What an out is
An out is a card still in the deck that would improve your hand to one you expect to be best. If you hold two hearts and the flop shows two more hearts, nine hearts remain among the cards you have not seen, so you have nine outs to a flush.
Counting outs is the first step in judging a draw. You need the number before you can estimate how often the draw arrives, and you need that estimate before you can compare it with the price you are being asked to pay.
Counting outs step by step
Start with what you are trying to make, then count the unseen cards that make it.
- Flush draw: 13 cards of a suit, minus the 4 you can see, leaves 9 outs.
- Open-ended straight draw: four consecutive cards with both ends open gives 8 outs (four cards of each of two ranks).
- Gutshot straight draw: one missing rank in the middle gives 4 outs.
- Two overcards: if you hold two cards higher than the board and pairing either would likely be best, that is 6 outs.
- Pocket pair to a set: two cards of your rank remain, so 2 outs.
When draws overlap, add them but do not count a card twice. A flush draw combined with an open-ended straight draw is 9 + 8 = 17 on paper, but two cards complete both draws and so appear in each count. Removing the double count leaves 15 outs.
Why the unseen cards number is 47 or 46
In Hold’em you see two hole cards and three flop cards, so 5 of the 52 cards are known, leaving 47 unseen. On the turn you see one more card, leaving 46. Treating every unseen card as equally likely is the same idea as a sample space of equally likely outcomes, and it is what makes the arithmetic possible.
The chance of hitting on one card is simply outs divided by unseen cards. Nine outs on the turn is 9/47, about 19.1%. On the river with one card still to come, 9/46 is about 19.6%.
The rule of four and two
Doing division at the table is slow, so players use a shortcut:
- On the flop, with two cards still to come, multiply your outs by 4.
- On the turn, with one card to come, multiply your outs by 2.
The result is an approximate percentage chance of hitting by the river.
For a flush draw on the flop, 9 outs times 4 gives 36%. The exact figure is the chance of at least one hit in two cards: 1 minus (38/47 times 37/46), which is about 35%. The shortcut is off by about one point, which is fine for a decision made in seconds.
On the turn, 9 outs times 2 gives 18%, against an exact 19.6%. Slightly low, but close.
Checking the shortcut against exact figures
| Draw | Outs | Rule of four (flop to river) | Exact, two cards |
|---|---|---|---|
| Gutshot | 4 | 16% | about 16.5% |
| Two overcards | 6 | 24% | about 24% |
| Open-ended straight draw | 8 | 32% | about 31.5% |
| Flush draw | 9 | 36% | about 35% |
| Flush draw plus open-ended draw | 15 | 60% | about 54% |
The rule works well for small and medium draws. It overstates large ones, because the true calculation is the probability of at least one success, and the chances of hitting on each card overlap more as outs grow. A common adjustment for draws of more than eight outs is to subtract the number of outs above eight from the product. With 15 outs, 60 minus 7 gives 53, closer to the exact 54%.
Using the number once you have it
An equity estimate is only useful alongside a price. If your chance of completing the draw is about 35% by the river, a call is more justifiable when the bet you face is small relative to the pot, and less so when it is large. That comparison is the subject of how pot odds work, and it also depends on whether you will see both remaining cards or be forced to put in more money before the river.
The rule of four assumes you see both cards. If an opponent bets again on the turn, you are really paying for one card at a time and the rule of two is the better guide for that decision.
When outs are not clean
Counting outs assumes each one gives you the best hand. Several things can undermine that:
- Shared draws: if the board has three of a suit and you have the flush draw, a card that completes your flush might also give an opponent a full house or a higher flush.
- Paired boards: a card that makes your straight can pair the board and leave you behind someone with a full house.
- Hidden cards: if you can reasonably infer an opponent holds one of your outs, the true number is lower. Updating a count as information arrives is an application of conditional probability, though at the table it is usually just a rough discount.
Many players reduce a draw by one or two outs when they suspect some of them are tainted. There is no precise rule, so treat the discounted number as a judgment rather than a fact.
A short practice routine
Away from the table, deal yourself two cards and a flop, name your draws, and count the outs before checking. Then multiply and compare with the exact figure. After a few dozen repetitions the common numbers (4, 8, 9, 12, 15) become automatic.
Remember that an estimate of a percentage chance describes the long run. A 35% draw misses about two times in three, and in short-run results that can happen many times in a row without anything being wrong with your maths.