Outs, the rule of 4 and 2, and pot odds
After the flop 47 cards are unseen, after the turn 46. With o outs, the turn hits o/47 of the time, and the turn or river hits 1 − (47−o)(46−o)/(47×46). Below, that formula is applied to 1–20 outs and set against the mental rule of 4 and 2.
A gutshot (4 outs) gets there 16.5% of the time; a flush draw plus open-ender (15 outs) 54.1%, better than even. The rule of 4 is close up to 8 outs and runs 3 points or more too high from 12 outs. Whether to call comes from comparing with the required-equity table below.
Outs and odds for common draws
| Draw | Example | Outs | Turn | By the river | Odds against |
|---|---|---|---|---|---|
| Pocket pair to a set | 77 on A-K-2 | 2 | 4.26% | 8.42% | 10.9 to 1 |
| Gutshot straight draw | 98 on T-6-2 (needs a 7) | 4 | 8.51% | 16.5% | 5.1 to 1 |
| One pair to two pair or trips | AJ on A-8-3 | 5 | 10.6% | 20.4% | 3.9 to 1 |
| Two overcards to a pair | AK on 9-6-2 | 6 | 12.8% | 24.1% | 3.1 to 1 |
| Set to a full house or quads | 77 on 7-K-2 | 7 | 14.9% | 27.8% | 2.6 to 1 |
| Open-ended straight draw | 98 on T-7-2 | 8 | 17.0% | 31.5% | 2.2 to 1 |
| Flush draw | A♠5♠ on K♠-8♠-2♦ | 9 | 19.1% | 35.0% | 1.9 to 1 |
| Flush draw plus gutshot | 9♥8♥ on J♥-7♥-2♣ | 12 | 25.5% | 45.0% | 1.2 to 1 |
| Flush draw plus open-ender | 9♥8♥ on T♥-7♥-2♣ | 15 | 31.9% | 54.1% | 0.8 to 1 |
Exact odds against the rule of 4 and 2
Gap = rule minus exact. Positive means the rule overestimates.
| Outs | By river (exact) | ×4 | Gap | Adjusted | Next card (exact) | ×2 | Gap |
|---|---|---|---|---|---|---|---|
| 1 | 4.26% | 4% | -0.3 | 4% | 2.13% | 2% | -0.1 |
| 2 | 8.42% | 8% | -0.4 | 8% | 4.26% | 4% | -0.3 |
| 3 | 12.5% | 12% | -0.5 | 12% | 6.38% | 6% | -0.4 |
| 4 | 16.5% | 16% | -0.5 | 16% | 8.51% | 8% | -0.5 |
| 5 | 20.4% | 20% | -0.4 | 20% | 10.6% | 10% | -0.6 |
| 6 | 24.1% | 24% | -0.1 | 24% | 12.8% | 12% | -0.8 |
| 7 | 27.8% | 28% | +0.2 | 28% | 14.9% | 14% | -0.9 |
| 8 | 31.5% | 32% | +0.5 | 32% | 17.0% | 16% | -1.0 |
| 9 | 35.0% | 36% | +1.0 | 35% | 19.1% | 18% | -1.1 |
| 10 | 38.4% | 40% | +1.6 | 38% | 21.3% | 20% | -1.3 |
| 11 | 41.7% | 44% | +2.3 | 41% | 23.4% | 22% | -1.4 |
| 12 | 45.0% | 48% | +3.0 | 44% | 25.5% | 24% | -1.5 |
| 13 | 48.1% | 52% | +3.9 | 47% | 27.7% | 26% | -1.7 |
| 14 | 51.2% | 56% | +4.8 | 50% | 29.8% | 28% | -1.8 |
| 15 | 54.1% | 60% | +5.9 | 53% | 31.9% | 30% | -1.9 |
| 16 | 57.0% | 64% | +7.0 | 56% | 34.0% | 32% | -2.0 |
| 17 | 59.8% | 68% | +8.2 | 59% | 36.2% | 34% | -2.2 |
| 18 | 62.4% | 72% | +9.6 | 62% | 38.3% | 36% | -2.3 |
| 19 | 65.0% | 76% | +11.0 | 65% | 40.4% | 38% | -2.4 |
| 20 | 67.5% | 80% | +12.5 | 68% | 42.6% | 40% | -2.6 |
Equity needed to call each bet size
Required equity = call ÷ (pot + bet + call). Future winnings (implied odds) are not included.
| Bet | Equity needed | Outs that cover it (to river) | Outs that cover it (one card) |
|---|---|---|---|
| 1/4 pot | 16.7% | 5+ | 8+ |
| 1/3 pot | 20.0% | 5+ | 10+ |
| 1/2 pot | 25.0% | 7+ | 12+ |
| 2/3 pot | 28.6% | 8+ | 14+ |
| 3/4 pot | 30.0% | 8+ | 15+ |
| Pot | 33.3% | 9+ | 16+ |
| 1.5× pot | 37.5% | 10+ | 18+ |
| 2× pot | 40.0% | 11+ | 19+ |
The "to river" column assumes no further bet on the turn (an all-in, for example). If you will have to pay again on the turn, use the one-card column.
FAQ
What are outs?
The cards still in the deck that would give you the winning hand. A flush draw has 9, an open-ended straight draw 8. Count them as if no other player's cards block any.
What is the rule of 4 and 2?
A mental shortcut: on the flop multiply your outs by 4 to estimate the chance of hitting by the river; on the turn multiply by 2 for the river alone. With 9 outs the rule says 36%; the exact figure is 35.0%. With many outs the rule of 4 overshoots — by 3 points or more from 12 outs — and subtracting the outs above 8 (4 × outs − (outs − 8)) brings it back.
How often does a flush draw get there?
35.0% from the flop to the river (1.9 to 1 against), 19.1% on the turn alone and 19.6% on the river after a blank turn.
How do I work out the equity I need to call?
Divide the call by the total pot after you call (pot + bet + call). A pot-sized bet needs 33.3%, a half-pot bet 25.0% and a third-pot bet 20.0%. If your chance of winning is higher, the call makes money.