Pot Odds and Break-Even Percentage

Overview

We should be familiar with the concepts of equity and EV, but how might we put that into practice?

We use pot odds to quantify the price our opponent is giving us to call and break-even percentage to determine if the pot odds we’re given are good enough for us to call.

Pot Odds

Pot odds apply when an opponent has bet, and is calculated as the ratio between the pot – including the bet – and the price to call. In other words, it is the reward to risk ratio of calling.

Break-Even Percentage

If an opponent makes a 100 chip bet into a 100 chip pot on the river, giving you 2:1 pot odds, how often does your hand have to be good to make it a profitable call?

• If you call and lose, you lose 100 chips. We do not count the money we already put in the pot as that is “dead money” and we do not care where it came from. You may think of this as putting in 100 chips on the river and receiving 0 back.
• If you call and win, you win 200 chips. You may think of this as putting in 100 chips on the river and receiving 300 back.

If we profit 200 chips when we win and lose 100 chips when we lose, the point at which calling would be exactly 0 EV is if we lose twice as often as we win. Losing twice as often as winning occurs when we have a win percentage of 33.3%. Therefore, if our hand is stronger than our opponent’s 33.3% of the time, calling is exactly 0 EV.

Since folding is by definition 0 EV – remember that money in the pot is already dead money – if our hand wins at the break-even percentage, calling and folding have the exact same expected value. If we think our hand wins more, it is +EV to call. If we think our hand wins less, it is -EV to call and we should fold instead.

Calculating Break-Even Percentage

To calculate break-even percentage we must start from pot odds. First express the pot odds as a ratio A:B where A is the pot size including the bet from the opponent and B is the price to call. The break-even percentage is then calculated as B / (A + B). Some common examples:

You will notice that the break-even percentage asymptotically approaches 50%. This should be intuitive – if you have at least a 50% chance to win, you should call no matter how large the opponent bets.

Examples

Try some examples to test your understanding of pot odds and break-even percentage: