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Importance of Expected Value in Poker

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Although they’re quite similar, EV or expected value should never be confused with equity. In a nutshell, the expected value is the money you’re either going to win or lose in a bet (in this case, when you’re playing poker). The +EV or positive expected value is computed by multiplying the money you’re going to win with the probability of winning. The –EV or negative expected value, on the other hand, is the money you’re going to lose with a poor bet. You can get your –EV by multiplying the money you’re going to lose on a bad bet with the probability of losing.

It’s probably simpler if we set this equation on an even 1:2 probability. The most common setting used by poker players to explain EV is when you’re tossing a coin. Since there are only two sides of the coin, the probability of getting both heads and tails are both 1:2, or 0.5. If you win $1.00 every time the tail turns up, and lose $1.50 every time the head appears, the computation should look like this.

+ EV = $1.00 x 0.5

-EV = -$1.5 x 0.5

Ergo, the money you can expect to win is $0.5 and the money you can expect to lose is -$0.75. If you add these two products together, you get your total EV.

EV = $0.5 + -(0.75) = -$0.25

This means that you’re at the losing end if you agree with this set up.

This seems easy enough to understand if you only have to worry about coin tossing. How can you apply this principle to poker? Let’s apply the basic example of a flush draw. Let’s say that our hand is A 2 and the flop side is Q K 3 7 , the pot contains $100 and our opponent goes all in with $50, this means that we have a chance to win $150. The probability of hitting a flush is 0.2, though, and the probability of losing our flush is 0.8. The formula would look like this:

($150 x 0.2) + ($50 x 0.80)

($30) + ($40)

$30 $40

EV = -$10

This just means that every time we bet on these odds, we lose an average of $10, making this a call only idiots should make.

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