Staking
Expected value calculator
Expected value is the average result of a bet if it could be repeated indefinitely at the same price. It answers one question: given what you believe the true chance of the outcome is, does the price on offer pay you more or less than that belief is worth?
The arithmetic is trivial. The difficulty is entirely in the probability estimate, and that is where an expected-value figure stops being a fact and becomes an opinion with a decimal point. A credible estimate comes from somewhere you can name — a consensus of several bookmakers with the margin removed, or a model you can describe. A figure quoted without saying where the probability came from is not a measurement.
Inputs
Say where this came from. A de-vigged consensus of several books is a defensible source; a hunch is not.
Result
- Expected valueAverage result per bet over the long run, not the result of this bet
- €2.00
- Expected value as a share of stake
- +20.00%
- Fair odds at your probabilityThe price at which this bet would break even
- 2.500
- Break-even probability of the offered priceYou need to be at least this confident for the bet to be worth taking
- 33.33%
- Edge over fair
- +20.00%
A positive expected value does not mean this bet wins. It is a long-run average, and the variance around it is large — a positive-EV bet loses most of the time at long odds. The figure is also only as good as the probability you entered; if that estimate is out by a little, the sign of the answer can change.
How this is calculated
EV = S x (p x o - 1)
S is the stake, o the decimal odds and p your estimated probability. The bet wins p of the time and returns S x (o - 1); it loses the remaining (1 - p) of the time and costs S. Multiplying out gives S x p x (o - 1) - S x (1 - p), which simplifies to S x (p x o - 1). The bet breaks even exactly when p x o = 1, i.e. when the offered price equals 1 / p. That is why the break-even probability of a price is simply its implied probability: at odds of 3.00 you need to win more than one time in three.
Worked example
A EUR 10 bet at 3.00 where a de-vigged consensus of several bookmakers puts the true chance at 40%.
- 01The offered price of 3.00 implies a probability of 1 / 3.00 = 33.33%. That is the break-even point.
- 02Your estimate is 40%, which is higher, so the price is longer than it should be.
- 03Fair odds at 40% would be 1 / 0.40 = 2.50.
- 04EV = 10 x (0.40 x 3.00 - 1) = 10 x 0.20 = EUR 2.00.
- 05As a share of stake that is +20%, and the price is 3.00 / 2.50 - 1 = 20% longer than fair.
- 06Over many such bets you would expect to average EUR 2 profit per EUR 10 staked — but this individual bet still loses 60% of the time.
Questions
Where should the probability estimate come from?
The most defensible everyday source is the market itself: take the prices several bookmakers offer on the same market, remove the margin, and use the resulting consensus. That gives you a probability derived from the aggregate opinion of people with money at stake. Using a single bookmaker's price is circular — it will always tell you the bet is break-even.
Why is my long-run result worse than the expected value suggested?
Usually because the probability estimate was optimistic, which is the most common failure and the hardest to notice. Other causes are real: prices shorten before you can place, stakes get limited or refused, and accounts get restricted precisely when the estimates are good. Expected value describes the price you actually got on the stake you actually placed.
Does positive expected value mean the bet is a good idea?
It means the price is favourable relative to your estimate. It says nothing about whether the stake is appropriate for your bankroll, how long you would need to bet for the average to assert itself, or whether you can absorb the losing runs on the way. Stake sizing is a separate question.
Related calculators
These calculators are information tools. They describe the arithmetic of the prices you enter — they are not advice, and they do not predict outcomes. Betting involves risk. 18+ only. If gambling is causing you harm, support is available from Peluuri.