Expected Value (EV)

Expected value (EV) is the average result of a bet if it were repeated indefinitely. It is calculated as EV = (probability of winning × amount won) − (probability of losing × amount lost). A fair coin flip at even money has an EV of zero; any bet carrying a house edge has negative EV for the player, while a genuine value bet has positive EV. Worked example: a single-number bet on European roulette pays 35:1 and wins with probability 1/37. Staking £1, EV = (1/37 × £35) − (36/37 × £1) = £0.946 − £0.973 = −£0.027. That −2.7% is precisely the house edge. Over 1,000 spins at £1, you would expect to lose around £27, regardless of any short-term swings. EV matters because it is the single clearest explanation of why the house wins over time and why professional bettors hunt for positive-EV prices. Decisions that look good in the moment can be quietly negative; decisions that feel risky can be positive. The common mistake is judging a bet by its last result rather than its expectation — a few wins can mask a steadily negative EV, and the belief that an outcome is overdue is simply the Gambler's Fallacy. A negative-EV game cannot be beaten by staking systems alone. See House Edge, Value Bet, Implied Probability and Variance.