The three formulas
EV of a call = equity × (pot + bet) − (1 − equity) × bet
Bluff break-even = bet / (bet + pot)
General EV = P(win) × win amount − P(lose) × loss amount
Examples
Calling. Pot $150, bet $100, your equity 30%. EV = 0.30 × 250 − 0.70 × 100 = 75 − 70 = +$5. Marginal, but a call.
Bluffing. Pot $100, you bet $75. The opponent must fold 75 / 175 = 42.9% of the time for the bluff to break even, ignoring the times you get called and still win.
General. A 40% shot at winning $150 while risking $50 has EV = 0.4 × 150 − 0.6 × 50 = +$30.
Where the numbers come from
Equity comes from the Hold’em, Omaha or range calculators. Fold frequencies are estimates about the opponent, which is why bluff EV is always less certain than call EV. Tournament decisions also need ICM, because chips and money are not the same thing.
Frequently asked questions
What is expected value in poker?
The average amount you win or lose by making a decision, if you could repeat the exact situation many times. A +$5 call earns $500 over 100 repetitions even though any single instance wins or loses the whole pot.
How often must a bluff work?
Bet divided by bet plus pot. A pot-sized bluff needs a fold 50% of the time; a half-pot bluff needs 33%; a 2× overbet needs 67%. If the opponent folds more often than that, the bluff shows a profit even when it never wins at showdown.
Is a +EV call always right?
It is better than folding, but a raise might be even better. EV compares options; always ask what the EV of the alternative is.