Pokeriad / Learn / Expected value
Updated November 2026
Expected value, or EV, is what a decision makes on average if you could repeat it forever. List what can happen, multiply each result by how often it happens, and add them up. If the total is above zero, the play makes money.
EV = chance × result + chance × result + ...
Say someone offers you $3 if a coin lands heads, and you pay $1 if it's tails. You win $3 half the time and lose $1 half the time, so the average is $1 per flip.
You could lose four flips in a row, and it'd still be a great bet. EV tells you what's good. It doesn't tell you what's going to happen next.
Take a flush draw on the turn, with one card to come and no more betting.
He bets $25, so you can win $125 by paying $25. You have 9 outs out of 46 unseen cards.
That part is worth 0.196 × $125, or +$24.46.
You lose your $25. That part is worth −$20.11.
Add them up. Every time you make this call, it earns $4.35 on average, and you'll still lose it four times out of five.
The same sum. You bet $50 into a $100 pot and he folds 45% of the time. When he folds you win $100, and when he calls you lose $50.
It's worth +$17.50, assuming you give up whenever he calls. How to bluff has a calculator for this.
Work out the EV of each and choose the bigger one. Folding is worth zero from this point, because anything you already put in is gone either way.
A call worth +$4 beats a fold. A call worth −$6 loses to a fold. A raise worth +$10 beats a call worth +$4, even though both make money.
A raise has more branches, so write them down one at a time. Say the pot is $100, he bets $50 and you have a flush draw that hits 35% of the time. To keep it simple, the money stops going in after this.
If you raise to $150 and he folds 30% of the time, you win $150. If he calls, you win $250 with 35% and lose $150 with 65%, and that branch is worth −$10.
Putting the branches together gives +$38. A plain call, at $50 to win $150, is worth +$20. So the raise earns more, and you'd never have known without doing the sum.
Yes, when every other option is worse. You're in the small blind with 10 big blinds and you've got 0.5 in the pot. Fold and you've lost that 0.5.
Shove with a hand that wins 40% when called, against a player who folds 62% of the time, and the sum comes to −0.14 big blinds. That's a loss, and it's still 0.36 better than folding.
They add a result you haven't won yet. A gutshot on the turn hits 8.7% of the time. Facing a $50 bet into a $100 pot, the call loses money on the current pot alone.
For it to break even you need another $375 from him when you hit. So write that into the sum, and then ask whether he has that much left and would really pay it.
Because it's gone. The money you put in on earlier streets belongs to the pot now. All you need to count is what you pay from here and what you can win.
"I've already put so much in" is one of the most expensive thoughts in poker.
Because EV is an average, and any single result sits far from it. The +$4.35 call above loses most of the time, and it can take hundreds of tries to show up. Variance covers how long that takes.
Players measure their win rate in big blinds per 100 hands. A win rate of 5 at a $1/$2 live game means $10 for every 100 hands, and at 30 hands an hour that's about $3 an hour.
That's a good win rate and a very small wage. It's one reason to play for the enjoyment of the game and keep your job.
In a cash game, yes. In a tournament, no. Near the prize money, the chips you could lose are worth more than the chips you could win, so a play that gains chips can still lose money. ICM is how players measure that.
Twelve spots in three rounds, with new numbers each time.
The play makes money on average. -EV means it loses money on average.
In a cash game with a proper bankroll, yes. If the risk could knock you out, you may want a safer play with a lower EV.
Rough versions, yes. Do the exact sums away from the table so you know how the common spots come out.
The play neither makes nor loses money on average. You'd do as well folding.
These are simple multiplications, shown as they go. The chance of hitting comes from counting the unseen cards. The figures for being ahead come from an exact formula for one call repeated many times.
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