Poker EV

EV (Expected Value) in Poker

What is EV?

EV is a poker term that stands for “Expected Value”. Simply put, it is the amount of money you can expect to win or lose by taking a specific action in a specific circumstance, if you could repeat that action an infinite number of times.

Using dice games as an example, imagine a friend offers to pay you 6 times your bet if your number comes up on a single die. If you bet $1 that the number 6 will come up, your EV will be 0. For every 6 times you roll the die, you will win once, (Wining $6, minus the $1 you bet, for $5 profit on that roll), and lose 5 times (losing $1 each time =$5 loss). Therefore if you repeat the situation an infinite number of times, you can expect to come out exactly even in the long run. Your EV is therefore 0.

Now lets say that your friend offers you $12 if your number comes up. If you make this bet an infinite number of times, you can assume that for every 6 times you play, it will cost you $6, and you will win $12 once, for a net profit of $6. Your EV in this situation is 100%, because for every dollar you bet, you stand to make $1 profit on average. Obviously you might get unlucky and lost 20 in a row, or you might get lucky and win 20 in a row. The important thing to understand is that mathematically, you can expect to make an average of 100% profit each time you roll the die.

How is EV used in Poker?

The most common use for EV (“Expected Value”) in poker is to determine the long-term profit or loss of taking a specific action in a specific situation. As a poker player, you goal should be to only play hands in +EV situations (ie a situation where you expect to win money in the long run, rather than lose money).

Here’s an example of EV in action.

You’re in a hand with 78 offsuit, and the flop comes 2 5 6 rainbow, giving you an open ended straight draw. There is $100 in the pot, and your opponent bets all in for $20, and everyone else folds. You are pretty sure that you are behind at the moment (since you only have 8 high), but any 4 or 9 will give you a straight, which will almost certainly be good enough to win.

If you call, it will cost you $20, and the pot will become $140 (the $100 pot, plus his $20 all in, plus your $20 call =$140). An open ended straight will complete about 33% of the time, so if you call, you can expect to win about 1 time in 3. It turns out that your 33% equity in the $140 pot is worth about $46, and since it only cost you $20 to call, it proves that calling is a very +EV play in this situation.

If your Opponent had bet all in for $300 however, it would be a different story. It would have cost you $300 to call, making the pot $700 total. 33% equity in a $700 pot works out at $231, meaning that the $300 call would only return you $231 on average, for a net loss of $69 every time you called in this exact situation. This play would be –EV.
In practice it’s not usually necessary to work out the exact amount that a play is +EV or -EV. It’s just important to work out which is which. If a play is +EV, you should usually do it, no matter if its +5% EV or +100% EV. If you will make money on the play, go ahead and do it. Likewise it’s not necessary to know exactly how –EV a play is, because you don’t want to do –EV plays that are -1%, or –50%. Just knowing that a play is –EV should be enough for you to decide not to play the hand.