Poker: Expected Value

It’s a term that you see frequently in online poker forums and in articles like this, but now it’s time to explain expected value and what it means to poker players, no matter how experienced they are at the game.

So, what is expected value? It’s the amount of money a certain play will win or lose on average. In any given situation at the table, a decision is going to have certain expected value on its return to you. Some of these are going to win money, some are going to lose money and those that win you money and some are going to win more than others. Your aim is, of course, to make the play with the greatest possible expected value at any given time.

Expected value is not that difficult to work out: simply multiple the results of the possible outcomes by their probability of happening, then you add them. Let’s look at an example using a flush draw that will help you understand things more than any simple “coin flip” example will.

You’re holding Ac2c and the board reads QckH3c7d. The pot is at $100 and your opponent moves all-in for $50. This means that to win the $150 that’s now in the pot, you’re going to have to call that $50. Now, let’s assume that the only way that you’re going to win the hand is by hitting your flush on the last card, what is the expected value of calling. Is it profitable for you to call?

You can work out if calling is profitable by using pot odds, but with expected value, you can work out exactly how much you expect to win or lose on average by making the call.

If you call and hit the flush, you win $150. The probability of hitting the flush is (roughly) 20%. The odds of not hitting that flush are (roughly) 80%. So, the math works out as follows: ($150 x 0.2) + (-$50 x 0.8) or ($30) + (-$40), which equals -$10 as the expected value. This is usually stated as -$10EV, which means that every time you call this bet and try to hit your flush, you are losing $10 on average. This means that this is a negative expected value play and you should fold.

While you usually can’t easily work out EV on the fly like you can pot odds, it’s perfect for post-game analysis where you try to work out how your decisions affected your play. It also helps you understood why some plays are good while others are not, even if they seem like they might be a good idea at the time.