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40
1 to 20 outs on 2 streets
- Flop, by the riverfrom 1 out to 20 outs4.26% to 67.53%
- Nine outs on the flop34.97%
- Nine outs on the turn19.57%
The flop: two cards to come
From the flop you have 47 unseen cards and two to come, so the chance by the river is higher than the chance on the next card alone. Pick a count to open its page.
| Outs | Chance by the river | Next card | Rule of 4 estimate | Rule error |
|---|---|---|---|---|
| 1 | 4.26% | 2.13% | 4% | -0.26 points |
| 2 | 8.42% | 4.26% | 8% | -0.42 points |
| 3 | 12.49% | 6.38% | 12% | -0.49 points |
| 4 | 16.47% | 8.51% | 16% | -0.47 points |
| 5 | 20.35% | 10.64% | 20% | -0.35 points |
| 6 | 24.14% | 12.77% | 24% | -0.14 points |
| 7 | 27.84% | 14.89% | 28% | +0.16 points |
| 8 | 31.45% | 17.02% | 32% | +0.55 points |
| 9 | 34.97% | 19.15% | 36% | +1.03 points |
| 10 | 38.39% | 21.28% | 40% | +1.61 points |
| 11 | 41.72% | 23.40% | 44% | +2.28 points |
| 12 | 44.96% | 25.53% | 48% | +3.04 points |
| 13 | 48.10% | 27.66% | 52% | +3.90 points |
| 14 | 51.16% | 29.79% | 56% | +4.84 points |
| 15 | 54.12% | 31.91% | 60% | +5.88 points |
| 16 | 56.98% | 34.04% | 64% | +7.02 points |
| 17 | 59.76% | 36.17% | 68% | +8.24 points |
| 18 | 62.44% | 38.30% | 72% | +9.56 points |
| 19 | 65.03% | 40.43% | 76% | +10.97 points |
| 20 | 67.53% | 42.55% | 80% | +12.47 points |
The turn: one card to come
From the turn you have 46 unseen cards and one to come, so the chance on the river is the same as the chance on the next card. Pick a count to open its page.
| Outs | Chance on the river | Next card | Rule of 2 estimate | Rule error |
|---|---|---|---|---|
| 1 | 2.17% | 2.17% | 2% | -0.17 points |
| 2 | 4.35% | 4.35% | 4% | -0.35 points |
| 3 | 6.52% | 6.52% | 6% | -0.52 points |
| 4 | 8.70% | 8.70% | 8% | -0.70 points |
| 5 | 10.87% | 10.87% | 10% | -0.87 points |
| 6 | 13.04% | 13.04% | 12% | -1.04 points |
| 7 | 15.22% | 15.22% | 14% | -1.22 points |
| 8 | 17.39% | 17.39% | 16% | -1.39 points |
| 9 | 19.57% | 19.57% | 18% | -1.57 points |
| 10 | 21.74% | 21.74% | 20% | -1.74 points |
| 11 | 23.91% | 23.91% | 22% | -1.91 points |
| 12 | 26.09% | 26.09% | 24% | -2.09 points |
| 13 | 28.26% | 28.26% | 26% | -2.26 points |
| 14 | 30.43% | 30.43% | 28% | -2.43 points |
| 15 | 32.61% | 32.61% | 30% | -2.61 points |
| 16 | 34.78% | 34.78% | 32% | -2.78 points |
| 17 | 36.96% | 36.96% | 34% | -2.96 points |
| 18 | 39.13% | 39.13% | 36% | -3.13 points |
| 19 | 41.30% | 41.30% | 38% | -3.30 points |
| 20 | 43.48% | 43.48% | 40% | -3.48 points |
How to use the numbers
Use the street to pick the table. Two cards to come give a bigger chance than one, as 9 outs show: 34.97% on the flop against 19.57% on the turn.
- Outs calculator: Enter any count, street and shared outs.
- Pot odds by bet size: The equity a call needs for each of the twelve bet sizes.
- Call or fold by count and bet: The answer for a count of outs against a bet size.
- Hand equity: Your chance to win against a named hand.
How this is computed
From the flop the chance to hit by the river is 1 - C(u - k, 2) / C(u, 2) with u = 47, and from the turn it is k / 46. The next-card chance is k divided by the unseen cards. Each rule figure is 4k on the flop or 2k on the turn, with its error in percentage points beside it.
Every unseen card is counted as equally likely and no card is removed for an opponent, so the tables give the chance to hit your outs, not your equity against a particular hand. All figures are exact, with no simulation, and rounded only when they are shown.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
How do I turn a count of outs into a chance?
Use the exact tables above, or the rule of 4 from the flop and the rule of 2 from the turn. With 9 outs the exact chance is 34.97% by the river from the flop and 19.57% on the river from the turn, against rule figures of 36% and 18%.
Which draws have a well-known count of outs?
Common counts are these: a pocket pair that wants a set has 2 outs, one overcard to top pair has 3 outs, a gutshot straight draw has 4 outs, two overcards have 6 outs, an open-ended straight draw has 8 outs, a flush draw has 9 outs, a flush draw with a gutshot has 12 outs, and a flush draw with an open-ended straight draw has 15 outs. Any other count comes from combining draws and removing cards that count twice, so no single draw is named for it.
When does the rule of 4 stop working well?
It stays within 2 points up to 10 outs, then runs high as the count grows. At 20 outs it says 80% against an exact 67.53%, an error of +12.47 points. The adjusted rule gives 68%, an error of +0.47 points.
What do I compare my chance with?
Compare it with the equity a call needs. A half-pot bet needs 25.00%, so 7 outs from the flop and 12 from the turn are the fewest that clear it by the river.
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