- Maths reviewed by Josh Miller
- Tested by Diana Westfield
A royal flush comes along about once every 30,940 Texas Hold’em hands if you see the river. In five-card video poker it’s 1 in 649,740. The CasinoCalcs poker hand odds chart below lists every hand both ways, and the calculator above turns any of them into what it means for you: the chance it shows up in your next 500 hands, or the odds of hitting your outs on the turn and river. It’s free and the numbers are exact.
Texas Hold’em odds chart: hands by the river
These are for the best five-card hand from seven cards: your two plus the five on the board, if you stay to the end.
| Hand | Chance (7 cards) | 1 in | Chance (5 cards) | 1 in |
|---|---|---|---|---|
| Royal flush | 0.0032% | 30,940 | 0.00015% | 649,740 |
| Straight flush | 0.028% | 3,590 | 0.0014% | 72,193 |
| Four of a kind | 0.168% | 595 | 0.024% | 4,165 |
| Full house | 2.60% | 38.5 | 0.144% | 694 |
| Flush | 3.03% | 33 | 0.197% | 509 |
| Straight | 4.62% | 21.6 | 0.392% | 255 |
| Three of a kind | 4.83% | 20.7 | 2.11% | 47 |
| Two pair | 23.5% | 4.3 | 4.75% | 21 |
| One pair | 43.8% | 2.3 | 42.3% | 2.4 |
| High card | 17.4% | 5.7 | 50.1% | 2.0 |
Seven cards change everything. Two pair goes from a 1 in 21 hand to nearly one in four, which is why two pair is weaker in Hold’em than it feels.
Starting hands and the flop
| Situation | Chance | 1 in |
|---|---|---|
| Dealt pocket aces | 0.45% | 221 |
| Dealt any pocket pair | 5.9% | 17 |
| Dealt ace-king | 1.2% | 83 |
| Pocket pair flops a set or better | 11.8% | 8.5 |
| Unpaired hand pairs on the flop | 32.4% | 3.1 |
| Suited cards make a flush by the river | 6.4% | 15.6 |
Draws: outs to odds
| Draw | Outs | Turn only | Turn and river |
|---|---|---|---|
| Gutshot straight | 4 | 8.5% | 16.5% |
| Open-ended straight | 8 | 17.0% | 31.5% |
| Flush draw | 9 | 19.1% | 35.0% |
| Flush + gutshot | 12 | 25.5% | 45.0% |
| Flush + open-ended | 15 | 31.9% | 54.1% |
Switch the calculator to outs mode for any number. Then compare it with what the pot is offering in the pot odds calculator, or run real hands against each other in the poker odds calculator.
Odds of a royal flush
The odds of a royal flush are 1 in 649,740 in five cards and about 1 in 30,940 by the river in Hold’em. Why the gap? It depends on how many cards you get to use: five dealt straight, or your two plus five on the board. Holding a suited ace-king, the chance the board brings the other three is about 1 in 1,960, and flopping it outright is 1 in 19,600. Plenty of regular players go years without seeing one.
Odds of four of a kind
Four of a kind is 1 in 4,165 in five cards and about 1 in 595 by the river in Hold’em, roughly once every 600 hands you see through to the end. With a pocket pair, the chance of flopping quads is 1 in 408. Getting quads beaten is far rarer; the bad beat jackpot calculator has the numbers.