Understanding Expected Value (EV)
Expected Value (EV) is the average amount you expect to win or lose per bet if you made the same bet many times.
Think of it this way: if you could make the exact same bet 1,000 times, what would your average profit or loss be per bet? That's your EV.
Building Intuition with Coin Flips
Let's start with coin flips to build intuition:
| Scenario | EV per Flip |
|---|---|
| Win $10 on heads, lose $10 on tails | $0 (break-even) |
| Win $12 on heads, lose $10 on tails | +$1 (profit) |
| Win $9 on heads, lose $10 on tails | -$0.50 (loss) |
EV in Prop Betting
In prop betting:
- If you believe a prop hits 55% of the time, but the odds only require 52.4% to break even (typical -110), you have +EV
- If you believe it hits 50% but you need 52.4%, you have -EV
- If you believe it hits exactly 52.4%, you have 0 EV (break-even)
Warning
Here's the uncomfortable truth: most bets you see are -EV. The sportsbook has priced them to ensure they make money over time. Your job is to find the exceptions—the bets where your probability estimate is better than theirs.
The Golden Rule
Key Insight
Only bet when you have positive expected value.
Long-term profit comes from EV, not streaks. You can lose 10 +EV bets in a row and still be making the right decision. You can win 10 -EV bets in a row and still be making a mistake.
The EV Formula
To compute EV, you need:
- p = your estimated probability of winning
- win_profit = how much you profit if you win
- risk = how much you lose if you lose
Expected Value Formula
EV = p × win_profit - (1 - p) × risk=(p*win_profit)-((1-p)*risk)Worked Example
Odds: -110
Risk: $110 to win $100
p (your estimate): 55% (0.55)
EV = 0.55 × 100 - 0.45 × 110
EV = 55 - 49.5
EV = +$5.50 per bet
This means that if you made this exact bet 1,000 times, you would expect to profit $5,500 total, or $5.50 per bet on average. Some bets will win, some will lose, but the average will converge to +$5.50.
Tip
Notice that even though your edge is small (55% vs 52.4% break-even), you're still making money. Small edges compound over volume. This is how professional bettors make a living—not by finding "locks," but by finding small edges and betting them repeatedly.
EV vs. ROI
EV is dollars-per-bet. ROI is EV divided by risk.
A $5.50 EV on a $110 risk is a 5% ROI.
Both numbers matter:
- EV tells you your absolute profit
- ROI tells you your efficiency
EV Convergence Over Time
Even with a positive edge, results swing wildly in the short term. Over many bets, your average outcome approaches your true EV.
This is why you need bankroll management—to survive the swings until the math catches up.
| Number of Bets | Expected Variance |
|---|---|
| 10 bets | Results could be anywhere from 3-7 to 7-3 |
| 100 bets | Results typically within 45-55 to 55-65 |
| 1,000 bets | Results converge much closer to true EV |
Note
The "long run" in betting isn't a weekend or even a month. It's hundreds or thousands of bets. This is why patience and proper bankroll management are essential.
Try the EV Calculator
Use this calculator to quickly determine the expected value of any bet:
Expected Value Calculator
Try the interactive calculator for this concept
📝 Exercise
Instructions
Practice calculating Expected Value with these scenarios.
You bet $100 at +150 odds (win $150 profit). You estimate a 45% chance of winning. What is your EV?
A bet has +EV of $8 per $100 risked. What is the ROI?
You make 100 bets with +$5 EV each. What is your expected total profit?