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Expected value
What expected value means, how to compute it for a call or for a bet that can win the pot at once, and why folding is the zero point.
A reference page: an idea the course assumes, without practice or progress. Lessons link here the first time they use the term.
On this page
- Work out EV by weighting each outcome by its chance and adding them up.
- Treat folding as the zero baseline every other option is measured against.
- Compute the EV of a call and of a bet that can make the opponent fold.
- Explain why many profitable plays still lose more often than they win.
- Read Rail's EV loss as the gap between your choice and the best option.
The average over everything that can happen
Expected value is what a decision wins or loses on average, if you could make it many times. Take each way the hand can go, multiply what it pays by how often it happens, and add the results up.
EV equals the sum, over every outcome, of its probability times its result.
- result
- what you win or lose from this point on, in big blinds
Count from where you stand now. Chips you put in earlier are part of the pot, not yours, so folding is always worth exactly 0. Every other option is measured against that.
The EV of a call
On the river the pot is 20 bb and your opponent bets 10 bb. You think your hand wins 30% of the time. Calling has two outcomes: 30% of the time you win the 30 bb in the middle, and 70% of the time you lose your 10 bb.
EV = 0.3 × 30 − 0.7 × 10 = 9 − 7 = +2 bb. The pot-odds shortcut gives the same answer in one line: equity × final pot − call = 0.3 × 40 − 10 = 12 − 10 = +2 bb.
Bets that can win two ways
A bet wins in two ways: your opponent folds and you take the pot now, or he calls and you play on with your equity. Its EV adds the two branches together.
The EV of a bet equals how often they fold times the pot, plus how often they call times the bet's EV when called.
On the turn the pot is 20 bb and you bet 10 bb with a draw. Say he folds 40% of the time, and when he calls you have 25% equity with no more betting. When called, the bet is worth 0.25 × 40 − 10 = 0. So the bet is worth 0.4 × 20 + 0.6 × 0 = +8 bb.
Now make it a pure bluff that never wins when called. The called branch costs 10 bb: 0.4 × 20 − 0.6 × 10 = 8 − 6 = +2 bb. The draw's equity is worth 8 − 2 = 6 bb here.
- Alpha: folds needed
- 33.3%
- EV if it never wins when called
- +2 bbProfitable
Winning pots is not the goal
The +2 bb call above loses 7 times out of 10. A player who only calls when he is ahead wins more of the pots he plays, and less money. The bluff that works 40% of the time loses more often than it wins, and still earns.
So count EV in big blinds, never pots won. Many of the best plays in poker lose most of the time; they just win more than they lose when they work.
EV loss: the gap to the best option
Every option in a spot has an EV, and the best one sets the bar. Rail's EV loss is the best option's EV minus the EV of the one you chose. In the 30% river spot, calling is worth +2 bb and folding 0, so a fold loses 2 bb. At 20%, folding is best and the call loses 2 bb.
Two of Rail's checks are pure EV logic. Folding when you could check for free always loses, because checking keeps your share of the pot at no cost. And folding the best possible hand gives up everything it would have won.
- Grade
- Perfect
- EV loss
- 0.03 bb · 0.3% of the pot
- Score
- 97
Rules of thumb
- EV = the sum of probability × result over every outcome, counted from now.
- Folding is worth 0; every other option is measured against it.
- A bet's EV = fold share × pot + call share × EV when called.
- Judge plays by EV in big blinds, not by how often they win the pot.
When they break
- These trees assume no more betting after a call. With streets still to come, what happens later changes the EV of the called branch in both directions.
- The inputs are estimates. A tree built on a wrong fold rate or equity gives a precise-looking wrong answer.