Expected Value

Expected value (EV) is the average outcome of a bet if you placed it thousands of times. Positive EV (+EV) means the bet is a long-run winner. Negative EV (-EV) means it loses money over time, even if it wins individual flips.

The formula

EV = (probability of winning × profit) − (probability of losing × stake)

Example: a coin-flip bet at +120 odds (decimal 2.20) where you actually believe the true probability is 50%.

• True probability of winning: 0.50
• Profit if you win: $120 (on a $100 bet)
• Probability of losing: 0.50
• Loss if you lose: $100

EV = (0.50 × $120) − (0.50 × $100) = $60 − $50 = +$10 per bet.

Over 1,000 of those bets you’d expect to net $10,000. That’s +EV.

EV vs implied probability

The implied probability of +120 is 100/(120+100) = 45.5%. The book is saying “this happens 45.5% of the time.” If you think it actually happens 50% of the time, you have an edge — and EV is the way to quantify it.

The whole game of sharp betting reduces to: find odds where your true probability is higher than the implied probability. Everything else (bankroll management, line shopping, hedging) is just downstream of that core idea.

Why most retail bettors are -EV

The vig guarantees that every leg of a coin-flip line is below 50% true probability for a sportsbook with a fair model. To overcome that, you need an edge above 52.4% on -110 lines. Most bettors don’t have one — which is why most retail players are slow-bleeding their bankroll over years.

Tools that exploit EV

• Closing line value (CLV): if you consistently beat the line that closes (the price right before the game starts), you have +EV.
• Vig removers: strip the book’s margin to estimate the “true” probability behind a line, then compare to your own.
• Kelly criterion: sizes each bet proportional to your edge, maximizing long-run growth.