Outs and pot odds

An out is an unseen card that would make your hand the likely winner. Outs × 2 is roughly your chance of hitting on the next card; outs × 4, by the river with two cards to come. Compare that with the pot odds: a call pays when your chance beats the share of the final pot you pay for.

Take a flush draw on the flop: 9 outs. 9 × 4 = 36%; the exact figure is 35.0%. If an opponent bets 300 into a pot of 600, you pay 300 to win 900 — 25% of the final 1,200. Against an all-in, 35% covers that price with room to spare. If only the next card is guaranteed (19.1%), it does not.

Count the cards that complete your hand and that you have not seen. After the flop you have seen five cards — your two and the three on the board — so 47 are unknown. Your opponents’ cards are unknown to you as well, so they count among the unseen.

• Flush draw: four cards of one suit, 13 − 4 = 9 outs.
• Open-ended straight draw: 8-7 on a 6-5-K board; any nine or four makes a straight, 8 outs.
• Gutshot: J-10 on Q-8-3; only a nine fills the gap, 4 outs.
• Two overcards: A-K on 9-6-2; any of three aces or three kings gives top pair, 6 outs.
• Pocket pair to a set: 5-5 on A-K-9; two fives are left, 2 outs.

Watch for two traps. First, never count a card twice: a flush draw plus an open-ended straight draw looks like 9 + 8 = 17 cards, but two of them are both the right suit and the right rank, so it is 15. Second, discount outs that help your opponent too. On K♥ 7♥ 2♣, 9♥ 8♥ has nine hearts to come, but against a set of kings the 2♥ pairs the board and gives him a full house: eight clean outs, not nine.

With one card to come, the exact chance is outs / 47 from the flop and outs / 46 from the turn. With two cards it is easier to count the misses: 1 − (47 − outs) / 47 × (46 − outs) / 46. The rule of 2 and 4 approximates both and is almost spot on for small draws. For big draws ×4 overshoots: at 15 outs it says 60% while the truth is 54.1%. Above 8 outs, 4 × outs − (outs − 8) is closer.

Pick a draw or set your own number of outs. The tool shows the exact chance and checks it against the price of a call:

Nominal odds assume that every out wins and every other card loses. Real hands are messier, so we took eight typical spots and had our engine play out all 990 turn-and-river pairs against a specific opponent hand.

Most draws do a little better than their outs, because hands made with both the turn and the river — two pair, trips, a backdoor straight — add a few percent. Overcards do worse: 22.1% instead of 24.1%, because 10♦ 9♦ can improve too, to two pair or trips, and an ace or a king does not always save you. And the 15-out combo draw is a favourite even against aces, at 56.3%. Holding one, getting all-in on the flop is usually right.

Pot odds weigh the price of a call against what you can win. Add the opponent’s bet and your call to the pot and divide your call by the total. That is the share of the final pot you are paying for, and the minimum equity the call needs.

At the Scribes’ Table the pot is 600 and your opponent bets 300. You pay 300 to win 900; the final pot is 1,200 and your share of it is 300 / 1,200 = 25%. Players also say “3 to 1”: 900 to win for 300 paid.

Now put the two numbers side by side. With a flush draw on the flop facing a half-pot bet, the next card brings the flush 19.1% of the time and you need 25%, so on pot odds alone the call loses a little. Against a quarter-pot bet (16.7%) it wins. And against an all-in, when you are sure to see both cards, 35.0% beats even a pot-sized bet (33.3%).

Pot odds only count the chips already in the middle. When you hit, you often win more on later streets — those are your implied odds. With the flush draw facing 300 into 600, how much do you need to win later for the call to break even? Solve 19.1% × (900 + X) = 80.9% × 300 and X comes out at about 367 debens. If you expect a made flush to collect at least that much more, the call is fine.

Implied odds are biggest when your draw is well hidden and the stacks are deep. They shrink, and can turn negative, when the draw is obvious, when your opponent is short of chips, or when you can hit and still lose: a small flush against a bigger one, a straight on a paired board. That last case is called reverse implied odds.

1. All-in on the flop with a combo draw. You hold J♥ 10♥ on 9♥ 8♥ 2♣. The pot is 1,000 and an opponent moves all-in for 2,000. You need 2,000 / 5,000 = 40%. Against aces you have 56.3%. Call.
2. Flush draw against a big bet. You hold 9♥ 8♥ on K♥ 7♥ 2♣, the pot is 600 and your opponent bets 600. You need 33.3% and the turn gives you 19.1%. For the call to pay, the flush would have to win about 1,333 more debens later. Unless the stacks are deep and he is the type to pay off, fold.
3. The river, nothing left to draw. The pot is 2,000 and your opponent bets 1,000. There are no outs any more; the question is whether he is bluffing at least one time in four (25%). If you win at least every fourth such hand, calling breaks even.