What expected value means in betting

Expected value (EV) is the average amount you'd win or lose per bet if you placed the exact same bet thousands of times. Positive EV means the bet is profitable long-run; negative EV means the house edge is bigger than your estimated advantage. A single bet can win or lose — EV tells you what happens over a large sample of identical decisions.

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. Books build in a vig, so the book-implied probability is usually a few points higher than the vig-free fair probability — see the No-Vig Calculator to back out fair odds before running EV.

Why long-run EV is the only strategy that works

Sports betting has a lot of short-run variance. Even a clearly +EV bet loses roughly the implied percentage of the time. What matters is that you repeatedly make +EV decisions. Over 500 bets at +3% EV each, your bankroll grows. Over 500 -EV bets (even small ones), it shrinks. Variance gets smaller as sample size grows; EV doesn't. This is why serious bettors obsess over edge per bet and sample size, not individual outcomes.

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) are an alternative ground truth — sharps' lines are the market consensus for the true probability minus a small vig.
• 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.