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Outs, and the rule of 2 and 4

An out is a card that turns your losing hand into the winning one. Count them, multiply, and you have your chance of getting there — close enough to decide at the table, and this page shows exactly how close.

Counting outs

Look at the cards you cannot see — the deck and everyone else's hands are all the same to you — and count the ones that would win. Holding two hearts on a flop with two more, any of the nine remaining hearts makes your flush: nine outs. Holding 7-8 on a 6-9-2 board, any five or any ten makes a straight: four of each, eight outs.

Draw Outs
Gutshot straight draw (one rank fills it) 4
One pair, hoping for two pair or trips 5
Two overcards, hoping to pair either 6
Open-ended straight draw (either end fills it) 8
Flush draw 9
Flush draw and a gutshot 12
Flush draw and an open-ended straight draw 15

Count cards that win, not cards that merely improve you. If the board has three spades and you are drawing to a straight, the spade that fills it may hand someone a flush — many players count that card as half an out, or not at all.

The rule of 2 and 4

On the flop, with two cards still to come, multiply your outs by 4. On the turn, with one card to come, multiply by 2. That is your rough chance of hitting, as a percentage:

9 outs on the flop → 9 × 4 = 36% · on the turn → 9 × 2 = 18%

The real figures are 35.0% and 19.6%. The rule is meant to be done in your head in the two seconds you have, and for the draws you see most it is within a point or two.

Where the shortcut is off, and by how much

Nobody publishes the exact column beside the rule — so here it is. From the flop there are 47 cards you have not seen; from the turn, 46. The exact chance of hitting on the next card is your outs divided by that number, and the chance of hitting by the river is one minus the chance of missing twice. The rule overshoots more the more outs you have, because it counts the cases where you hit both cards twice.

Outs Next card, exact Rule (× 2) By the river, exact Rule (× 4)
1 2.1% 2% 4.3% 4%
2 4.3% 4% 8.4% 8%
3 6.4% 6% 12.5% 12%
4 8.5% 8% 16.5% 16%
5 10.6% 10% 20.4% 20%
6 12.8% 12% 24.1% 24%
7 14.9% 14% 27.8% 28%
8 17.0% 16% 31.5% 32%
9 19.1% 18% 35.0% 36%
10 21.3% 20% 38.4% 40%
11 23.4% 22% 41.7% 44%
12 25.5% 24% 45.0% 48%
13 27.7% 26% 48.1% 52%
14 29.8% 28% 51.2% 56%
15 31.9% 30% 54.1% 60%
16 34.0% 32% 57.0% 64%
17 36.2% 34% 59.8% 68%
18 38.3% 36% 62.4% 72%
19 40.4% 38% 65.0% 76%
20 42.6% 40% 67.5% 80%

Two things stand out. Up to eight outs the rule is never more than a point off, which is why it works. From about twelve outs the "× 4" column runs away — a fifteen-out draw is 54%, not 60%, and twenty outs is 67.5%, not 80%. A common fix past twelve outs is outs × 3 + 9: fifteen outs gives 54, which is right on.

"Next card" from the flop uses 47 unseen cards; on the turn there are 46, so the same outs are worth slightly more: nine outs is 19.1% on the turn card and 19.6% on the river card. The rule of 2 does not distinguish, and does not need to.

Turning the percentage into a decision

The number on its own decides nothing. Compare it with the price of the call: if the pot offers you 3-to-1, you need to hit more than 25% of the time, and a flush draw on the flop (35%) is a clear call while a gutshot (16.5%) is a clear fold. That comparison is what pot odds are, and the calculator does both halves for you — the exact chance you have and the chance you need — with a plain verdict.