Expected value of a bet: from odds and your own estimate to a result
Expected value (EV) is the average result of a bet if your own probability estimate were right: stake × (probability × decimal odds − 1). At odds of 2.00 and an estimate of 45%, an A$20 stake has an EV of −A$2.00. Your estimate is an opinion, not a fact, and a positive figure on paper does not predict any single result.
Calculate
Enter a stake in A$, decimal odds of 1.01 or more, and your own estimate of the chance as a percentage. The tool shows the implied probability, the break-even point and the expected value.
Use Calculate to run it and Reset to clear it. Results are illustrative, not a price.
If the tool does not load, the formulas and the six worked examples below work without it.
Where this stands: the tool runs in the browser; the static table below repeats its logic.
The formulas
- Implied probability q = 1 ÷ O, where O is the decimal odds.
- Expected value EV = S × (p × O − 1), where S is the stake and p is your estimate as a fraction.
- Break-even probability = q. At p equal to q, EV is zero.
- Market margin = (sum of 1 ÷ O for every outcome) − 1.
The inputs are a stake S, odds O of at least 1.01, and an estimate p from 0 to 100%. These are definitions and are rechecked once a year.
Where this stands: four formulas, all stated in full and checkable by hand.
Six worked examples
| Stake | Odds | Your estimate | Implied probability | Expected value |
|---|---|---|---|---|
| A$20 | 2.00 | 45% | 50.00% | −A$2.00 |
| A$25 | 3.50 | 30% | 28.57% | +A$1.25 |
| A$50 | 1.60 | 60% | 62.50% | −A$2.00 |
| A$15 | 6.00 | 15% | 16.67% | −A$1.50 |
| A$40 | 2.20 | 50% | 45.45% | +A$4.00 |
| A$100 | 1.25 | 75% | 80.00% | −A$6.25 |
Working for the first row: 20 × (0.45 × 2.00 − 1) = 20 × (−0.10) = −2.00.
Where this stands: two of the six examples are positive, and only because the invented estimate beats break-even.
Reading the result
A positive EV says your estimate is above the break-even chance. It does not say the estimate is right. Market prices already carry a margin: prices of 1.85 and 2.05 imply 54.05% and 48.78%, a total of 102.83%, so the margin is 2.83%.
Learn more in implied probability and the overround page. For the evidence on long-run results, see can you win consistently betting online? and are bookmaker odds fair?.
Where this stands: EV compares your estimate with the price; it says nothing about a single bet.
What this tool does not do
It does not suggest bets, rank prices or forecast results. It does not store what you enter. Set limits before you play: set a deposit limit, and register with BetStop if you want to exclude yourself. Other help is on the responsible gambling page.
Where this stands: the tool teaches arithmetic and makes no recommendation.
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FAQ
What is expected value?
It is the average result of a bet if your own probability estimate were right: stake × (probability × odds − 1). It is not the result of any single bet.
What does a negative expected value mean?
On your estimate, the bet loses money on average. At odds of 2.00 and an estimate of 45%, an A$20 stake has an expected value of −A$2.00.
Does a positive figure mean I will win?
No. It shows only that your estimate beats the break-even chance. Any single bet still wins or loses outright, and your estimate is an opinion, not a fact.
What odds can I enter?
Decimal odds of 1.01 or more. Anything lower returns the message: Enter odds of 1.01 or more.
How is the market margin worked out?
Add 1 ÷ odds for every outcome in the market and subtract 1. For prices of 1.85 and 2.05 that gives 0.5405 + 0.4878 − 1 = 2.83%.