Smarter Than Free calculator
Expected Value Calculator
Stake, odds (any common format) and your win probability -> expected value, EV%, edge and break-even probability.
Calculator
How do you calculate expected value for a bet?
EV = p × profit_if_win − (1 − p) × stake. Positive EV means the price is good if your probability is right.
What is break-even probability?
Break-even = 1 ÷ decimal odds. Your edge is your probability minus that break-even.
Can a positive EV bet still lose?
Easily. At 40% to win on decimal 3.0 the EV is +£2 on £10, and you still lose 60% of the time. Ten straight losses has a probability of 0.6%, which over enough bets is a Tuesday.
What if your probability estimate is wrong?
The EV moves fast. Same £10 at decimal 3.0: at 40% EV is £2.00, at 35% it is £0.50, and at 30% it is −£1.00. Ten points of overconfidence turns a good bet into a bad one.
What is the difference between expected value and Kelly?
EV tells you whether a bet is worth making. Kelly tells you how much of your bankroll to put on it. You need the first answer before the second is any use.
A £10 bet at decimal odds of 3.0, by your win probability
Break-even is 1 ÷ 3.0 = 33.3%. Below that, the bet loses on average however good it feels.
| Your probability | Edge | EV | EV % |
|---|---|---|---|
| 25.0% | −8.3 pp | −£2.50 | −25.0% |
| 30.0% | −3.3 pp | −£1.00 | −10.0% |
| 33.3% | 0.0 pp | £0.00 | 0.0% |
| 35.0% | 1.7 pp | £0.50 | 5.0% |
| 40.0% | 6.7 pp | £2.00 | 20.0% |
| 50.0% | 16.7 pp | £5.00 | 50.0% |
The formula
Profit if win = stake × (decimal odds − 1) EV = p × profit_if_win − (1 − p) × stake EV% = EV ÷ stake Break-even probability = 1 ÷ decimal odds Edge = your probability − break-even probability
Worked example
Stake £10 at decimal 3.0. You think win chance is 40%.
Break-even = 33.3%. Edge = 6.7 percentage points.
EV = 0.4×20 − 0.6×10 = £2. EV% = 20%.
Methodology
How it calculates
- EV from stake, decimal odds and your probability. Also shows break-even probability and edge.
Formula
Profit if win = stake × (decimal odds − 1) EV = p × profit_if_win − (1 − p) × stake EV% = EV ÷ stake Break-even probability = 1 ÷ decimal odds Edge = your probability − break-even probability
Assumptions
- EV assumes your probability is right. Variance still hurts.
Edge cases
- Break-even probability = 1 ÷ decimal odds. Edge = your probability − break-even.
Sources
None. Pure maths; no external rate or spec feed.
FAQ
Is positive EV a guarantee?
No. It is an average if your probability is right. Variance still hurts.
Not financial advice. This calculator is for education only. Double-check results before you make money decisions. Past moves do not predict future ones.