What is expected value in betting?

The average result of a bet if it could be repeated many times: probability of winning times profit, minus probability of losing times stake. Positive expected value means the price is longer than your probability justifies.

Your probability multiplied by the decimal price, minus one — the expected value per unit staked. A 50% chance at 2.20 is 0.5 × 2.2 − 1 = 10%. It is the number this site’s value detection uses, with a 4% minimum.

A bet has positive expected value. Will it win?

No more often than the probability says. A 10% edge at 2.20 still loses half the time. Expected value is about the long run, and even a genuine edge produces losing runs of fifteen or more.

How reliable is my probability?

That is the whole question, and no calculator can answer it. A model fitted on results and expected goals carries real error; a hunch carries more. Treat a thin edge as noise, and treat a huge edge with suspicion: it usually means the market knows something you do not.

Free tool

Expected value calculator

Your probability against the price: the edge, the value per unit, and where break-even sits.

Your probability

How likely you think the outcome is.

Price on offer

Any format.

Stake

Any currency or units.

Edge: +10.0%; probability × price − 1
Expected value per unit: +0.100
Expected value of this stake: +1.00
Break-even probability: 45.5%; the chance at which this price is fair
Your fair price: 2.00

Positive expected value at the threshold we use ourselves (4%). Whether it is a bet still depends on how much you trust the probability: the edge is only as good as the estimate behind it.

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The one calculation that matters

A bet is worth making, on your numbers, when the price on offer is longer than the fair price for your probability. Expected value puts that in units: probability × (price − 1) − (1 − probability), which simplifies to probability × price − 1. Positive means the average outcome over many such bets is a profit; negative means a loss.

The break-even probability is the other way of reading the same thing. It is one divided by the price — the chance at which the bet is exactly fair. If your probability is above it, the price is value to you.

Why a threshold, and why a cap

This site advises a bet only when the modelled edge is at least 4%, because probability estimates carry error and an edge of one or two per cent is indistinguishable from noise. It also declines to advise when the edge exceeds 50%: a disagreement that large between a model and every bookmaker is far more likely to be a flaw in the model — a missing line-up, a side it has barely seen — than a mispriced market.

Questions

What is expected value in betting?: The average result of a bet if it could be repeated many times: probability of winning times profit, minus probability of losing times stake. Positive expected value means the price is longer than your probability justifies.
What is the edge?: Your probability multiplied by the decimal price, minus one — the expected value per unit staked. A 50% chance at 2.20 is 0.5 × 2.2 − 1 = 10%. It is the number this site’s value detection uses, with a 4% minimum.
A bet has positive expected value. Will it win?: No more often than the probability says. A 10% edge at 2.20 still loses half the time. Expected value is about the long run, and even a genuine edge produces losing runs of fifteen or more.
How reliable is my probability?: That is the whole question, and no calculator can answer it. A model fitted on results and expected goals carries real error; a hunch carries more. Treat a thin edge as noise, and treat a huge edge with suspicion: it usually means the market knows something you do not.

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A calculator turns your numbers into other numbers. It does not know whether your numbers are right, and no arithmetic makes an outcome certain. Never stake money you cannot afford to lose.