Expected Value Formula

The Expected Value Formula is the calculation that multiplies each possible outcome's payout by its probability, then sums those results, to reveal whether a bet is profitable over the long run. Written out, EV = (probability of winning x amount won per bet) minus (probability of losing x amount staked). A positive result means the wager gains value over time; a negative result means it loses value. Every bookmaker margin and casino house edge exists to keep the player's EV negative, so finding positive-EV opportunities is the core skill of any sharp bettor or advantage player. To use it, convert the odds into a decimal figure, translate the true probability into a percentage, and plug both into the equation. The gap between the bookmaker's implied probability and your own estimate is where value hides. Worked example: you back a team at decimal odds of 2.50 and stake 100 units. You judge the true win probability at 45%, so the loss probability is 55%. A win returns 150 units profit; a loss costs your 100-unit stake. EV = (0.45 x 150) minus (0.55 x 100) = 67.5 minus 55 = +12.5 units. On average this bet earns 12.5 units per attempt, marking it a value bet worth repeating. Because EV is a long-run average, a single wager can still lose despite positive EV; variance dominates the short term. Bankroll management and staking discipline let the mathematical edge play out over hundreds of bets. Compare with expected value, value bet, implied probability and the Kelly criterion.