CALCULATING EV

[Cody1982]

I have a few basic questions. I hear these terms and see them in them in forums and think it's about time I found out what they were. Hope you can help.

What is EV and how do you calculate it ?

What is fold equity and how do you determine it ?

Is cEV the same as EV ?

[ChrisV]

EV is short for expected value. It is the amount you would win or lose over the long term, on average, by making a certain play. You should always try to maximise your EV.

For instance, suppose the pot is $100 and you are facing a bet of $50. Your opponent's betting range is such that you will win 40% of the time if you call. The times you call and win you will win $150 and the times you call and lose you will lose $50. Therefore the EV of calling is:

40% * $150 - 60% * $50

= $60 - $30

= +$30

The EV of folding is zero, so you should call.

Fold equity is a gain in EV that comes from making your opponent fold by betting or raising. For instance, suppose you are currently ahead in a $100 pot, but that your opponent will draw out on you 25% of the time. If you check it down, his EV will be $25. You can steal that EV from him by betting $100 instead. He doesn't have the odds to call, so he must fold, making his EV zero (and increasing yours from $75 to $100). Fold equity is one of three ways you might increase your EV by betting; the others are bluffing (making your opponent fold a better hand) and getting value (having your opponent call with a worse hand). Fold equity and value are two sides of the same coin - by betting with a better hand, you make your opponent give you one or the other.

cEV is short for chip EV. It is used in tournaments because the amount of money chips are worth changes over the course of the tournament. To see that this is so, imagine you're in a 100-player tournament with a $5,000 buyin and 5,000 starting chips. If you manage to collect all the chips (500,000) then you will win the tournament and get typically around 40% of the prize pool - around $200,000. In a cash game, if you won 500,000 chips, you would actually have $500,000, because all the chips are still worth a dollar. So cEV is your expected value from a tournament chip point of view, and its counterpart $EV is your expected value from a real world money point of view.