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Poker maths

Pot odds

How to tell in seconds whether a call is worth it, by comparing the price you are offered with your chance of winning.

Pot odds answer one question: is this call worth it? You compare what you must pay with what you can win. If your chance of winning is higher than the share of the final pot you are paying, calling makes money over time.

The one formula you need

Equity needed = amount to call ÷ (pot after you call)

The pot after you call is everything already in the middle, plus your opponent's bet, plus your call.

Example

The pot is 100. Your opponent bets 50. To call, you pay 50 to win a pot that will then be 100 + 50 + 50 = 200.

50 ÷ 200 = 25%

If you win this hand more than 25% of the time, calling is profitable in the long run, even though you will lose most of the time.

Bet size decides the price

Because bets are usually a fraction of the pot, the price you need depends only on that fraction. Learn this chart and you never have to calculate at the table:

Equity you need to call, by bet size Bet size (of the pot) → Equity you need to call
25% 16.7%
33% 19.9%
50% 25.0%
66% 28.4%
75% 30.0%
100% 33.3%
150% 37.5%
200% 40.0%

Two numbers worth memorising: against a half-pot bet you need 25%, and against a pot-sized bet you need 33%. Bigger bets give you worse prices.

Pot odds as a ratio

Players often say odds as a ratio, like "3 to 1". A 50 bet into a pot that is now 150 means you are calling 50 to win 150: 3 to 1. To turn that into a percentage, add the two numbers and divide: 1 ÷ (3 + 1) = 25%. Same answer.

Putting it together with your draw

Pot odds tell you the price. Your equity - the chance your hand wins - tells you whether it is worth paying. On the flop, you hold A♥10♥ and the board is K♥7♥2♣: a flush draw with 9 outs.

  • On the flop your opponent bets half the pot, so you need 25%. With two cards to come you make the flush by the river about 35% of the time - but only if you see both cards for this one price. Calling is fine.
  • On the turn the heart did not come, and they bet half the pot again. You still need 25%, but with one card left you hit only 9 out of 46 times: 19.6%. On its own, that call loses money, unless you expect to win more on the river when you hit. That extra is called implied odds.

See outs and equity for how to count your outs.

Implied odds

Pot odds only count the money already in the pot. Implied odds add the money you expect to win on later streets when you hit. If your opponent has a big stack and will pay you off when the flush comes in, a call that looks slightly too expensive now can still be profitable.

Implied odds are strongest when:

  • your draw is hidden (a flush draw on a board with three suits is obvious; a gutshot straight is not);
  • your opponent is likely to pay off with a strong but second-best hand;
  • stacks are deep enough that there is something left to win.

They are weakest when your opponent is short-stacked or careful, or when your draw is to a hand that might not be the best even if it comes.

Reverse implied odds

The opposite trap: you call with a hand that, when it improves, can still lose a big pot. Drawing to a low flush, or calling with a weak top pair, can cost more than it wins. Prefer draws to the nuts (the best possible hand).