Poker Hand Odds and Probabilities
Exact numbers, worked out by counting every possible hand. No rounding tricks, no simulations.
5-card poker hand probabilities
There are 2,598,960 different five-card hands from a 52-card deck.
| Hand | Combinations | Probability | Odds against |
|---|---|---|---|
| Royal Flush | 4 | 0.000154% | 649,739 : 1 |
| Straight Flush | 36 | 0.001385% | 72,192 : 1 |
| Four of a Kind | 624 | 0.0240% | 4,164 : 1 |
| Full House | 3,744 | 0.1441% | 693 : 1 |
| Flush | 5,108 | 0.1965% | 508 : 1 |
| Straight | 10,200 | 0.3925% | 254 : 1 |
| Three of a Kind | 54,912 | 2.11% | 46 : 1 |
| Two Pair | 123,552 | 4.75% | 20 : 1 |
| One Pair | 1,098,240 | 42.26% | 1.37 : 1 |
| High Card | 1,302,540 | 50.12% | 1.00 : 1 |
| Total | 2,598,960 | 100% |
Straight flush here excludes the royal flush. Straights and flushes exclude straight flushes.
Texas Hold'em (best 5 of 7 cards)
By the river in Hold'em you have seven cards: two in your hand and five on the board. There are 133,784,560 seven-card combinations. Because you choose the best five, strong hands are far more common than in 5-card poker. You are actually more likely to finish with one pair than with nothing.
| Hand | Combinations | Probability | Odds against |
|---|---|---|---|
| Royal Flush | 4,324 | 0.003232% | 30,939 : 1 |
| Straight Flush | 37,260 | 0.0279% | 3,590 : 1 |
| Four of a Kind | 224,848 | 0.1681% | 594 : 1 |
| Full House | 3,473,184 | 2.60% | 38 : 1 |
| Flush | 4,047,644 | 3.03% | 32 : 1 |
| Straight | 6,180,020 | 4.62% | 21 : 1 |
| Three of a Kind | 6,461,620 | 4.83% | 20 : 1 |
| Two Pair | 31,433,400 | 23.50% | 3.26 : 1 |
| One Pair | 58,627,800 | 43.82% | 1.28 : 1 |
| High Card | 23,294,460 | 17.41% | 4.74 : 1 |
| Total | 133,784,560 | 100% |
Starting hand odds in Hold'em
There are 1,326 possible two-card starting hands.
| Starting hand | Combos | Probability | Odds against |
|---|---|---|---|
| Any pocket pair | 78 | 5.88% | 16 : 1 |
| Pocket aces (AA) | 6 | 0.4525% | 220 : 1 |
| Any specific pocket pair (e.g. KK) | 6 | 0.4525% | 220 : 1 |
| Suited cards | 312 | 23.53% | 3.25 : 1 |
| Ace-King (any suits) | 16 | 1.21% | 82 : 1 |
| Ace-King suited | 4 | 0.3017% | 331 : 1 |
How these were calculated
Every 5-card and 7-card combination was enumerated and its best hand classified. The totals match the standard combinatorics: for example there are 4 royal flushes (one per suit) and 13 × 48 = 624 four of a kinds in 5-card poker. In 7-card hands, finishing with only high card (about 17.4%) is less likely than finishing with one pair or two pair. Rankings still follow the 5-card order, because every hand you show down is five cards.