Poker odds chart
Pocket aces beat pocket kings about 82% of the time, you’re dealt aces 1 in 221 hands, and a royal flush turns up once in 30,940 seven-card Hold’em hands. Every number on this page is counted exactly — each matchup over all 1,712,304 possible boards.
Preflop all-in: who wins?
AA 81.1%split 0.38%KK 18.6%
Pair vs smaller pair. Kings need one of the two kings left, or a straight or flush.
Exact: 1,388,072 wins, 6,538 splits and 317,694 losses over all 1,712,304 boards.
Preflop matchups: the classic all-ins
Most preflop all-ins fall into a few shapes, and each shape has a typical price. A pair against a smaller pair is about 4 to 1. A pair against two higher cards is the “coin flip”, close to even. A dominated hand — ace-queen against ace-king, king-queen against ace-king — wins about a quarter of the time. Here are the exact numbers:
| Matchup | Type | First wins | Split | Second wins |
|---|---|---|---|---|
| vs | Pair vs smaller pair | 81.1% | 0.4% | 18.6% |
| vs | Pair vs dominated hand | 87.2% | 1.3% | 11.5% |
| vs | Pair vs one overcard | 69.6% | 0.8% | 29.6% |
| vs | Pair vs two overcards | 53.6% | 0.4% | 46.0% |
| vs | Pair vs two overcards | 57.0% | 0.3% | 42.7% |
| vs | Pair vs two overcards | 52.7% | 0.6% | 46.7% |
| vs | Small pair vs suited connector | 45.3% | 1.4% | 53.3% |
| vs | Pair vs one overcard | 70.6% | 0.3% | 29.1% |
| vs | Pair vs smaller pair | 81.1% | 0.4% | 18.5% |
| vs | Pair vs suited connector | 76.8% | 0.3% | 22.9% |
| vs | Domination (shared ace) | 71.7% | 4.6% | 23.7% |
| vs | Domination (shared king) | 73.6% | 1.1% | 25.3% |
| vs | Higher cards vs lower cards | 62.4% | 0.4% | 37.2% |
| vs | Two overcards vs suited connector | 58.2% | 0.6% | 41.2% |
| vs | Two overcards vs suited connector | 58.6% | 0.4% | 41.0% |
| vs | Ace-rag vs two big cards | 57.5% | 0.5% | 42.0% |
| vs | Best hand vs worst hand | 87.2% | 0.4% | 12.4% |
| vs | Same hand, one suited | 7.2% | 90.7% | 2.2% |
AA vs KK: why the number moves
Suits change the result slightly. When the kings share a suit with the aces, their flush draws are weaker, because the aces block cards of that suit and can make a higher flush. Every combination of aces against kings falls into one of three cases:
| Suits | Example | AA wins | Split | KK wins |
|---|---|---|---|---|
| No shared suit (1 of 6) | vs | 81.1% | 0.4% | 18.6% |
| One shared suit (4 of 6) | vs | 81.7% | 0.5% | 17.8% |
| Both suits shared (1 of 6) | vs | 82.4% | 0.5% | 17.1% |
| Average, all 36 combinations | 81.7% | 0.5% | 17.8% |
So the rule of thumb “aces are 82% against kings” is the average; with no shared suit it’s 81.1%, plus 0.4% splits. To run any matchup you like — including three or more hands and a board — use the poker calculator.
Odds of being dealt a hand
There are 1,326 ways to be dealt two cards from a 52-card deck (52 × 51 ÷ 2). Every probability below is a count of those combinations:
| Starting hand | Combos | Chance | Odds |
|---|---|---|---|
| Pocket aces (or any one specific pair) | 6 | 0.45% | 1 in 221 |
| Aces or kings | 12 | 0.90% | 1 in 110 |
| Any pocket pair | 78 | 5.88% | 1 in 17 |
| Ace-king, suited or offsuit | 16 | 1.21% | 1 in 82.9 |
| Ace-king suited | 4 | 0.30% | 1 in 332 |
| At least one ace | 198 | 14.93% | 1 in 6.7 |
| Two cards ten or higher (pairs included) | 190 | 14.33% | 1 in 7.0 |
| Any two suited cards | 312 | 23.53% | 1 in 4.3 |
| Suited connectors, 32s up to AKs | 48 | 3.62% | 1 in 27.6 |
At a table, the question is often whether anyone has aces. With nine players, somebody is dealt pocket aces on 4.06% of hands — about 1 in 24.6. For how each of the 169 hands plays, see the starting hands chart.
