Pot Equity - Hand Equity

by Jesse Knight


Poker Equity
Equity - Your "rightful" share of a pot.

When most people hear the word “equity,” they think of the equity in their home. In this context it means the difference between the amount your house is worth, and the amount of money you owe on the mortgage. Imagine, for example, that your house is worth $400,000, but you only owe $300,000 on your mortgage. In this situation, you would have $100,000 in equity. So long as your house is worth more than you owe, you have equity. One way to think about this is that you own a portion of your home, and the bank also owns a portion. In other words, there is an item of value (your house), and stakeholders (you and the bank) who each have a claim to a portion of that value. Over time, events occur which affect how much equity you have. These include mortgage payments you make, which increase your equity, and fluctuations in the value of your house, which can increase or decrease your equity. Eventually, you pay the house off and have 100% equity.

In a poker game, during a given hand, players build a pot, and at the end of the hand someone wins it. Here, you also have an item of value (the pot), and a group of stakeholders (the players with live hands), who each have a claim to a portion of that value. You also have events which occur over time which affect each player’s equity in the pot. These events include the delivery of another card or round of cards, and the elimination of player’s contending for the pot. Eventually, someone will win the pot and will therefore have 100% equity in it. You can see that the players have equity in the pot in much the same way as you may have equity in your house. In a poker game, the main thing that determines how much equity you have in the pot is the value of your hand, relative to the value of your opponents’ hands. Imagine that you are playing in a poker game, and you become involved in a hand with three other players. The pot is $40. You calculate that you have a 40% chance of winning the pot, while your other three opponents each have a 20% chance of winning. Your equity would be 40% of $40, or $16, and each of your opponents has 20% equity, or $8. If one of your opponents were to muck their hand, it would change the equity equation substantially, most likely raising everybody’s equity. If another card is delivered, it may help or hurt your chances of winning the pot, and it may help or hurt your opponents as well. This also changes the equity of everybody involved.

It is important that you understand and are able to calculate equity, because you can use the information to determine what the correct play is. Consider again the previous situation. The pot is $40, and you have a 40% chance of winning the pot if you call, so your equity is $16. Should you call? That depends on how much it costs to continue on in the hand, and what the odds are that you will win it. In the above situation, you have a 40% chance of winning the pot, and each of your opponents has only a 20% chance. Clearly, you are the favorite here and should be willing to call or raise any amount. In this situation the money in the pot is irrelevant; because you are a clear favorite over the field you should be willing to build as large a pot as possible, even if there were no money in the pot.

Now, consider a different question about the same situation: Should your opponents call? The answer depends on how much it costs them to call, keeping in mind that they also must take into account any changes in equity resulting from any of the other players mucking their hands. If you, as the favorite, bet $15, it would cost your next opponent, $15 to keep his 20% equity in the pot which would stand at $70 ($40 that was in the pot plus the $15 bet and the $15 call). 20% of $70 is $14. So it would cost your first opponent $15 to keep their $14 in equity. At first glance, you would say that it would cost this opponent $15 to retain $14 in equity, and therefore he should not call. This is not necessarily the case, and this is where game theory comes into play. Let’s say that your first opponent correctly suspects that you are in the lead with a 40% chance of winning the pot, and that he and the other two opponents each have a 20% chance. When you bet out $15, he knows that if he calls the $15, your other two opponents will also have enough equity to call, because if they do, the pot will stand at $100 20% equity in a $100 pot is $20, but the call is only $15. Clearly, it is worth $15 to keep $20 in equity. In this situation the equity is implied. In poker, this type of implied equity is called implied odds.

Alternatively, consider a situation where you bet $15 into the $40 pot, and your first two opponents muck. Now, you have one opponent remaining and he must call $15 to win $70. Should he call? It depends if he picked up any of the equity released by your other opponents when they released their hands. Let’s say your last remaining opponent is on a flush draw which he must complete in order to win the pot, and he still has only a 20% chance of doing so. In this situation, you have picked up all of the equity released by the other players, and now have 80% equity, while your one remaining opponent still has 20%. Here, your opponent would have to call $15 to retain $14 in equity (20% of $70). Since $15 is too much to pay for $14 in equity, your opponent should muck. However, if he receives any of the equity from the other two players who have folded, it changes the equation. Let’s say that of the 40% equity released by the other two, your receive 30% and you remaining opponent receives 10%. Now your equity stands at 70% and your opponent’s is 30%. 30% of $70 is $21. In this case, it is clearly worth it for your opponent to call $15 in order to retain $21 in equity.

There is also an advanced concept in tournament play called "Fold Equity".

Also compare to "Expectation" linked below.

Usage: Equity in the pot

Previous Poker Term: Draw
Next Poker Term: Expectation


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