The Math behind Poker Equity

What is Equity in Poker?

Equity in poker is the share of the pot that is yours based on the odds that you will win the pot at that point in play. Equity changes after each street– pre-flop, flop, turn, and river. The strategy around poker equity is pretty simple; if you feel you have more equity in the pot than your opponent, i.e., you have the better hand at that moment, then you generally want to bet.

Using your equity

The first chance you get to use equity is pre-flop. If you feel you have the best hand but don’t raise, you’ve missed a big chance to increase your equity. Besides increasing your equity in the pot, raising pre-flop has many other advantages: it reduces the number of players in the pot, establishes your image as being strong, and aggressive and can often result in you having “position” in the hand.

Remember, just as you would not really know your equity at any given point in the hand, neither does your opponent. Everyone is trying to determine what each other’s equity is by putting them on a range of hands. If you are the aggressor, opponents will naturally think you are playing a stronger hand and perhaps give you credit for more equity than you really have, which you can exploit by continuation betting on dry or strong boards.

A situation

Three players go to the flop. You are the last to act and have 10s-9s. Player 1 has Ah/8h, and player 2 has Qc-Qd. The flop comes up 8s-7h-2s. If you stopped the hand right then, you would lose to both players. Player 1 has a pair of eights (not to mention a backdoor, nut flush draw), and Player 2 has a pair of queens.

Your combined open-ended straight draw and flush draw actually gives you more equity than your opponents. At this point, you are a 55% favourite to win the hand. Player 2 is at 28%, and Player 1 is at 17%.

Therefore, Equity would dictate that you bet. Let’s say you are in position, and both players check. You only have a 10-high at this point and figure to be behind both players, but your potential is so good that it makes sense to try a semi-bluff, so you put out a bet of 2,000, and both players call.

In terms of equity, you gained 55% of the 6,000 chips bet, or roughly 3,300 chips – almost twice what you bet.

Let’s say the turn is a brick for all three players: the 3 of diamonds. Your equity — the chance you will win the hand — has dropped to 36%. Player 1, with the pocket queens, is now at 55%, and Player 2, 9%.

Tip of the Iceberg

Equity is not a hard and fast concept unless your opponent has shown you their cards and you have a pot odds calculator at your disposal. You never really know your equity in a given situation, and you certainly can’t predict what your equity will be after the turn and river. Still, understanding the concept and how to apply it will undoubtedly provide more insight when making in-game decisions.