Pot odds: the price of a call

The pot is 100 and your opponent bets. To call, you add the same amount. The pot odds compare the chips already available to win with the call you risk. To express that price as required equity, divide your call by the final pot, including your call:

Against a half-pot bet of 50, you call 50 and play for a pot of 100 + 50 + 50 = 200.

Against a pot-sized bet of 100, you call 100 to play for 300.

Against an overbet of 200, twice the pot, you call 200 to play for 500.

That number is your required equity. If your hand wins more often than that, the call makes money over many hands. If it wins less often, the call loses money even on the nights it happens to win.

Doubling the bet from half pot to pot does not double the price. It goes from 25% to 33.3%, and doubling again only takes it to 40%. The required percentage rises more slowly than the bet size because your opponent's chips also go into the pot you can win.

The pot size drops out once you write the bet as a share of the pot. A bet of a fraction f of the pot asks for f ÷ (1 + 2f). For the sizes you see most:

Three rows are worth knowing by heart: half pot asks for a quarter, pot asks for a third, and twice the pot asks for two in five. The rest sit between them.

Players often say the price the other way round: "I'm getting 3 to 1." That ratio is what you could win against what you risk. Against the half-pot bet you risk 50 to win the 150 already in the middle, so 150 to 50, or 3 to 1.

To turn a ratio of x to 1 into the percentage you need, divide 1 by x + 1:

The ratio and the percentage say the same thing. Use whichever you can compare faster with your hand. Percentages are easier to set against a chance of winning, since that is usually a percentage too.

Pot odds improve when another player calls before you. The pot is 100, the first player bets 50 and the second player calls 50. Now you call 50 to play for 250:

The price fell from 25% to 20%. Your hand now has to beat two players, though, so you must estimate its equity against both ranges; the better price alone does not justify a call. A draw to the nuts can still face a redraw on a later street or split the pot with the same hand. One pair now has to beat two hands instead of one.

Say you raised before the flop and now face a bet. It is tempting to count your earlier raise as a reason to call: you have "too much in the pot to fold". The sum above already counts those chips once, as part of the pot. They are no longer yours, and folding does not lose them a second time.

The only question is whether the next call wins more than it costs. A big pot does lower the price, and the pot odds already include that. Counting your old chips again is the sunk cost mistake, and it leads to calls the price does not support.

Pot odds tell you how often the call needs to win. To decide, you still need your equity: from your outs when you are drawing, or from how often your opponent bluffs when your hand can only beat a bluff. On the river, against a three-quarter-pot bet, the price is 30%: you call if you think they are bluffing at least 3 times in 10.

When you are drawing and the price is slightly too high, the money still to come can make up the gap. That is implied odds, the next step after this one.