Expected Value Calculator

What expected value means in betting

For a win-or-lose bet with no push, expected return on stake is model probability × decimal odds − 1. Multiply by 100 to express it as EV%. A bet is positive EV under the model only when its probability exceeds the breakeven probability of the offered odds. The estimate depends on the model being accurate; it is not a guaranteed profit.

How EV is calculated

EV combines three inputs: the payout if you win (derived from the odds), the loss if you lose (your stake), and the probability you assign to winning.

• Profit if win = stake × (decimal odds − 1)
• Loss if lose = stake
• EV$ = (win probability × profit) − (lose probability × loss)

Worked example: You bet $100 at +150 odds (decimal 2.50). You estimate a 45% chance of winning. Profit if you win: $100 × 1.50 = $150. Loss if you lose: $100. EV = 0.45 × $150 − 0.55 × $100 = $67.50 − $55 = +$12.50. That's +12.5% EV on stake — over a long sample of identical bets, you'd average $12.50 of profit per bet.

Breakeven probability

The book's odds imply a probability. At +150, the implied probability is 40% (100 / (150+100) × 100). If your estimate of the true probability is higher than 40%, the bet is +EV. If lower, it's -EV. Use the offered price to calculate return. A vig-free probability can provide a separate market reference, but does not change the payout or its breakeven threshold. The No-Vig Calculator estimates that reference from a complete market.

Expected return and variance

If the true win probability is 60%, the bet loses 40% of the time regardless of whether its offered price gives it positive EV. Positive EV describes an expected average, not a promise that a particular bet or a sequence of 500 bets will profit. With independent, comparable bets, the uncertainty in average return decreases as the sample grows, but total dollar swings can still grow. Model error and correlated outcomes add risks that a larger sample does not remove.

Estimating true probability is the hard part

The math of EV is trivial. The hard part is knowing your win probability with enough accuracy to beat the book. Most bettors dramatically overestimate their edge. Disciplined approaches:

• Models that simulate the event (like Mongoose Bets' 2,500-sim Monte Carlo for MLB) produce probability distributions you can compare to book-implied fair probability.
• Sharp-book fair odds (from Pinnacle, Circa) provide a market-based reference after removing the margin. That reference is an estimate, not ground truth.
• Calibration tracking — record your probability estimates and actual outcomes. If you say 60% and outcomes hit 51%, your estimates are overconfident and need a haircut.