
- Texas hold 'em en.wikipedia.org Supports the use of outs in Texas hold 'em for estimating hand strength.
- 343 arxiv.org Supports the distinction between hand rankings and probability.
- Ranking of Poker Hands pagat.com Supports the distinction between hand rankings and probability.
Sources are drawn from regulators, universities and published research, and each one is labelled with what it actually is — a preprint is not called a paper. Bookmaker and affiliate pages are never cited here, because a page that sells betting is not a neutral authority on it.