Odds on the flop
Once you hold two cards, 50 remain, so there are 19,600 possible flops. These are the odds of each outcome after one specific kind of hand:
| You flop | Flops | Chance | Odds |
|---|---|---|---|
| Pocket pair | |||
| Set or betterat least one of the 2 cards of your rank | 2,304 | 11.76% | 1 in 8.5 |
| Full houseset + a board pair, or trips on board | 192 | 0.98% | 1 in 102 |
| Four of a kindboth remaining cards of your rank | 48 | 0.24% | 1 in 408 |
| At least one overcard (with jacks)any of the 12 aces, kings and queens | 11,164 | 56.96% | 1 in 1.8 |
| Two unpaired cards | |||
| Pair or better with a hole cardany of the 6 cards matching your ranks | 6,356 | 32.43% | 1 in 3.1 |
| Two pair using both cardsone of each rank + a card of neither | 396 | 2.02% | 1 in 49.5 |
| Three of a kind with a hole cardtwo of one rank + a card of neither | 264 | 1.35% | 1 in 74.2 |
| Suited cards | |||
| Flushthree of the 11 cards left in your suit | 165 | 0.84% | 1 in 119 |
| Flush draw (four to a flush)exactly two of your suit | 2,145 | 10.94% | 1 in 9.1 |
| Backdoor flush drawexactly one of your suit | 8,151 | 41.59% | 1 in 2.4 |
| Connected cards | |||
| Straight (with J-T)AKQ, KQ9, Q98 or 987 in any suits | 256 | 1.31% | 1 in 76.6 |
| Suited ace-king | |||
| Royal flushexactly Q-J-T of your suit | 1 | 0.01% | 1 in 19,600 |
The two numbers to remember: a pocket pair flops a set or better 1 in 8.5 times, and suited cards flop a flush draw 10.9% of the time. That’s why small pairs are played for their set value — they miss the flop about seven times in eight.
How often each final hand happens
By the river, each Hold’em player makes the best five-card hand from seven cards. We counted all 133,784,560 seven-card combinations with the game’s evaluator; seven cards make strong hands far more often than a five-card deal (2,598,960 hands).
How rare is it?
| Hand | 7-card hands | Hold’em chance | Hold’em odds | 5-card chance |
|---|---|---|---|---|
| Royal flush | 4,324 | 0.0032% | 1 in 30,940 | 0.0002% |
| Straight flush (not royal) | 37,260 | 0.0279% | 1 in 3,591 | 0.0014% |
| Four of a kind | 224,848 | 0.17% | 1 in 595 | 0.0240% |
| Full house | 3,473,184 | 2.60% | 1 in 38.5 | 0.14% |
| Flush | 4,047,644 | 3.03% | 1 in 33.1 | 0.20% |
| Straight | 6,180,020 | 4.62% | 1 in 21.6 | 0.39% |
| Three of a kind | 6,461,620 | 4.83% | 1 in 20.7 | 2.11% |
| Two pair | 31,433,400 | 23.50% | 1 in 4.3 | 4.75% |
| One pair | 58,627,800 | 43.82% | 1 in 2.3 | 42.26% |
| High card | 23,294,460 | 17.41% | 1 in 5.7 | 50.12% |
One result surprises people: with seven cards, finishing with no pair at all (17.4%) is rarer than one pair (43.8%) and even rarer than two pair (23.5%). High card still ranks lowest, because the hand rankings follow five-card odds. See the full order on the poker hand rankings page.
