Direct Answer
Expected value (EV) is the probability-weighted average payoff of a bet repeated infinitely. Positive-EV bets gain money on average over many trials; negative-EV bets lose money on average. Long-run profit is the sum of expected values, not the count of winners and losers.
Key Takeaways
- EV is the probability-weighted sum of outcomes.
- A losing bet can be the correct bet.
- Long-run profit equals total EV, not win count.
- Beating the closing line validates EV estimates.
The formula
EV = Σ p(outcome) × payoff(outcome). For a single binary bet of $100 at +150 on a 45% outcome: EV = (0.45 × $150) + (0.55 × -$100) = $12.50 per $100 staked.
Why outcomes mislead
A correct bet can lose. A wrong bet can win. Evaluating decisions on single outcomes is the single most expensive habit in amateur betting. Professionals evaluate inputs (price, probability estimate, execution) and results only over large samples.
Where EV comes from
Every EV estimate rests on a probability estimate. If your probabilities are not better-calibrated than the market's, your perceived edges are noise. Closing line value is the cleanest real-world proxy for whether your estimates beat the market.
Frequently asked questions
Is positive EV guaranteed to profit?+
Over enough trials, yes. Over small samples, variance dominates and any single positive-EV bet can lose.
How do I know my probability estimate is right?+
Track closing line value. If you consistently beat the close, your estimates are well-calibrated.
Educational only. Not wagering, financial, or legal advice. See our editorial policy.