How to calculate pot odds

You do not need to do the division at the table. The answer only depends on the bet as a fraction of the pot, so there are about six numbers and they never change.

Read the whole table as one sentence: the bigger the bet, the more often you have to be right. A half-pot bet asks you to win a quarter of the time. Nobody can bet you off a hand for free, and the price they set is the only thing their bet actually tells you for certain.

The common mistake is dividing by the pot as it stands rather than the pot after your call. It makes every price look better than it is, which is a direction of error that costs money.

An out is a card that gives you the best hand. After the flop there are 47 cards you have not seen, and the count of outs among them is your estimate of how often you get there.

A flush draw is nine outs. There are thirteen cards in a suit, you can see four of them, and nine are left. Everything else is counted the same way, by working out which cards change the answer.

The shortcut is the rule of 4 and 2: multiply your outs by 4 for both cards, or by 2 for one card. It is close enough at small numbers and it drifts as the count grows. At nine outs it says 36 where the true figure is 35. At fifteen it says 60 where the truth is 54.1, and fifteen outs is exactly the situation where people talk themselves into stacking off.

The “by the river” number is only yours if you are going to see both cards.

You are on the flop, you have a flush draw, and someone bets. You will not necessarily see the turn and the river. You will see the turn, and then they get to bet again. Unless one of you is already all-in, or the bet has been checked through, the card you are buying is one card, not two.

So the number to compare against the price is 19.1%, not 35%.

Facing a half-pot bet on the flop you need 25%. A bare flush draw does not have it. That is not an opinion about aggression, it is subtraction, and it is the single most useful thing on this page because the popular version of this advice has it backwards.

There is a real defence of that call, and it is not the 35%. It is implied odds, below.

Counting outs assumes your card wins and nothing else does. Both halves of that are approximations. Below are five real spots, each one worked out by playing every single one of the 990 possible turn-and-river runouts and counting the results.

The same nine outs are worth 39.3% in one row and 27.4% in the next. In the first, the extra value is all the things the count ignores: running straights, running pairs, cards that back into a hand you never planned. In the second, the opponent has flopped three queens, so every card that pairs the board makes them a full house and your flush arrives second. Nine outs, and a third of their value gone.

Two lessons, and take the second one more seriously than the first.

Outs undercount when nothing is wrong. On a dry board against one pair, your real equity is a few points above the count, because backdoor cards are worth something.

Outs overcount when something is wrong. A paired board, a board of one suit, an opponent who has been raising every street. Those are the moments the count flatters you, and they are the moments you are being bet at hardest.

If you take one habit from this section: when the board pairs, stop counting and start subtracting.

Pot odds only price the money on the table now. Implied odds are the money you expect to win later on the streets where you hit.

This is the honest argument for calling a flop bet with a draw that immediate odds say to fold. You are not claiming 19.1% beats 25%. You are claiming the times you hit are worth more than the pot you are currently being offered, because they will pay you on the river.

Three conditions, and all three have to hold.

The money has to exist. Implied odds against a short stack are imaginary. There has to be enough behind to win.

They have to pay. A flush that arrives on an obvious board gets checked back all day. The value is in the hands that cannot fold, not the ones that cannot call.

It has to be a hand you will get paid on and not one you get stacked with. The other half of this is reverse implied odds, which is what happens when you hit and lose anyway: the small flush against the big one, the straight on a paired board, the ace-high flush draw’s little brother. Draws to the second-best hand are how the price stops mattering at all.

Implied odds are real and they are also the standard excuse for a call somebody wanted to make anyway. If you are appealing to them on every street, you are not using them, you are decorating.

You have about four seconds, so you are not doing long division.

One. What does it cost me, as a fraction of the pot? Half pot, two-thirds, that is enough precision.

Two. So how often do I need to be right? Half is a quarter. Two-thirds is roughly 29%. Pot is a third.

Three. Am I better than that? One card, not two, unless the money is already in.

Then fold most of the time, because the answer is usually no. Pot odds tell you when a call is not losing money. They do not tell you it is the best thing you could do with the hand, and they say nothing at all about the times raising is better than either. The hands worth being in these spots with are the ones on the starting-hand chart, and the seat you are in decides how often you get to make the decision at all, which is the position guide. From the other side of the table, the same arithmetic is how much to bet.

One more caution. Everything above is a one-on-one calculation. With three players still in, the price on offer is better and your chance of winning is worse, and the second effect is usually the bigger one.