Expected value calculator
Expected value (EV) is what a bet returns on average, per bet, if you could place it many times. Enter the decimal odds, the win probability you believe and your stake to see the EV in money, as a share of the stake, and the probability at which the bet breaks even.
Averaged over many bets like this one, you would expect to gain 9.20 per bet (9.20% of the stake). Any single bet still either wins or loses.
- Profit if it wins
- 110.00
- Loss if it loses
- 100.00
- EV as % of stake
- 9.20%
- Break-even probability
- 47.62%
What expected value means
A single bet either wins or loses, so its result never equals its EV. EV is the average over many identical bets. A bet with positive EV is one whose price pays more than your probability requires; a bet with negative EV loses on average even when it wins today.
The EV formula
With stake s, decimal odds d and win probability p, the profit if the bet wins is s × (d − 1) and the loss if it loses is s.
A worked expected value example
Stake 100 at decimal odds of 2.10 with a 52% win probability. A win pays 110 and a loss costs 100, so EV = 0.52 × 110 − 0.48 × 100 = 57.20 − 48.00 = +9.20, which is 9.20% of the stake. The break-even probability at 2.10 is 47.62%.
If the true probability is 45% instead, EV = 0.45 × 110 − 0.55 × 100 = −5.50. The same price is a losing bet when the probability estimate is lower. That is why the estimate matters more than the arithmetic.
EV, margin and fair odds
A sportsbook's prices for all outcomes add up to more than 100%. The excess is its margin, so backing an outcome at the quoted price is negative EV against the fair price. The implied probability calculator removes the margin to show fair odds, which is the usual reference for judging whether another sportsbook's price has positive EV.
What an EV figure leaves out
Read a positive EV as an estimate, not a result:
- It depends on your probability, which is an estimate and can be wrong.
- It is an average: a run of losses is normal even at positive EV, which is why stake size matters (see the Kelly criterion calculator).
- Prices move, bets can be rejected or voided, and stake limits apply.
- Fees, taxes and currency conversion are not in the figure.
Frequently asked questions
How do I calculate expected value in betting?
Multiply the profit if the bet wins by the win probability, then subtract the stake times the probability of losing. At 2.10 with a 52% probability and a stake of 100 the result is +9.20.
What is +EV betting?
A bet with positive expected value: its price pays more than your win probability requires, so it gains on average over many similar bets. It does not mean any single bet wins.
What is the break-even probability?
It is 1 divided by the decimal odds, the probability at which the EV is exactly zero. At 2.10 it is 47.62%; a bet is worth backing only if you believe the probability is higher.
Is positive EV the same as arbitrage?
No. An arbitrage covers every outcome and returns more than the total staked on every result, if all bets are placed and settled as expected. A positive EV bet covers one outcome and can still lose.
How do I find a fair probability?
Remove the margin from a sportsbook's prices with the implied probability calculator, or use your own model. The result is only as good as the source.
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