Poker Strategy - Equity

Players' equity in a pot is their expected share of the pot, expressed either as a percentage (probability of winning) or expected value (amount of pot * probability of winning). Negative equity, or loss in equity, occurs when contributing to a pot with a probability of winning less than 1 / (number of opponents matching the contribution+1).

Example

Alice contributes $12 to a pot and is matched by two other opponents. Alice's $12 contribution "bought" the chance to win $36. If Alice's probability of winning is 50%, her equity in the $36 pot is $18 (a gain in equity because her $12 is now "worth" $18). If her probability of winning is only 10%, Alice loses equity because her $12 is now only "worth" $3.60 (amount of pot * probability of winning).

If there is already money in the pot, the pot odds associated with a particular play may indicate a positive expected value even though it may have negative equity.

Texas hold 'em example

Alice holds J♦8♠. Bob holds K♥7♠. After the flop, the board is 5♥6♥7♦. If both hands are played to a showdown, Alice has a 45% chance to win, Bob has a 53% chance to win and there is a 2% chance to split the pot. The pot currently has $51. Alice goes all-in for $45 reasoning Bob has to call to stay in the game. Alice's implied pot odds for the all-in bet are 32%. Bob's simple pot odds for the call are also 32%. Since both have a probability of winning greater than 32%, both plays (the raise and the call) have a positive expectation. However, since Bob has more equity in the pot than Alice (53% vs. 45%), Alice would have been better off playing the pot as cheaply as possible. When Alice went all-in, she gave up the difference in equity on the money she contributed to the pot.