Poker Hands: Odds and Probability Explained
Poker hands probability is the mathematical likelihood of being dealt each hand rank from a standard 52-card deck. A five-card deal produces exactly 2,598,960 distinct combinations, and each hand type — from high card to royal flush — occupies a fixed share of that total. Because the reader already knows the hand rankings by name, this entry focuses on the numbers underneath them: how many combinations exist per hand type, how often each rank appears, and how that math connects to outs and pot odds during a live hand.
How Many Poker Hands Are Possible in a 52-Card Deck
A standard 52-card deck yields C(52,5) = 2,598,960 unique five-card combinations, and this figure is the denominator for every probability calculation on this page. Each hand rank's probability equals its combination count divided by that total. For tie-break rules within a single hand rank, the hands glossary entry covers that ground in full.
| Hand Type | Combinations | Probability | Odds Against |
|---|---|---|---|
| Royal flush | 4 | 0.0002% | 1 in 649,740 |
| Straight flush | 36 | 0.0014% | 1 in 72,193 |
| Four of a kind | 624 | 0.0240% | 1 in 4,165 |
| Full house | 3,744 | 0.1441% | 1 in 694 |
| Flush | 5,108 | 0.1965% | 1 in 509 |
| Straight | 10,200 | 0.3925% | 1 in 255 |
| Three of a kind | 54,912 | 2.1128% | 1 in 47 |
| Two pair | 123,552 | 4.7539% | 1 in 21 |
| One pair | 1,098,240 | 42.2569% | 1 in 2.4 |
| High card | 1,302,540 | 50.1177% | 1 in 2 |
Poker Hands Combinations by Rank
Two pair accounts for 123,552 of the 2,598,960 possible combinations, which places its poker hands probability at roughly 4.75%, or one in 21 deals. That count comes from choosing two ranks for the pairs out of 13, choosing two suits for each pair, then choosing one of the remaining 44 cards for the kicker. Three of a kind sits close behind at 54,912 combinations, while a full house — a pair combined with three of a kind — drops to just 3,744 combinations because both rank groups must align in the same five-card hand.
Flushes total 5,108 combinations once straight flushes are removed from the raw suit count, giving a poker hands probability near 0.196%, or about one in 509 hands. That number surprises many players because a flush feels rarer at the table than a straight, yet straights actually outnumber flushes at 10,200 combinations. The gap exists because flush odds depend on suit matching across five cards, a stricter condition than the sequential rank requirement behind a straight.
How Common Are Poker Hands at the Table
High card and one pair dominate real play, together accounting for more than 92% of all possible five-card hands. High card alone makes up 50.12% of combinations, and one pair adds another 42.26%. Every hand rarer than two pair — three of a kind through royal flush — combines for under 3% of total combinations, which is why premium hands feel like rare events rather than routine ones.
Static Deal vs. Live Hand Odds
How Poker Odds Work: Outs and Pot Odds
An out is any unseen card that improves a hand to a probable winner, and counting outs is the standard method for converting poker hands probability into a decision at the table. A player holding four cards to a flush after the flop has 9 outs — the remaining cards of that suit — out of 47 unseen cards, since 13 total cards minus the 4 already held leaves 9, and the deck minus the 5 known cards (hole cards plus board) leaves 47.
The rule of 2 and 4 turns an out count into an approximate percentage: multiply outs by 4 with two cards to come, or by 2 with one card to come. Nine outs with two cards left equals roughly 36% equity, which then compares against pot odds to judge whether a call is justified. This out-based framework is the general concept; matching starting hands to specific situations sits in the starting hands strategy guide.
Pot odds and hand probability work together. If a pot holds $80 and a player faces a $20 bet, calling risks $20 to win $100 total, a 5-to-1 return. Comparing that 20% breakeven threshold against a calculated equity figure — say, 36% from a flush draw — shows whether the call profits over the long run. A standard external reference on the subject is Wikipedia's poker probability article.