Odds of making each hand
In five random cards a pair appears 42% of the time and a royal flush once in 649,740 deals; with seven cards, as in Texas Hold’em by the river, every hand gets commoner. These tables are exact: our calculator engine enumerated all 2,598,960 five-card hands and all 133,784,560 seven-card combinations, so the numbers are counted, not estimated.
| Hand | 5 cards | 5-card odds | 7 cards | 7-card odds |
|---|---|---|---|---|
| Royal flush | 0.0002% | 1 in 649,740 | 0.0032% | 1 in 30,940 |
| Straight flush | 0.0014% | 1 in 72,193 | 0.0279% | 1 in 3,591 |
| Four of a kind | 0.0240% | 1 in 4,165 | 0.17% | 1 in 595 |
| Full house | 0.14% | 1 in 694 | 2.60% | 1 in 38.5 |
| Flush | 0.20% | 1 in 509 | 3.03% | 1 in 33.1 |
| Straight | 0.39% | 1 in 255 | 4.62% | 1 in 21.6 |
| Three of a kind | 2.11% | 1 in 47.3 | 4.83% | 1 in 20.7 |
| Two pair | 4.75% | 1 in 21.0 | 23.5% | 1 in 4.3 |
| One pair | 42.3% | 1 in 2.4 | 43.8% | 1 in 2.3 |
| High card | 50.1% | 1 in 2.0 | 17.4% | 1 in 5.7 |
“7 cards” is the chance your best five-card hand is at least this rank by the river. Straight-flush rows exclude royals, which are listed separately. What beats what is in the hand rankings.
Odds of being dealt it
| Hand | Probability | Odds |
|---|---|---|
| A specific pocket pair (say, aces) | 0.45% | 1 in 221 |
| Any pocket pair | 5.88% | 1 in 17 |
| Aces or kings | 0.90% | 1 in 111 |
| Ace-king, any suits | 1.21% | 1 in 83 |
| Ace-king suited | 0.30% | 1 in 332 |
| Any two suited cards | 23.53% | 1 in 4.25 |
| A suited connector | 3.92% | 1 in 25.5 |
| A premium hand (A-A to J-J or A-K) | 3.02% | 1 in 33 |
Odds of improving on the flop and by the river
| Situation | Probability | Odds |
|---|---|---|
| Pocket pair → set or better on the flop | 11.76% | 1 in 8.5 |
| Pocket pair → set or better by the river | 19.18% | 1 in 5.2 |
| Two unpaired cards → pair at least one on the flop | 32.43% | 1 in 3.1 |
| Two unpaired cards → pair or better by the river | 48.74% | 1 in 2.1 |
| Two suited cards → flush on the flop | 0.84% | 1 in 119 |
| Two suited cards → flush draw on the flop | 10.94% | 1 in 9.1 |
| Two suited cards → flush by the river | 6.40% | 1 in 15.6 |
| Backdoor flush: runner-runner from the flop | 4.16% | 1 in 24 |
Odds of completing a draw
| Outs | Typical draw | Turn | River | By the river |
|---|---|---|---|---|
| 4 | Gutshot straight draw | 8.5% | 8.7% | 16.5% |
| 8 | Open-ended straight draw | 17.0% | 17.4% | 31.5% |
| 9 | Flush draw | 19.1% | 19.6% | 35.0% |
| 12 | Flush draw + gutshot | 25.5% | 26.1% | 45.0% |
| 15 | Flush draw + open-ended | 31.9% | 32.6% | 54.1% |
To turn a draw into a decision, compare these numbers with the price of the call in the pot odds calculator; the full 1–20 outs table is on the odds calculator page.
Classic pre-flop matchups
Chance to win with all five board cards dealt, from simulations of 20,000–300,000 deals per matchup with the calculator engine (±0.1%).
| Matchup | First hand | Second hand |
|---|---|---|
| A-A vs K-K | 82% | 18% |
| A-K suited vs Q-Q | 46% | 54% |
| A-K offsuit vs 2-2 | 47% | 53% |
| A-Q offsuit vs A-K offsuit | 24% | 76% |
| A-A vs one random hand | 85% | 15% |
| 7-2 offsuit vs one random hand | 35% | 65% |
Equities for all 169 starting hands against one to five opponents are in the odds calculator and the starting hands chart.
Poker probabilities FAQ
What are the odds of being dealt pocket aces?
Exactly 6 of the 1,326 possible two-card combinations are A-A, so the odds are 1 in 221, or 0.45%. Over a long session of 60 hands you will see aces about once every 3.7 sessions on average. Any specific pocket pair has the same odds; some pair arrives once every 17 hands.
What are the odds of flopping a set?
With a pocket pair, the chance that the flop brings at least a set is 11.76%, about 1 in 8.5 (exactly: 1 − C(48,3)/C(50,3)). By the river it grows to 19.18%. This is why small pairs are played cheaply before the flop: they win chips mainly when the set arrives.
What are the odds of a royal flush?
In five random cards, 4 in 2,598,960, or 1 in 649,740. Using all seven cards in Texas Hold’em (your two plus the board), 4,324 of 133,784,560 combinations contain a royal flush: 1 in 30,940. Rare, but a regular player sees a few in a lifetime.
What is the chance of making a flush by the river?
Starting with two suited cards, 6.40% (1 in 15.6) counting every way the board can fall. With a flush draw already on the flop (9 outs) it is 34.97%, and 19.15% with one card to come on the turn.
How many starting hands and boards are there in Texas Hold’em?
There are 1,326 two-card starting combinations, grouping into 169 distinct hands (13 pairs, 78 suited, 78 offsuit). After your two cards, the board can come in 2,118,760 ways. All five community cards plus your two give 133,784,560 seven-card combinations, which is the number our tables above enumerate.
Are these probabilities exact or simulated?
The hand-frequency, dealt and draw tables are exact: our engine enumerated every 5-card hand (2,598,960) and every 7-card combination (133,784,560) rather than sampling. Only the matchup equities are Monte Carlo, with 300,000 deals per hand, so they can move by about ±0.1%.