A nine-out draw has a 34.9676% chance of hitting at least one of those outs from the flop to the river, if 47 cards are unseen and both cards are dealt. This is the chance of hitting a fixed set of cards, not necessarily winning. Use the calculator for your own out count and street.
Exact poker outs calculator
Chance of hitting at least one out
Standard 52-card deck; your two hole cards and the current board are known. No other cards are known. Outs remain the same fixed set; future bets, opponent redraws and runner-runner paths are not modelled.
Exact outs chart
| Outs | Next card from flop | River from turn | Two cards from flop |
|---|---|---|---|
| 1 | 2.1277% | 2.1739% | 4.2553% |
| 2 | 4.2553% | 4.3478% | 8.4181% |
| 4 | 8.5106% | 8.6957% | 16.4662% |
| 8 | 17.0213% | 17.3913% | 31.4524% |
| 9 | 19.1489% | 19.5652% | 34.9676% |
| 12 | 25.5319% | 26.0870% | 44.9584% |
| 15 | 31.9149% | 32.6087% | 54.1166% |
How the exact calculation works
For one card, divide the number of outs by the unseen cards. On the turn, nine outs means 9 / 46 = 19.5652%. For two cards, calculate the chance of missing twice and subtract it from one. With nine outs on the flop: 1 − (38 / 47 × 37 / 46) = 34.9676%.
More generally, with N unseen cards, O fixed outs and D cards to come, the probability is 1 − C(N − O, D) / C(N, D). C means combinations: choose cards without regard to order. We draw without replacement, so the unseen count decreases after the first card.
Counting outs without double-counting
If you hold A♥ Q♥ on 9♥ 6♥ 2♣, there are nine hearts left unseen: 13 hearts minus the four you can see. They complete a flush, but they do not guarantee you win after further cards. If an out completes two draws at once, count that card once.
For example, 8♥ 7♥ on 6♥ 5♣ K♥ has a flush draw and an open-ended straight draw. The nine remaining hearts and eight cards of rank 4 or 9 overlap at 4♥ and 9♥. That is 9 + 8 − 2 = 15 distinct cards, not 17. Some cards can still leave you behind a stronger hand; this is not an equity calculation.
Why the rule of 2 and 4 is approximate
Multiplying outs by two for one card or four for two cards is a shortcut. Nine outs over two cards gives 36% by the shortcut but about 34.97% exactly. Fifteen outs gives 60% by the shortcut but about 54.12% exactly. The error grows for larger draws.
Backdoor draws need a different treatment. Three hearts among your five known cards require two more hearts, so they are not a fixed nine-out draw. The calculator answers “hit at least one card in this fixed set”, not “complete any possible hand”.
Hitting a draw is different from making a profitable call
You may improve and still lose, or win without improving. If you must pay another bet on the turn, you cannot automatically compare two-card odds with today's call price. Use the pot odds calculator and future-betting explanation for that decision. For a one-out example, see set-to-quads odds.
Method: exact counting of draws without replacement. The combination-counting approach is explained in MIT's probability class solutions. We independently calculate the figures above and test the calculator against fixed examples. Method and examples checked 30 October 2026.