Expected value is a decision rule, not a prediction

Weight each outcome by its probability

Expected value is the probability-weighted average of net outcomes. A bet can lose most of the time and still have positive EV when its winning outcome is sufficiently valuable.

For a final call with 35% equity, a pot of 150 and a call of 50, the EV is 0.35 × 150 − 0.65 × 50 = 20 chips.

E[X] = Σ pᵢxᵢ

Apply the same model to a bluff

Suppose you bet 60 into a pot of 100 and have no chance to win if called. Your opponent folds 45% of the time. A fold wins the existing 100; a call loses your 60. Your own bet returning to you is not additional profit.

The expected value is 0.45 × 100 − 0.55 × 60 = 12 chips, relative to checking and losing. The break-even fold frequency is 60 / 160 = 37.5%.

EV(bluff) = fP − (1 − f)B

A result is not a verdict

A positive-EV call can lose. A negative-EV call can win. Assessing the choice requires the information available when it was made, not hindsight.

Expected value also does not capture every constraint. Variance, risk limits, bankroll and model uncertainty can matter even when the estimated mean is positive.