Fold Equity

Hand Equity in Poker Tournaments

by Jesse Knight


Fold Equity
Fold equity is somewhat of an advanced poker concept, and while the logic is straightforward, the math can be tricky. The concept of fold equity is base on the truism that if nobody calls your bet, you will win 100% of the time. Stated in another way, you have 100% equity in all pots in which you bet and nobody calls. Of course you cannot know in advance if your opponents will all fold to you. When you make a bet, sometimes your opponents will all fold and sometimes they will not. When calculating fold equity, you must make an educated guess about the probability that each will occur. For this reason, a fold equity calculation is a type of implied odds calculation, and can be either positive or negative.

Here is how you construct a fold equity calculation mathematically. For simplicity’s sake, we will consider your bet as an all in gambit, although in real life this will not always be the case.

Consider Pf as the probability that all opponents will fold if you bet, Es as your showdown equity, Pw as the probability you will win at showdown, and Pl as the probability you will lose at showdown, such that Fold Equity = (Pf * Pot amount before your wager) + Es. And Es = [(Pw *Pot amount after your wager) +( Pl * Pot amount after your wager)] (1-Pf)

What this means is that the percentage of time that all opponents fold multiplied by the amount of the pot prior to your bet can be considered as your equity, but you also have to include in the equation what occurs when you are called. When you are called, some percentage of the time you will win, and some percentage of the time you will lose. When you win, you will win the amount in the pot after betting and being called. Likewise, when you lose, you will lose the same amount. Multiply each by the probability of each occurring. Then add these two products together. This sum can be a negative or positive amount, depending upon whether or not you have the best starting hand. Even if you have the worst hand, and Es is negative, and it often will be, fold equity can still be positive, because you still have to add the equity you receive when you steal the pot successfully.

Fold equity is an important concept to master for effective bluffing in both live and tournament play. It is most frequently applied to the stealing of blinds in the later stages of tournaments, where it is absolutely crucial for success. In tournament play, a missed opportunity to steal the blinds can be fatal. Understanding when you have fold equity is absolutely critical. A key aspect to this is making a good prediction about the value of Pf, the probability that all opponents will fold. Remember, you are estimating this, and you will have to consider many things if you are to come up with an accurate estimate. Things to consider when predicting how often your opponents call include, how loose or tight they are, your table image, the size of your bet, the size of your stack and your opponents’ relative to each other as well as to the size of the blinds, and many other factors.

See more explanations on Implied Odds, Pot Odds, and Equity

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