The Concept That Changes Everything
Expected value (EV) is the mathematical foundation of all successful betting. It answers the question: "On average, how much will this bet make or lose?"
Every bet has an expected value. Positive EV bets make money over time. Negative EV bets lose money over time. The goal of betting is simple: make more positive EV bets than negative ones.
The Basic Formula
Expected Value = (Probability of Winning × Amount Won) - (Probability of Losing × Amount Lost)
Or, for a standard bet where you lose your stake if wrong:
EV = (Probability × Profit) - ((1 - Probability) × Stake)
Let's work through examples.
Example 1: A Coin Flip at Even Money
You bet €10 on a fair coin at odds of 2.00 (even money):
- Probability of winning: 50%
- Profit if you win: €10
- Probability of losing: 50%
- Loss if you lose: €10
EV = (0.50 × €10) - (0.50 × €10) = €5 - €5 = €0
This bet has zero expected value. Over time, you neither win nor lose. The odds are fair.
Example 2: The Same Coin at Better Odds
You find odds of 2.20 on the same fair coin:
- Probability of winning: 50%
- Profit if you win: €12 (€10 × 2.20 - €10)
- Probability of losing: 50%
- Loss if you lose: €10
EV = (0.50 × €12) - (0.50 × €10) = €6 - €5 = +€1
This bet has positive expected value of €1 per €10 staked. Over time, you profit. The odds exceed fair value.
Example 3: A Football Match
You believe Team A has a 45% chance of winning. Odds are 2.50:
- Probability of winning: 45%
- Profit if you win: €15 (€10 × 2.50 - €10)
- Probability of losing: 55%
- Loss if you lose: €10
EV = (0.45 × €15) - (0.55 × €10) = €6.75 - €5.50 = +€1.25
This bet has positive expected value. Even though Team A is more likely to lose than win, the bet makes money over time because the potential profit exceeds what fair odds would offer.
Why Positive EV Matters
The law of large numbers ensures that results converge toward expected value over sufficient sample sizes. One bet might win or lose regardless of EV. A hundred bets start showing patterns. A thousand bets approximate expected returns closely.
This is why process matters more than results. A positive EV bet that loses was still the right bet. A negative EV bet that wins was still a mistake.
Finding Positive EV
Positive EV exists when your probability estimate exceeds the implied probability from the odds:
Your probability > Implied probability = Positive EV
At odds of 2.50, implied probability is 40%. If you believe the true probability is 45%, you have positive EV.
At odds of 1.80, implied probability is 55.5%. If you believe the true probability is only 50%, betting would be negative EV.
The Edge
The percentage difference between your probability and implied probability is your edge:
Edge = Your Probability - Implied Probability
Believing a team has a 45% chance at 40% implied probability gives a 5% edge. This edge, multiplied by your stake, approximates expected profit.
Different bettors require different minimum edges:
- 2-3% edge: Acceptable for high-volume strategies with low variance
- 5% edge: Standard target for most value betting
- 10%+ edge: Rare opportunities worth significant stakes
Expected Value Is Not Guaranteed Value
EV represents long-term expectation, not short-term certainty.
A bet with +5% EV and a 40% win probability will lose more often than it wins. Each individual loss might feel like a mistake. It isn't. The mathematics work over time, not per bet.
This creates the psychological challenge of EV betting: doing the right thing often feels wrong in the moment.
Practical Application
Before every bet, calculate expected value:
- Estimate your probability
- Convert odds to implied probability
- Compare the two
- If your probability exceeds implied, calculate the EV
- If EV is sufficiently positive, consider betting
This process prevents emotional betting. It forces probability thinking. It reveals whether potential bets actually have value.
The bettor who internalizes expected value thinks differently about every match. They stop asking "will this win?" and start asking "is this price right?"