Calculate fold equity in poker
What is fold equity anyway
With Fold equity is defined as the cleanly the probability that an opponent will fold to a bluff. The term equity is used here as a semi-bluff wins e.g. a raise with a flush draw by the likelihood that the opponent folds of its value.
A simple example
Let us look at a simple example: A player calls pre flop with a raise in place and play heads-up against one opponent. The flop comes. In the center are $ 100 and your opponent bets $ 80. Our protagonist calls and the turn come. The opponent checks in the pot are $ 260 and our protagonist has $ 200 stack. These he represents as a semi-bluff all-in. Now he can win in two ways also his opponent folds or his opponent calls and the river brings a third heart.
If our protagonist is called he has only 9 outs 1 and thus about 20 percent winning gain also called “equity” called. Initially that does not sound very much but this winning percentage works hand in hand with the likelihood that the opponent folds a give like TT or 88. One can calculate that the opponent must fold in only 21 percent of cases a better hand so an all-in on the turn will be profitable.
First the required variables:
P: amount in the pot s: Effective residual stack e: equity (winning percentage) if the opponent’s bet or raise the calls b: If the opponent has already placed a bet and it rises, as a (semi) Bluff are b the Height at the Bet otherwise b zero. F: probability that the opponent folds to the (semi) bluff the fold equity. If the opponent folds on the All-In, the gain is the amount in the pot, plus the eventual bet that he has already made:
p + b
If the opponent calls, the profit (or loss) depends on how big the effective stacks are, how big the own equity is and how much is in the pot. The formula looks like this:
e * (p + 2 * s) – s
The case that the opponent folds occurs with probability f a case that he does not folds according to the probability 1 – f. Thus, for the expected value of a Bluffs following formula:
EV = f * (p + b) + (1 – f) * (E * (p + 2 * s) – s)
Now we are interested in how big the fold equity f must be so that the expected value is greater than zero. For this, you simply point above formula for f around to the slightest fold equity for a profitable push:
f> ((e * (p + 2 * s) – s) / (s * p (p + 2 * s) – S – B – p)
This specifies the minimum fold equity that is required in order for a (semi) -Bluff is profitable. This formula looks something monstrous and hardly anyone will be able to solve such a formula on the fly in the head. There are but our fold equity calculator.
A few concrete examples Bluff
The following examples are rather instructive nature, to show how you calculate the required fold equity and how much fold equity you need in certain situations. This does not necessarily mean that an all-in bluff is the correct or best play in all the examples.
Example 1 – straight draws on the flop
On a -Flop has player A and one opponent who has already checked. In pot is $ 100 and player A has one more $ 150 via, his opponent has more. Player A has a straight draw with 8 outs, and thus approximately 32% equity on the flop. Substituting p = 100 , s = 150 , e = 0.32 and b = 0 in the above formula we can calculate that player A needs only 18% fold equity, so that he can bluff profitable on the flop. That is if his opponent in now over one in five cases a better hand folds a bluff has a positive expected value.
Example 2 – flush draws on the turn
Player A calls a pre-flop raise with in place. His opponent bets the -Flop. Turn: There is $ 70 in the middle and the opponent plays $ 40. Player A has a stack of $ 160 his opponent has been covered him. With his flush draw has player A approximately 20% winning percentage and not getting the right odds to call the bet. However, perhaps his opponent has itself not a fine hand and has to fold to an all-in raise. If in the above formula the values p = 70, s = 160, e = 0.20 and b = 40 A, one sees that the opponent must fold in about 43 percent of cases, so an all-in raise is profitable.