Betting Math

Expected Value (EV)

The average profit or loss per bet if you made the same wager thousands of times. Positive EV means long-term profit.

Also known as: EV, +EV, positive expected value

Definition

Expected value (EV) is the mathematical average of all possible outcomes weighted by their probabilities. A +EV bet is one where your estimated probability of winning exceeds the implied probability of the odds.

EV = (probability of winning × profit if win) - (probability of losing × loss if lose)

Professional bettors focus exclusively on +EV opportunities. A single bet can lose, but over thousands of bets, EV converges to your actual profit. This is the law of large numbers.

Finding +EV requires knowing (or estimating) the true probability better than the market.

Formula

EV = (P_win × profit) - (P_lose × stake)
EV = (P_win × (decimalOdds - 1)) - (1 - P_win)
EV% = EV / stake × 100

Worked Example

You estimate a team wins 55% of the time. Odds are +110 (decimal 2.10). EV = (0.55 × $110) - (0.45 × $100) = $60.50 - $45 = +$15.50 per $100 bet (15.5% EV).

Try It Yourself

EV Calculator

Find +EV bets by comparing rec book odds against sharp lines

PM EV Calculator

Expected value and Kelly sizing for prediction market contracts

Related Terms

Vig

The bookmaker's built-in commission. The difference between true odds and what you're offered.

Implied Probability

The probability of an outcome implied by the odds. Includes the bookmaker's margin (vig).

Kelly Criterion

A formula for optimal bet sizing that maximizes long-term bankroll growth based on your edge and the odds.

Closing Line Value (CLV)

Getting better odds than the final line at market close — the strongest indicator of long-term betting skill.