After the flop, 47 cards are unseen. On the turn, 46 remain. Turn in the table is the chance the next card is an out. River is the chance from the turn, one card left. Turn and river together is the chance of hitting on either card when you are all in on the flop.
One card is outs ÷ 47, or outs ÷ 46 from the turn. Two cards is one minus the chance of missing both:
1 − ((47 − outs) ÷ 47) × ((46 − outs) ÷ 46)
| Outs | Turn | River | Turn + river | Rule of 4 | Error |
|---|---|---|---|---|---|
| 1 | 2.1% | 2.2% | 4.3% | 4% | −0.3 |
| 2 | 4.3% | 4.3% | 8.4% | 8% | −0.4 |
| 3 | 6.4% | 6.5% | 12.5% | 12% | −0.5 |
| 4 | 8.5% | 8.7% | 16.5% | 16% | −0.5 |
| 5 | 10.6% | 10.9% | 20.4% | 20% | −0.4 |
| 6 | 12.8% | 13.0% | 24.1% | 24% | −0.1 |
| 7 | 14.9% | 15.2% | 27.8% | 28% | +0.2 |
| 8 | 17.0% | 17.4% | 31.5% | 32% | +0.5 |
| 9 | 19.1% | 19.6% | 35.0% | 36% | +1.0 |
| 10 | 21.3% | 21.7% | 38.4% | 40% | +1.6 |
| 11 | 23.4% | 23.9% | 41.7% | 44% | +2.3 |
| 12 | 25.5% | 26.1% | 45.0% | 48% | +3.0 |
| 13 | 27.7% | 28.3% | 48.1% | 52% | +3.9 |
| 14 | 29.8% | 30.4% | 51.2% | 56% | +4.8 |
| 15 | 31.9% | 32.6% | 54.1% | 60% | +5.9 |
| 16 | 34.0% | 34.8% | 57.0% | 64% | +7.0 |
| 17 | 36.2% | 37.0% | 59.8% | 68% | +8.2 |
| 18 | 38.3% | 39.1% | 62.4% | 72% | +9.6 |
| 19 | 40.4% | 41.3% | 65.0% | 76% | +11.0 |
| 20 | 42.6% | 43.5% | 67.5% | 80% | +12.5 |
Multiply outs by 2 for one card and by 4 for two. The ×2 version stays close on every row, a little low. The ×4 version is useful through about 8 outs, then it overshoots: 3 points at 12 outs, 5.9 at 15, and 12.5 at 20, where it claims 80% and the count is 67.5%. A common patch above 8 outs is ×4, then subtract (outs − 8). For 15 outs that patch says 53, against a true 54.1%.
Outs to equity: exact chance versus quick rules
These counts are for study and post-session review. Where a row comes from a simulation, the caption names how many deals were run. Where a stack or a pot is made up, the caption says so. None of these figures is an instruction for a live pot.