Expected value (EV) in betting: formula and examples

The formula

Expected value is calculated as: EV = probability × odds − 1. The result is expressed as a percentage or in euros per unit staked: a positive EV means the bet should turn a profit over time, a negative one a loss. The higher the positive EV, the more value in each bet, but the outcome of any single bet doesn't follow directly from this number — it only describes the average over many repetitions.

The EV figure is best understood as a long-run average, not a promise about any single bet. It's a bit like how an insurance company knows in advance it will profit on average across thousands of policies, even though any one customer could file an expensive claim — a positive EV only pays off once many independent bets are added together.

Implied vs true probability

Every set of odds carries an implied probability — one divided by the odds. But that implied probability is always a bit higher than the true one, because it includes the bookmaker's margin. To calculate EV correctly you need your own probability estimate with the margin removed — the best source is a sharp line, or several bookmakers' prices agreeing with each other.

The formula EV = probability × odds − 1 can also be read the other way round: the implied probability of a set of odds is 1 / odds, so EV is positive exactly when your probability estimate is higher than that implied probability. Because the implied probability always includes the bookmaker's margin, the comparison only makes sense once that margin is stripped out — otherwise you're comparing your estimate to a number that's inflated from the start.

Variance and sample size

Variance in betting is large: even with a clear edge you can run into a losing stretch in the short term, and without an edge you can win several times in a row by pure luck. The more independent bets you add together, the closer the actual result moves toward the expected one — which is why the result of a single day, or a single bet, proves nothing about your strategy.

Picture it this way: if you flip a coin with a small edge toward one side, a run of ten flips can still be misleading, but a run of a thousand flips makes the edge obvious. Betting works on the same logic, just with real money and a real expectation attached.

Judge the decision, not the result

Because the short-term result says almost nothing about the quality of a decision, it's worth recording the odds you took and the fair odds you estimated at the time — not just whether the bet won. Over time, comparing the price taken against the fair price shows whether your decisions systematically carry a positive EV, regardless of how any single match turned out.

Rank by EV, not by the raw odds

Choosing between several bets, it's natural to look at the highest number, but a high number often just means high risk rather than high value. The right comparison isn't the odds themselves but the EV: a bet at 1.80 with a clearly positive EV can be a better pick than a bet at 4.00 whose EV is negative or barely positive.

This matters most when you're looking at several matches or markets at once: when deciding what to bet on first, it's worth sorting by EV percentage rather than by the size of the odds. That ordering naturally puts the prices that deviate the most from the true probability at the top, regardless of whether they look “big” or “small”.