- Bookie Ledger
- Expected value of a bet: calculator, formula and limits
Tool
Expected value of a bet: calculator, formula and limits
Expected value (EV) of a bet is stake × (your probability × decimal odds − 1). It needs odds above 1.00 and your own estimate of the chance of winning. The break-even probability is 1 ÷ odds. Every number on this page is an example, and the probability is your estimate, not ours.
How do you calculate expected value?
Enter decimal odds O, your probability p and your stake S. The result is EV = S × (p × O − 1), in euro.
If the script does not run, use the formula by hand and the table of examples in the next section. This tool does not place bets. Numbers are examples unless you enter your own.
Messages you may see: Enter odds greater than 1.00. · Enter a probability between 0% and 100%. · Stake must be more than €0.
Buttons: Calculate · Reset.
Bottom line: EV = S × (p × O − 1), and the break-even probability is 1 ÷ O.
What do worked examples look like?
| Example | Decimal odds | Your probability | Stake | Break-even probability | Expected value |
|---|---|---|---|---|---|
| Example A | 3.00 | 40% | €10.00 | 33.33% | €2.00 |
| Example B | 2.00 | 45% | €20.00 | 50.00% | −€2.00 |
| Example C | 6.00 | 20% | €10.00 | 16.67% | €2.00 |
| Example D | 1.50 | 70% | €30.00 | 66.67% | €1.50 |
| Example E | 4.00 | 20% | €5.00 | 25.00% | −€1.00 |
| Example F | 2.50 | 40% | €10.00 | 40.00% | €0.00 |
In Example A, 40% × 3.00 = 1.20, so each euro staked returns €1.20 on your estimate and EV is €2.00. In Example F the estimate equals the break-even probability, so EV is €0.00.
A positive EV only means your estimate is higher than the break-even probability. It says nothing about whether the estimate is right.
Bottom line: Example A is positive, Example B is negative and Example F is exactly zero.
What is overround?
For a market with n outcomes, overround = Σ(1 ÷ Oᵢ) − 1. A fair probability for one outcome is (1 ÷ Oᵢ) ÷ Σ(1 ÷ Oⱼ).
| Example | Odds | Sum of 1 ÷ odds | Overround | Fair probabilities |
|---|---|---|---|---|
| Example G | 2.50 / 3.20 / 3.10 | 1.0351 | 3.51% | 38.64% / 30.19% / 31.16% |
| Example H | 1.91 / 1.91 | 1.0471 | 4.71% | 50.00% / 50.00% |
Example G shows three outcomes whose odds imply a total of 103.51%. The extra 3.51% is the margin. Removing it in proportion is one method among several.
Bottom line: Overround is the amount by which implied probabilities exceed 100%.
When is the result wrong?
- Your probability is an estimate. A small error in p changes EV by a large share of the result.
- The break-even probability ignores any margin that you pay in other ways.
- The model treats one bet in isolation and does not describe repeated bets.
- The proportional method for removing overround is one of several; others give different fair probabilities.
This page does not tell you to place a bet. For how we work, see the methodology, and to practise reading a slip, try the bet slip simulator. The comparison matrix holds the operator data.
18+ only. Gambling can be addictive – play responsibly. Free 24/7 support: Gambling Awareness Trust 1800 936 725 · gamblingcare.ie.
Bottom line: The result is only as good as your own probability estimate.