Texas hold'em odds
In hold'em you play other players, not the house. What you can know is the chance: two aces beat two kings 81.06% of the time, counted over every one of the 1,712,304 five-card boards that can come. And what it surely costs is the share of each pot the card room keeps.
Two hands, every board that can come
A card cannot be read. Write a rank and a suit, such as "Ah" or "10d".
Each hand has two cards.
The board holds none, 3, 4 or 5 cards.
A card is written twice. Each card is in the deck once.
The count did not finish in this browser. The table below shows 26 common match-ups.
A♥ A♠ wins 81.06% of the time, loses 18.55% and ties 0.38%.
Against K♦ K♣, your share of the pot, counting a split as half, is 81.26%. All 1,712,304 boards that can still come were counted.
The count runs in your browser and needs JavaScript. The tables below work without it.
Common match-ups before the flop
When two players are all in before the flop, a pair against two higher cards is close to a coin flip: two queens beat ace-king 56.99% of the time.
| Hand | Against | Wins | Loses | Split |
|---|---|---|---|---|
| A♥ A♠ | K♦ K♣ | 81.06% | 18.55% | 0.38% |
| A♥ A♠ | K♥ K♠ | 82.36% | 17.09% | 0.54% |
| Q♥ Q♠ | J♦ J♣ | 81.10% | 18.54% | 0.36% |
| A♥ A♠ | A♦ K♦ | 87.23% | 11.51% | 1.26% |
| A♥ A♠ | A♦ K♣ | 91.95% | 6.80% | 1.25% |
| K♥ K♠ | A♦ K♣ | 69.61% | 29.60% | 0.79% |
| A♥ K♣ | A♦ Q♣ | 72.35% | 22.97% | 4.68% |
| A♥ K♥ | A♦ Q♦ | 69.16% | 26.61% | 4.23% |
| A♥ K♣ | K♦ Q♣ | 74.30% | 24.53% | 1.17% |
| Q♥ Q♠ | A♦ K♦ | 53.59% | 46.02% | 0.39% |
| Q♥ Q♠ | A♦ K♣ | 56.99% | 42.66% | 0.34% |
| 8♥ 8♠ | A♦ K♣ | 55.42% | 44.28% | 0.30% |
| 10♥ 10♠ | A♦ Q♣ | 57.20% | 42.50% | 0.30% |
| 2♥ 2♠ | A♦ K♣ | 52.75% | 46.67% | 0.58% |
| 2♥ 2♠ | A♦ K♦ | 49.60% | 49.77% | 0.63% |
| K♥ Q♣ | 2♦ 2♣ | 48.38% | 50.73% | 0.90% |
| A♥ A♠ | 7♦ 2♣ | 87.24% | 12.40% | 0.36% |
| A♥ A♠ | 7♦ 6♦ | 76.81% | 22.87% | 0.32% |
| 9♥ 8♥ | A♦ A♣ | 22.47% | 77.22% | 0.30% |
| A♥ K♣ | 3♦ 2♣ | 65.68% | 33.74% | 0.58% |
| J♥ 10♥ | A♦ K♣ | 40.97% | 58.61% | 0.42% |
| 7♥ 6♥ | A♦ K♣ | 42.06% | 57.55% | 0.38% |
| A♥ K♣ | 8♦ 7♦ | 57.91% | 41.71% | 0.38% |
| 9♥ 9♠ | 8♦ 7♦ | 80.77% | 18.64% | 0.58% |
| A♥ J♣ | K♦ Q♦ | 55.62% | 43.94% | 0.44% |
| A♥ 5♥ | K♦ Q♣ | 60.38% | 39.16% | 0.45% |
The suits matter: when two hands share a suit, there are fewer flushes either can make.
How often a starting hand comes
| Hand | Ways out of 1,326 | Chance | That is |
|---|---|---|---|
| Any pocket pair | 78 | 5.88% | 1 in 17 |
| A given pocket pair, such as two aces | 6 | 0.45% | 1 in 221 |
| Ace-king of the same suit | 4 | 0.3% | 1 in 331.5 |
| Ace-king, any suits | 16 | 1.21% | 1 in 82.88 |
| At least one ace | 198 | 14.93% | 1 in 6.7 |
| Two cards of the same suit | 312 | 23.53% | 1 in 4.25 |
| Two cards from ten to ace | 190 | 14.33% | 1 in 6.98 |
A 52-card deck deals 1,326 different pairs of cards, all equally likely.
What the rake costs
The room does not play, but it keeps a share of every pot, usually up to a cap per hand. That is poker's certain cost. The figures here are an example; type in your own room's.
In many rooms a hand that ends before the flop pays no rake, so the share of hands that pay can be below 100%.
Check the figures: 2 to 10 players, a rake of at most 20%, and no field left empty.
Each player pays about €5.33 an hour, and €1,109.33 a year at 4 hours a week.
The room keeps on average €1.60 a hand, 4.00% of the average pot, or €48.00 an hour from the whole table. Split over 9 players of the same skill, a player has to win that much from the others just to stay level.
How it is checked
With two hands and no board, 48 cards remain and there are 1,712,304 ways the five board cards can come. Each one is counted: every player's best five cards out of seven, and who wins. All 26 match-ups in the table agree, to two decimals, with Deuces Cracked's published exact table, and the starting-hand figures with a second, independent count of the 1,326 deals. If a single figure differs, the page is not published.
What this leaves out
- The chances are for two hands that see every card, as in an all-in. In an ordinary hand, decisions and bets change who reaches the end.
- With more players at the table, every hand wins less often.
- The rake is the cost to a player of average skill. What anyone wins or loses against the other players is not counted here.
Sources
- Deuces Cracked, "Preflop poker equity matchups: exact data": the exact table of the 26 match-ups