Poker Equity & OddsPoker hand odds by the river, by starting hand
Short answer
With your two cards and the five on the board, the best hand at the river is a straight 4.6% of the time, a flush 3.0%, a full house 2.6% and four of a kind 0.17%. A royal flush comes one time in 30,940. Your starting hand moves these a lot: a pocket pair ends with a full house or better 9.4% of the time, AK suited with a flush or better 8.9%, and 76 suited with a straight or better 17.5%. All 133,784,560 seven-card hands are counted with the Poker Equity & Odds engine's hand evaluator.
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Every seven-card hand
| Best hand by the river | Hands | Chance | One in |
|---|---|---|---|
| Straight flush, royal included | 41,584 | 0.03% | 3,217 |
| Four of a kind | 224,848 | 0.17% | 595 |
| Full house | 3,473,184 | 2.6% | 38.5 |
| Flush | 4,047,644 | 3.0% | 33.1 |
| Straight | 6,180,020 | 4.6% | 21.6 |
| Three of a kind | 6,461,620 | 4.8% | 20.7 |
| Two pair | 31,433,400 | 23.5% | 4.3 |
| One pair | 58,627,800 | 43.8% | 2.3 |
| High card | 23,294,460 | 17.4% | 5.7 |
| Royal flush | 4,324 | 0.0032% | 30,940 |
One pair is the most common final hand, and two pair is more common than high card. That surprises people: with seven cards, ending with nothing at all is less likely than ending with two pair. The board is shared, so the same pairs help everyone, and that is why one pair so often loses at showdown.
By starting hand
| Best hand | A pocket pair (77) | AK suited | AK offsuit | 76 suited | J8 offsuit |
|---|---|---|---|---|---|
| Straight flush, royal included | 0.02% | 0.05% | 0.01% | 0.20% | 0.02% |
| Four of a kind | 0.84% | 0.13% | 0.13% | 0.13% | 0.13% |
| Full house | 8.5% | 2.2% | 2.2% | 2.2% | 2.2% |
| Flush | 1.9% | 6.5% | 2.0% | 6.4% | 2.0% |
| Straight | 2.3% | 3.1% | 3.3% | 8.5% | 6.1% |
| Three of a kind | 11.7% | 4.3% | 4.4% | 4.3% | 4.4% |
| Two pair | 39.5% | 22.1% | 22.7% | 21.8% | 22.5% |
| One pair | 35.2% | 43.3% | 45.6% | 40.6% | 44.3% |
| High card | never | 18.2% | 19.7% | 15.9% | 18.4% |
| Straight or better | 13.7% | 12.0% | 7.6% | 17.5% | 10.4% |
| Flush or better | 11.4% | 8.9% | 4.3% | 8.9% | 4.3% |
| Full house or better | 9.4% | 2.4% | 2.4% | 2.5% | 2.4% |
The exact cards counted, left to right: 7♠ 7♥, A♥ K♥, A♠ K♦, 7♥ 6♥, J♠ 8♦. The pair makes a full house 8.5% of the time, close to four times an unpaired hand. Suited cards roughly triple the flush: 6.5% for AK suited against 2.0% offsuit. And connected cards make straights: 76 suited ends with a straight 8.5% of the time, AK offsuit 3.3%. Only one straight, ten to ace, uses both an ace and a king. Four different straights use both a seven and a six.
Royal flush odds
I've been waiting for this one my whole life.
Over all seven-card hands a royal flush is 4,324 of 133,784,560, one in 30,940, if every hand went to the river. Most hands fold before then, so at a real table you see it far less. Holding AK suited, 1,084 of the 2,118,760 boards give you one, about one in 1,955: the queen, jack and ten of your suit, plus the few boards that hold a whole royal flush in another suit. AK offsuit has 94 such boards, and 76 suited only the 4 boards that are a royal flush by themselves.
Your hand or the board's
These tables count the best hand out of all seven cards, so a straight lying on the board counts as a straight for you, the same as for everyone else at the table. That is what "how often do I end with a flush" usually means, but it is not the same as "how often do I make a flush with my cards". The flopping a set guide counts flushes in your own suit, and the outs chart answers the question once the flop is out and you know what you need.
Once the flop is down
Outs & Odds lists the cards that improve you and the exact chance they arrive. After a calculator run, the Distribution sheet shows how often each hand ends as a pair, two pair, a flush and so on (the full list is Premium).
Questions
What are the odds of a royal flush in Texas Hold'em?
One in 30,940 for any seven cards, 0.0032%: 4,324 of the 133,784,560 seven-card hands. Holding AK suited it is one board in about 1,955.
What are the odds of getting a full house by the river?
2.6% for any seven cards, one hand in 38.5. With a pocket pair it is 8.5%, against 2.2% for AK.
How often does a pocket pair make a full house or better?
9.4% by the river, counting quads and straight flushes. An unpaired hand like AK gets there 2.4% of the time.
What are the odds of making a flush with suited cards?
AK suited ends the hand with a flush 6.5% of the time, against 2.0% for AK offsuit. That counts only boards where the flush is the best hand; a full house on the same board counts as the full house.
Where the numbers come from. Every figure on this page comes from the app's own engine, the code that runs on your phone. Outs come from the Outs & Odds tool, hit chances are exact counts, and equities count every runout with no sampling. Engine build 482550e8. More worked numbers: flush draw odds and the pot odds cheat sheet.
