progressOuts to equity: the exact table
The rule of 2 and 4 is a good shortcut up to about 8 outs and drifts after that.
An out is an unseen card that improves your hand to a likely winner. The probability of hitting is a simple count of unseen cards, so we can give the exact numbers.
How it is computed
- On the flop you see 5 cards (2 of yours, 3 on the board), so 47 are unseen. On the turn, 46 are unseen.
- Chance to hit on the next card = outs / unseen cards.
- Chance to hit by the river from the flop = 1 − C(47 − outs, 2) / C(47, 2), which is the chance of not missing twice in a row.
The table
| Outs | Next card from the flop (47 unseen) | By the river from the flop | Next card from the turn (46 unseen) | Rule of 4 | Rule of 2 |
|---|---|---|---|---|---|
| 1 | 2.1% | 4.3% | 2.2% | 4% | 2% |
| 2 | 4.3% | 8.4% | 4.3% | 8% | 4% |
| 3 | 6.4% | 12.5% | 6.5% | 12% | 6% |
| 4 | 8.5% | 16.5% | 8.7% | 16% | 8% |
| 5 | 10.6% | 20.4% | 10.9% | 20% | 10% |
| 6 | 12.8% | 24.1% | 13% | 24% | 12% |
| 7 | 14.9% | 27.8% | 15.2% | 28% | 14% |
| 8 | 17% | 31.5% | 17.4% | 32% | 16% |
| 9 | 19.1% | 35% | 19.6% | 36% | 18% |
| 10 | 21.3% | 38.4% | 21.7% | 40% | 20% |
| 11 | 23.4% | 41.7% | 23.9% | 44% | 22% |
| 12 | 25.5% | 45% | 26.1% | 48% | 24% |
| 13 | 27.7% | 48.1% | 28.3% | 52% | 26% |
| 14 | 29.8% | 51.2% | 30.4% | 56% | 28% |
| 15 | 31.9% | 54.1% | 32.6% | 60% | 30% |
The rule of 4 (multiply outs by 4 on the flop) matches well at low numbers and overshoots at high numbers: with 15 outs it says 60%, the exact figure is 54.1%. Use the rule of 2 for one card to come and the rule of 4 for two, but prefer the exact table when the decision is close.
Common draws
| Draw | Outs | By the river from the flop |
|---|---|---|
| Flush draw | 9 | 35% |
| Open-ended straight draw | 8 | 31.5% |
| Gutshot | 4 | 16.5% |
| Two overcards | 6 | 24.1% |
| Flush draw + open-ended (15 outs, if all clean) | 15 | 54.1% |
These numbers assume every out is clean: that the card gives you the best hand. Outs that also complete a draw for your opponent, or that make a second-best hand, should be discounted.
Use the outs calculator for any number of outs, and compare the result with the equity you need from the pot odds cheat sheet.
Free 7-day ICM course by e-mail
One short lesson a day, each with a worked example in exact numbers: chips vs. money, the bubble factor, who feels the pressure, payout structures, satellites. No account needed.
Related guides
Questions
What is the chance of hitting a flush draw by the river?
With 9 outs and 47 unseen cards it is 35% from the flop, and 19.6% on the turn.
Is the rule of 4 accurate?
It is close up to about 8 outs and overestimates the chance with more outs.
Do outs count if the opponent can improve too?
Only if they give you the best hand. Subtract outs that make you second best.
Share this page
progressGTO guides use our own solution book (v13, 8-max tournaments with ante, chip EV): an approximation of equilibrium with a modelled postflop, not an exact solution. Numbers are computed from the book and from the exact ICM model.
progressGTOGuidesGlossaryPreflop rangesDaily spotICM calculatorPot odds calculatorPush/fold chartsOpen the appPrivacyTerms