Drawing odds by number of outs
An out is an unseen card that completes your hand. On the flop you haven’t seen 47 cards (52 minus your two and the three on the board); on the turn, 46. The chance of hitting:
| Outs | Typical draw | Turn | River (from the turn) | Turn or river | Odds against |
|---|---|---|---|---|---|
| 1 | 2.1% | 2.2% | 4.3% | 23 : 1 | |
| 2 | Pocket pair to a set | 4.3% | 4.3% | 8.4% | 11 : 1 |
| 3 | 6.4% | 6.5% | 12.5% | 7.0 : 1 | |
| 4 | Gutshot straight draw | 8.5% | 8.7% | 16.5% | 5.1 : 1 |
| 5 | 10.6% | 10.9% | 20.4% | 3.9 : 1 | |
| 6 | Two overcards | 12.8% | 13.0% | 24.1% | 3.1 : 1 |
| 7 | 14.9% | 15.2% | 27.8% | 2.6 : 1 | |
| 8 | Open-ended straight draw | 17.0% | 17.4% | 31.5% | 2.2 : 1 |
| 9 | Flush draw | 19.1% | 19.6% | 35.0% | 1.9 : 1 |
| 10 | 21.3% | 21.7% | 38.4% | 1.6 : 1 | |
| 11 | 23.4% | 23.9% | 41.7% | 1.4 : 1 | |
| 12 | Flush draw + gutshot | 25.5% | 26.1% | 45.0% | 1.2 : 1 |
| 13 | 27.7% | 28.3% | 48.1% | 1.1 : 1 | |
| 14 | 29.8% | 30.4% | 51.2% | 1.0 : 1 | |
| 15 | Flush draw + open-ender | 31.9% | 32.6% | 54.1% | 0.8 : 1 |
| 16 | 34.0% | 34.8% | 57.0% | 0.8 : 1 | |
| 17 | 36.2% | 37.0% | 59.8% | 0.7 : 1 | |
| 18 | 38.3% | 39.1% | 62.4% | 0.6 : 1 | |
| 19 | 40.4% | 41.3% | 65.0% | 0.5 : 1 | |
| 20 | 42.6% | 43.5% | 67.5% | 0.5 : 1 |
“Turn or river” assumes you see both cards, as when you’re all-in on the flop. For the quick mental version — outs times 2 or 4 — and where it goes wrong, see poker outs and the rule of 2 and 4. To turn these odds into call-or-fold decisions, use the pot odds calculator.
The poker math behind the chart
Every number here comes from counting, with three tools:
- Combinations. The number of ways to choose k cards from n is n! ÷ (k! (n − k)!). Two cards from 52: 1,326. Three flop cards from the 50 you can’t see: 19,600. Five board cards once two hands are known: 1,712,304.
- Probability = favorable ÷ total. Pocket aces: 6 ways to pick two of the four aces, so 6 ÷ 1,326 = 0.45%.
- “Odds against” = misses ÷ hits. A draw that hits 35% misses 65%, so it’s 65 ÷ 35 ≈ 1.9 to 1 against. Compare that with the pot odds you’re offered to decide whether to call.
For “at least one” questions, count the opposite. A pocket pair flops a set unless all three flop cards miss your two remaining cards: 48 × 47 × 46 ÷ (50 × 49 × 48) = 88.2% miss, so 11.8% hit. The matchups and the final-hand counts are too big to do by hand, so we let the game’s own evaluator — the code that settles real showdowns on FizzPoker — check every board.
Odds are the long run. At the table, what counts is whether your decisions match the price. Signed-in players on FizzPoker get a post-game Fizz Score that labels each graded decision acceptable, inaccuracy, mistake or blunder — an advisory second opinion on the spots where the math was close.
Questions people ask
What are the odds of AA vs KK?
All-in before the flop, pocket aces beat pocket kings about 82% of the time. Averaged over every suit combination, aces win 81.7%, kings win 17.8% and 0.5% of boards split; the exact figure moves between 81.1% and 82.4% depending on how many suits the hands share.
What are the odds of being dealt pocket aces?
Exactly 1 in 221 (0.45%). There are 6 ways to make a pair of aces out of 1,326 possible two-card hands. The same odds apply to any one specific pair, and you’ll be dealt some pocket pair 1 in 17 hands.
What are the odds of getting a royal flush?
In Texas Hold’em, using your two cards plus five on the board, a royal flush shows up 1 in 30,940 times (4,324 of all 133,784,560 seven-card hands). In a five-card deal it is 1 in 649,740 — just 4 of the 2,598,960 possible hands.
What are the odds of flopping a set?
With a pocket pair you flop a set or better 11.8% of the time — 1 in 8.5. Two of the 50 unseen cards match your pair, and 2,304 of the 19,600 possible flops contain at least one of them.
What does a coin flip mean in poker?
A coin flip is an all-in where both hands are close to 50%, usually a pair against two higher cards. Queens against ace-king suited, for example, is 53.8% to 46.2% in pot share.
How do you calculate poker odds?
Count the ways something can happen and divide by all the ways the cards can fall. Two-card hands: 1,326. Flops for a known hand: 19,600. For a draw, count your outs: with 9 outs on the flop you miss both cards 38/47 × 37/46 = 65.0% of the time, so you hit 35.0%.