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Expected value (EV)

  • Foundations
  • 8 min
  • Updated October 20, 2026

You call, you lose. Bad decision? Not necessarily. You fold, and you see the card that would have made you win. Good decision? Not necessarily either. To judge a decision, you need a tool that doesn't depend on the result of a single hand: EV.

Definition

EV (expected value) is what a decision earns you on average if you repeated it a very large number of times in the same situation. A +EV decision is one that, repeated a large number of times under the same conditions, earns on average more than it costs; a -EV decision, less. A single hand tells you nothing: the average is what counts.

The formula

EV = Σ p × win

You list every possible outcome, multiply its probability p by its win (negative if you lose), and add them up. If you've listed all the outcomes, the probabilities complete each other.

One detail that prevents mistakes: count the win net. If you pay to win a pot, your win is the final pot minus what you put in.

Example 1: the EV of a call

Let's take a case from the lab's exercise series. You have a flush draw on the flop. The pot is 10 bb, the opponent puts in 7.5 bb all-in. Final pot if you call: 25 bb. Your exact equity is 38.4%.

Two outcomes:

  1. You win, with probability 38.4%. Your net win is 17.5 bb (the final pot minus your call).
  2. You lose, with probability 61.6%. You give up 7.5 bb.

Calculation:

  • Winning part: 38.4% × 17.5 bb = 6.7 bb
  • Losing part: 61.6% × 7.5 bb = 4.6 bb
  • EV of the call = 6.7 bb − 4.6 bb = +2.1 bb

The short formula gives the same result: EV = equity × final pot − your call, so 38.4% × 25 bb − 7.5 bb. The call is +EV.

Another hand, same type of spot: an open-ended straight draw against an overpair, pot of 10 bb, opposing all-in of 12 bb. Final pot 34 bb, exact equity 34.2%. EV of the call: 34.2% × 34 bb − 12 bb = −0.4 bb. Slightly negative: fold. Both situations look like "a draw facing an all-in," and one is good, the other isn't.

Example 2: the EV of a bluff and fold equity

A bluff has no showdown equity to count: it wins when the opponent folds. That probability is called fold equity.

River. The pot is 20 bb, you bet 15 bb with a hand that never wins at showdown. You estimate the opponent folds 50.0% of the time.

  • If he folds: you win the pot, 20 bb.
  • If he calls: you lose your bet, 15 bb.

EV of the bluff = 50.0% × 20 bb + 50.0% × (−15 bb) = +2.5 bb.

Now suppose your estimate was wrong: he only folds 30.0% of the time. The EV becomes 30.0% × 20 bb + 70.0% × (−15 bb) = −4.5 bb. Same bluff, same board, opposite result.

The threshold can be calculated: the minimum fold frequency for this bluff to be profitable is bet / (bet + pot), so here 42.9%. The EV of a bluff rests entirely on an estimate of your opponent's behavior, which is why reading your opponents matters.

A +EV decision can lose tonight

Take the call from example 1, at +2.1 bb. Your equity is 38.4%, so you lose 61.6% of the time. Three times in a row happens with a probability of 23.4%, almost one time in four. You can string together three correct calls and lose all three.

EV is an average: it plays out over many hands, not over one session. The gap between what EV predicts and what you observe is variance. It's neither bad luck following you around nor proof of a mistake: it's the normal way the game works. How many hands it takes for your results to resemble your EV, and how much capital to keep to get through the bad runs: that's the subject of the bankroll lesson.

In any case, judge your decision, not your result: "With what I knew, what was the +EV choice?"

Key points

  • EV is the average win of a decision: the sum of each outcome weighted by its probability, in net wins.
  • The EV of a call is equity × final pot − your call. The EV of a bluff is fold equity × pot, minus the rest of the time × your bet.
  • A +EV decision often loses in the short term: judge the choice, not the result.

Practice