Expected Value (EV)

Expected Value (EV) is the average amount you expect to win or lose on a bet over infinite repetitions. It's the fundamental concept in profitable betting: find +EV bets, avoid -EV bets.

The EV Formula

EV = (Probability of Win × Profit if Win) − (Probability of Loss × Loss if Lose)

Example: Betting $100 at +150 odds when true probability is 45%

• Win: 45% × $150 = $67.50
• Lose: 55% × $100 = $55.00
• EV = $67.50 − $55.00 = +$12.50

This bet has +$12.50 EV, meaning you expect to profit $12.50 on average.

EV at Different Odds

Your Edge	Odds	$100 Bet EV
+5%	-110	+$4.55
+5%	+150	+$12.50
+5%	+300	+$20.00
+10%	-110	+$9.09
-5%	-110	-$4.55

Higher odds amplify your edge (positive or negative). This is why edge at plus-money is especially valuable.

EV vs Outcome

Critical concept: a bet can be +EV and still lose.

If you bet +150 (40% implied) when true probability is 45%, you have +EV. But you'll still lose 55% of the time. Individual outcomes don't validate or invalidate EV—only large samples do.

Sharps focus on EV, not outcomes. One loss means nothing. A thousand +EV bets is a career.

Finding +EV Bets

+EV opportunities come from:

Mispriced lines: Market says 40%, you correctly believe 50%

Vig arbitrage: Different books offer different odds on the same event

Model edge: Your probability estimates are more accurate

Timing: Betting before lines adjust to information

PriceArb surfaces potential +EV by comparing historical probabilities to live market prices.

The -EV Trap

Most recreational bettors make -EV bets:

Bet Type	Typical EV
Standard spread (-110)	-4.5%
Props	-8 to -15%
Parlays	-15 to -30%
Futures	-15 to -40%

Without edge, you're just paying vig to gamble.

EV in Prediction Markets

On Kalshi, EV calculation is simpler:

• Buy YES at 40¢ when true probability is 50%
• Expected value = (50% × 60¢ profit) − (50% × 40¢ loss) = +10¢
• That's +25% EV on a 40¢ investment

Prediction market prices directly represent probabilities, making EV intuitive.

Related Terms

• Edge — The probability advantage that creates +EV
• Vig — The -EV built into standard odds
• Kelly Criterion — How to size +EV bets
• CLV — Evidence that you're actually betting +EV