Outs and the rule of 2 and 4
An out is a card still in the deck that would give you the best hand. Count your outs, and the chance of hitting one follows from simple counting. The rule of 2 and 4 is a quick way to do that counting in your head; here is how close it gets.
Counting outs
- Flush draw: 9 outs. Four cards of a suit between your hand and the board leave 9 of the 13 in the deck.
- Open-ended straight draw: 8 outs. Four cards in a row, such as 7-8-9-10, complete with any of four cards at either end.
- Gutshot straight draw: 4 outs. Only one rank fills the gap, as with 7-8-10-J needing a 9.
- Flush draw and open-ended straight draw: 15 outs, not 17. Two of the straight cards are also flush cards; count them once.
- Two overcards: 6 outs to pair one of them, if a pair of either would be enough to win.
- Pocket pair to a set: 2 outs. Only the two remaining cards of your rank.
Count only cards that make you the winner. If a flush card also pairs the board and gives someone a full house, it is a "dirty" out: take it off your count.
The exact chance
After the flop 47 cards are unseen: 52 minus your two and the three on the board. Cards in other players' hands and the burned cards are unseen too, so they count as unknown, not as dead. With one card to come your chance is outs divided by 47 on the turn, or by 46 on the river. With both cards to come it is one minus the chance that both miss.
| Outs | Turn (one card) | River (one card) | Turn or river (two cards) | Odds against, two cards |
|---|---|---|---|---|
| 1 | 2.1% | 2.2% | 4.3% | 22.5 to 1 |
| 2 | 4.3% | 4.3% | 8.4% | 10.9 to 1 |
| 3 | 6.4% | 6.5% | 12.5% | 7.0 to 1 |
| 4 | 8.5% | 8.7% | 16.5% | 5.1 to 1 |
| 5 | 10.6% | 10.9% | 20.4% | 3.9 to 1 |
| 6 | 12.8% | 13.0% | 24.1% | 3.1 to 1 |
| 7 | 14.9% | 15.2% | 27.8% | 2.6 to 1 |
| 8 | 17.0% | 17.4% | 31.5% | 2.2 to 1 |
| 9 | 19.1% | 19.6% | 35.0% | 1.9 to 1 |
| 10 | 21.3% | 21.7% | 38.4% | 1.6 to 1 |
| 11 | 23.4% | 23.9% | 41.7% | 1.4 to 1 |
| 12 | 25.5% | 26.1% | 45.0% | 1.2 to 1 |
| 13 | 27.7% | 28.3% | 48.1% | 1.1 to 1 |
| 14 | 29.8% | 30.4% | 51.2% | 1.0 to 1 |
| 15 | 31.9% | 32.6% | 54.1% | 0.8 to 1 |
| 16 | 34.0% | 34.8% | 57.0% | 0.8 to 1 |
| 17 | 36.2% | 37.0% | 59.8% | 0.7 to 1 |
| 18 | 38.3% | 39.1% | 62.4% | 0.6 to 1 |
| 19 | 40.4% | 41.3% | 65.0% | 0.5 to 1 |
| 20 | 42.6% | 43.5% | 67.5% | 0.5 to 1 |
| 21 | 44.7% | 45.7% | 69.9% | 0.4 to 1 |
The rule of 2 and 4
The shortcut: with one card to come, multiply your outs by 2; with two cards to come, multiply by 4. It works because each unseen card is a little over 2% of the deck. Here it is against the exact figures:
| Outs | Rule of 2 | Exact, one card | Rule of 4 | Exact, two cards | Rule of 4 minus exact, in points |
|---|---|---|---|---|---|
| 1 | 2% | 2.1% | 4% | 4.3% | −0.3 |
| 2 | 4% | 4.3% | 8% | 8.4% | −0.4 |
| 3 | 6% | 6.4% | 12% | 12.5% | −0.5 |
| 4 | 8% | 8.5% | 16% | 16.5% | −0.5 |
| 5 | 10% | 10.6% | 20% | 20.4% | −0.4 |
| 6 | 12% | 12.8% | 24% | 24.1% | −0.1 |
| 7 | 14% | 14.9% | 28% | 27.8% | +0.2 |
| 8 | 16% | 17.0% | 32% | 31.5% | +0.5 |
| 9 | 18% | 19.1% | 36% | 35.0% | +1.0 |
| 10 | 20% | 21.3% | 40% | 38.4% | +1.6 |
| 11 | 22% | 23.4% | 44% | 41.7% | +2.3 |
| 12 | 24% | 25.5% | 48% | 45.0% | +3.0 |
| 13 | 26% | 27.7% | 52% | 48.1% | +3.9 |
| 14 | 28% | 29.8% | 56% | 51.2% | +4.8 |
| 15 | 30% | 31.9% | 60% | 54.1% | +5.9 |
| 16 | 32% | 34.0% | 64% | 57.0% | +7.0 |
| 17 | 34% | 36.2% | 68% | 59.8% | +8.2 |
| 18 | 36% | 38.3% | 72% | 62.4% | +9.6 |
| 19 | 38% | 40.4% | 76% | 65.0% | +11.0 |
| 20 | 40% | 42.6% | 80% | 67.5% | +12.5 |
| 21 | 42% | 44.7% | 84% | 69.9% | +14.1 |
With one card to come the rule of 2 always understates your chance a little: by less than a point up to 7 outs, by about 2 points with 15. With two cards the rule of 4 is close for small draws and overstates big ones from 7 outs up, because the real chance grows more slowly than a straight line: with many outs, both cards are often outs, and you can only hit once. With 15 outs the rule says 60%, the exact chance is 54.1%. A common fix is "multiply by 4, then subtract the number of outs above 8".
A draw that is easy to get wrong: a set
With a set on a flop of three different ranks you have 7 outs to improve to a full house or four of a kind on the turn: the last card of your rank, and three cards to pair each of the other two board cards. It is tempting to use the two-card figure for 7 outs, 27.8%. The real figure is higher, 33.4%, because after a blank turn you have 10 outs on the river: the three cards that pair the turn card also give you a full house. We checked it by dealing every turn and river.
Putting it to use
Your chance to hit only matters against the price of continuing. Use the outs and pot odds calculator to compare them, and read pot odds explained for how the price is worked out.