Expected value

"Expected value" (EV) refers to the amount you will win or lose on a bet over the long run according to the mathematics of the situation. This is the same as "expectation" and may be either negative or positive.

For example. If you and a friend bet $1 on the flip of a coin, you each have a 50% chance of winning. On any given flip, you have an equal chance of winning. Furthermore, over the long run of thousands of flips, you should both end up with very close to the same number of wins. This proposition would have an expected value, or EV, of 0. Ultimately, neither player has the best of it.

Let's say, however, that your friend really wants to have heads, so he's willing to pay you $1.10 whenever tails comes up but you can pay him $1 whenever heads comes up. Perhaps he's superstitious and finds heads luckier for him. You agree, and start flipping.

Over 500 flips, you win 250 and your friend wins 250. You have paid him $250 and he has paid you $275, giving you a $25 edge. Your EV on each flip of the coin is $.05 (the $.10 divided by the expected number of losses over the long run). Whether you actually win or lose the flip, your EV on each flip is $.05. Even if your friend had gone on a very lucky run and you gave him more money than he gave you, you still have positive EV of $.05 on this proposition. You just need more trials to realize the profit.

The same applies to poker. Whenever you have the best of it, you are experiencing an EV+ situation.

Discussion threads

 * Question for Ed Miller - Retrieved from Archive.org -(Internet Texas Hold 'em forum, July 2004) - Describes how to calculate the EV of a hand preflop; see also leak.