Royal flush odds are 1 in 649,740 in a five-card hand. With seven cards to choose from, as in Texas Hold’em, they shorten to 1 in 30,940, and the poker hand odds for every other hand come from the same count.
| Hand | Combinations | Probability | Odds |
|---|---|---|---|
| Royal flush | 4 | 0.0001539% | 1 in 649,740 |
| Straight flush (not royal) | 36 | 0.001385% | 1 in 72,193 |
| Four of a kind | 624 | 0.02401% | 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 | 2.113% | 1 in 47.3 |
| Two pair | 123,552 | 4.754% | 1 in 21.0 |
| One pair | 1,098,240 | 42.26% | 1 in 2.4 |
| High card | 1,302,540 | 50.12% | 1 in 2.0 |
How the poker hand odds are counted
A 52-card deck can be dealt into 2,598,960 different five-card hands. We counted every one and sorted it by rank, with no wild cards and with a straight flush that is not royal kept in its own row. Four of those hands are royal flushes, one in each suit, which gives 1 in 649,740.
Seven cards give 133,784,560 possible sets, each ranked by its best five cards. A set holds a royal flush when five of its cards form the royal and the other two are any of the 47 cards left. There are 1,081 ways to add those two cards, so 4 x 1,081 = 4,324 sets contain a royal flush. Because the best five of seven are kept, every strong hand gets more chances to form and a hand with nothing in it gets rarer, so every row of the table moves.
Seven cards: the odds in Texas Hold’em
| Best five-card hand | Combinations | Probability | Odds |
|---|---|---|---|
| Royal flush | 4,324 | 0.003232% | 1 in 30,940 |
| Straight flush (not royal) | 37,260 | 0.02785% | 1 in 3,591 |
| Four of a kind | 224,848 | 0.1681% | 1 in 595 |
| Full house | 3,473,184 | 2.596% | 1 in 38.5 |
| Flush | 4,047,644 | 3.025% | 1 in 33.1 |
| Straight | 6,180,020 | 4.619% | 1 in 21.6 |
| Three of a kind | 6,461,620 | 4.83% | 1 in 20.7 |
| Two pair | 31,433,400 | 23.5% | 1 in 4.3 |
| One pair | 58,627,800 | 43.82% | 1 in 2.3 |
| High card | 23,294,460 | 17.41% | 1 in 5.7 |
Two extra cards change the order of the common hands. One pair, at 43.82%, is more common than no pair, at 17.41%. In five cards it runs the other way, with high card at 50.12% against 42.26% for one pair.
A flush is still harder to make than a straight. With seven cards a flush comes 3.025% of the time and a straight 4.619%. The ranking that puts the flush higher matches the count.
Starting hands
| Starting hand | Combinations | Probability | Odds |
|---|---|---|---|
| Any pocket pair | 78 | 5.88% | 1 in 17 |
| A specific pair (for example aces) | 6 | 0.45% | 1 in 221 |
| Ace-king, any suits | 16 | 1.21% | 1 in 82.9 |
| Ace-king suited | 4 | 0.3% | 1 in 331.5 |
| Two cards of the same suit | 312 | 23.53% |
In Hold’em each player gets two cards, from 1,326 possible starting hands. Of those, 78 are pocket pairs, so any pair is dealt 1 in 17. A named pair, aces for example, has 6 combinations and comes 1 in 221.
The table goes past pairs. Ace-king in any suits comes 1 in 82.9, and ace-king suited 1 in 331.5. Two cards of the same suit arrive 23.53% of the time.
The flop then changes these hands at fixed rates. A pocket pair flops a set or better 11.76% of the time. Two suited cards flop a made flush 0.84% of the time and four to a flush 10.94% of the time.
Drawing odds after the flop
After the flop, 47 cards are unseen by you. After the turn, 46 are. An out is an unseen card that completes your hand, and the exact chance counts every way the remaining cards can fall.
| Draw on the flop | Outs | Hit on the turn | Hit by the river | Rule of 4 says |
|---|---|---|---|---|
| Gutshot straight draw | 4 | 8.5% | 16.5% | 16% |
| Open-ended straight draw | 8 | 17% | 31.5% | 32% |
| Flush draw | 9 | 19.1% | 35% | 36% |
| Flush draw plus a gutshot | 12 | 25.5% | 45% | 48% |
| Flush draw plus open-ended straight draw | 15 | 31.9% | 54.1% | 60% |
The rule of 4 and 2 is a common shortcut: multiply your outs by 4 on the flop for the chance of hitting by the river, or by 2 for one card. For small draws it lands close. A gutshot, with 4 outs, reads 16% against an exact 16.5%. A flush draw, with 9 outs, reads 36% against 35.0%.
The error grows with the number of outs. With 12 outs the rule says 48%, and the exact chance is 45.0%, 3.0 points lower. With 15 outs, a flush draw plus an open-ended straight draw, the rule says 60% against an exact 54.1%: 5.9 points high.
Playing within limits
The odds start again with every shuffle. A royal flush is 1 in 30,940 on the next Hold’em hand, whatever the previous hands held.
Set a budget before you play and a time to stop, and keep to both. Our guide to responsible gambling covers setting those limits.
*Sources: every five-card and seven-card hand counted by Scores and Stats from a 52-card deck; starting-hand and drawing chances by exact combinatorics, November 2026.*