Expected value calculator
Compare the price you can take with your estimate of the chance of winning. Free, no sign-in.
Your bet
INSTANTNeed a fair estimate? Start with the no-vig calculator.
Positive EV under your estimate
Average modeled profit or loss for a $100.00 stake.
No pushes or refunds assumed. The break-even rate is the win chance needed at this price.
EV is an average under your probability estimate, not the result of this individual bet.
How to calculate expected value in sports betting
Check the offered price against your estimate
- Choose American or decimal odds, then enter the offered price and your stake.
- Enter your estimated win probability or switch to fair odds. Both express the same estimate.
- If the bet can push, enter its refund chance. The win estimate excludes refunded outcomes.
- Read expected profit in dollars, expected ROI and the break-even win rate.
For −110 odds and a 55% win estimate, a $100 stake has +$5.00 expected value and +5.00% expected ROI, assuming no refunds. The break-even win rate at −110 is 52.38%.
Convert prices with the odds converter. Use the no-vig calculator to remove proportional market margin before using a market-based fair estimate.
The betting EV formula
Let p be your win probability, d the offered decimal odds and S the stake. Without refunds: EV = S × [p × (d − 1) − (1 − p)]. Expected ROI is EV divided by stake, equivalent to p × d − 1. Profit excludes the returned stake.
With refund probability q, use a win estimate conditional on no refund: EV = S × (1 − q) × (p × d − 1). A 10% refund chance reduces the +$5.00 example to +$4.50. The conditional break-even win rate remains 1 ÷ d when some outcomes settle as wins or losses.
For parlays, use the actual combined quote and a joint win estimate. The NFL line comparison and alternate line tools compare prices under a historical model; neither proves your entered probability is correct.
Expected value examples for a $100 stake
| Offered odds | Win estimate | EV / ROI |
|---|---|---|
| −110 | 55% | +$5.00 / +5.00% |
| +150 | 45% | +$12.50 / +12.50% |
| −110 | 50% | −$4.55 / −4.55% |
A positive number depends on the win estimate being accurate. The no-vig calculator provides a market-based estimate by removing proportional margin from all opposing prices. It does not establish the true probability.
Expected value calculator FAQs
What is expected value in betting?
Expected value is the probability-weighted average profit or loss of a wager. Positive EV means the offered price is favorable under your estimate; negative EV means it is unfavorable. The result depends on the accuracy of that estimate.
What is the difference between EV, ROI and probability edge?
EV is expected profit in dollars. Expected ROI is EV divided by stake, shown as a percentage. Probability edge is your win estimate minus the price-implied break-even rate, measured in percentage points; it is not the same as ROI. A zero-dollar stake has $0 EV, but this calculator still shows the per-dollar expected ROI.
Where do I get a fair win probability?
Use a model you have tested or a market-based estimate from all opposing prices in the no-vig calculator. Removing margin is an assumption about how a market is priced, not proof of the true chance. The implied probability of the offered price alone is its break-even rate.
Can I enter fair odds instead of a percentage?
Yes. Select Fair odds and enter your estimate in American or decimal format. VigFox converts it using win probability = 1 ÷ fair decimal odds. Displayed American odds are rounded; calculations keep unrounded values. At 0% or 100%, use probability mode because there is no finite ordinary fair betting price.
How does the EV calculator handle pushes?
Enter the chance of a full stake refund separately. Your win estimate must be conditional on a result that does not push. With a 55% conditional win estimate and 10% refund chance, the unconditional chances are 49.5% win, 40.5% loss and 10% refund. A $100 bet at −110 then has +$4.50 EV. If all outcomes refund, EV is zero and a break-even win rate is not meaningful.
Can a positive EV bet still lose?
Yes. Positive EV describes an average under your assumptions, not a guaranteed result or a staking recommendation. A single bet can lose the full stake. This tool does not account for taxes, fees, partial settlements or promotions.
Can I calculate a parlay’s expected value?
Yes, using the combined offered price and your estimate of the chance that all active legs win. Multiplying leg probabilities assumes independence and can misprice correlated same-game legs. The parlay calculator supplies standard combined prices and winning payouts, not true win probabilities.