How to calculate expected value from betting odds

For a simple win-or-lose bet with decimal odds d and estimated win probability p, expected profit per unit staked is EV = p × d − 1. Decimal odds include the returned stake. This formula assumes no pushes, commission, tax or other fees.

At p = 0.50 and d = 2.10: EV = 0.50 × 2.10 − 1 = 0.05. That is an expected profit of 5% of the stake under the assumed probability. On a €10 stake, the model expectation is €0.50; the actual bet still wins or loses.

It must come from an estimate, such as a predictive model or a reference market. Taking 1 / odds from the same offered price gives its break-even probability, not proof of value. At odds of 2.10, that break-even probability is about 47.62%.

For two mutually exclusive, exhaustive outcomes each priced at 1.90, the implied probabilities are 1 / 1.90 ≈ 52.63% each. They sum to about 105.26%. Dividing each implied probability by that sum yields 50% per outcome.

This proportional normalization removes the overround arithmetically. It does not establish the true probability, and other margin-removal methods may produce different estimates on uneven markets.

Match the event, selection, line and settlement rules exactly. Check price freshness and market availability. Include exchange commission where applicable and handle pushes or void outcomes separately. Historical profitability requires proper out-of-sample testing; a positive calculated EV alone is not evidence of a profitable strategy.

Explore our value betting API or try the integration guide.