Expected Value Calculator

E[X] = sum of (each outcome × its probability). It's the long-run average result if the scenario were repeated many times, even if no single trial produces exactly that value.

A negative EV means that, on average, you lose over the long run — common in casino games and most gambling bets, where the house edge guarantees a negative EV for players.

Variance = E[X²] − (E[X])², where E[X²] is the sum of (each outcome squared × its probability). Standard deviation is the square root of variance.

Yes. For a valid probability distribution, all the probabilities must sum to exactly 1 (100%). If they don't, the expected value calculation isn't meaningful.