Expected Value (EV)
The average outcome of a bet over time. Positive EV bets profit in the long run.
Expected value (EV) is the mathematical measure of a bet's long-term profitability. A positive EV bet means you expect to profit over many repetitions; negative EV means you expect to lose.
EV Formula
EV = (Probability of Win × Amount Won) – (Probability of Loss × Amount Lost)
Example
A coin flip bet: you win $110 if heads, lose $100 if tails. If the coin is fair (50/50): EV = (0.5 × $110) – (0.5 × $100) = $55 – $50 = +$5 per flip
Why EV Matters
Professional bettors only take positive EV bets. Finding EV requires accurately estimating the true probability of an outcome and comparing it to the odds-implied probability.
Key Takeaways
- Positive EV bets profit in the long run; negative EV bets lose in the long run.
- All casino games and most sports bets offered to the public are negative EV.
- Finding positive EV requires having a more accurate probability estimate than the market.
- Variance can make positive EV bets lose in the short term. Sample size matters.
Examples
- You bet $100 at +150 on something you think wins 45% of the time. EV = (0.45 × $150) − (0.55 × $100) = $67.50 − $55 = +$12.50.
- A fair coin flip priced at -110: EV = (0.5 × $90.91) − (0.5 × $100) = −$4.55 for every $100 you bet.
Related Terms
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1 / 3Do you know what Implied Probability means?
The win probability implied by a set of odds, including the sportsbook's margin.
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Frequently Asked Questions
Does positive EV mean I will win the bet?
No. It means you would come out ahead if you made the same bet many times. Any single bet can still lose.
How do I find positive EV bets?
Estimate the true probability of an outcome, convert the odds to implied probability, and only bet when your estimate is higher. Comparing a book's price with sharper books' prices is a common shortcut.