Expected value in betting: what a bet is worth on average
Knowledge Base · Published · 5 min read
Every bet has a price and a chance. Expected value, usually shortened to EV, puts the two together into a single number: what the bet is worth on average if you could place it again and again. It will not tell you whether the next bet wins, but it explains why some bets are good and others bad over the long run.
The formula
For a bet with a single winning outcome, expected value per bet is:
EV = (probability of winning x profit if it wins) - (probability of losing x stake)
Profit equals stake x (decimal odds - 1). The result is in the same currency as the stake, and dividing by the stake gives the expected return as a percentage.
Worked example 1: a negative bet
Suppose you stake 10 at decimal odds of 2.00 on an outcome with a 45% chance.
- Chance of winning: 0.45, profit if it wins: 10 x (2.00 - 1) = 10.
- Chance of losing: 0.55, loss if it loses: 10.
- EV = 0.45 x 10 - 0.55 x 10 = 4.50 - 5.50 = -1.00.
The bet has an expected loss of 1 per 10 staked, or -10%. Some days it wins and you collect 10, but averaged over many repeats you lose about 1 each time.
Worked example 2: a positive bet
Now stake 10 at 3.00 on an outcome you believe has a 38% chance.
- Win: 0.38 x 10 x (3.00 - 1) = 0.38 x 20 = 7.60.
- Lose: 0.62 x 10 = 6.20.
- EV = 7.60 - 6.20 = +1.40.
Here the expected profit is 1.40 per 10 staked, or +14%. A shortcut gets the same answer: EV as a fraction of the stake equals probability x odds - 1, so 0.38 x 3.00 - 1 = 0.14.
Break-even probability
The break-even probability is the chance at which EV is exactly zero. It equals 1 / decimal odds, which is the implied probability. At 3.00 it is 33.3%. If your honest estimate is above that, EV is positive; below it, negative. This is the same idea described in our article on implied probability. The expected value calculator does the arithmetic for you and lets you test how sensitive the answer is.
Why the margin makes most bets negative
Bookmakers build a margin into every market. If two equally likely outcomes are both priced at 1.90 instead of the fair 2.00, each bet has an EV of 0.5 x 1.90 - 1 = -5%. Across typical markets, a bettor who picks at random loses roughly the margin over time. To have positive EV, your probability estimate must beat the bookmaker's price by more than the margin. We explain how to hunt for that gap in value betting.
Variance: the gap between EV and results
EV is an average, and averages need many repeats. Take the positive bet above, a 38% chance at 3.00. The most likely single result is a loss. Over 10 bets of 10 each:
- Expected profit is 10 x 1.40 = 14.
- Zero wins is not rare: 0.62 to the power 10 is about 0.8%, and fewer than 3 wins happens about one time in five.
- With 3 wins you collect 3 x 30 = 90 against 100 staked, a loss of 10.
- With 5 wins you collect 150 against 100 staked, a profit of 50.
Both outcomes are consistent with exactly the same positive EV. Short runs are dominated by luck. That is why a streak, good or bad, says little about whether a bet was a good decision. Size your stakes cautiously.
Combining bets
EV multiplies across accumulators, and so does the margin. Three bets each at -5% EV combine to roughly 0.95 x 0.95 x 0.95 = 0.857 of the stake returned on average, meaning about -14%. Accumulators can be fun, but each extra leg usually deepens the bookmaker's built-in edge. The accumulator calculator shows the combined price, and our article on accumulators explains the trade-off.
The limits of EV
EV looks precise, but it is only as good as its inputs.
- The probability is an estimate. If you move 38% to 33%, the +14% bet becomes -1%. Small errors in probability produce large swings in EV.
- Overconfidence is common. People tend to overrate their picks, which inflates calculated EV.
- EV says nothing about your risk tolerance. A bet with positive EV can still be too large for your bankroll.
A sensible approach is to treat EV as a way of thinking, not a promise: ask what chance the price requires, then ask honestly whether you believe the chance is higher.
Common mistakes
- Confusing likely with valuable. A 90% outcome at 1.05 has an EV of 0.90 x 1.05 - 1 = -5.5%, because the price is too short for the chance.
- Judging a single result instead of the decision.
Key takeaways
Expected value turns odds and probability into one number. A positive figure means the price is better than your estimate of the chance, a negative figure means it is worse, and zero means break-even. Because results swing widely around the average and the inputs are uncertain, EV is a guide to better decisions rather than a guarantee of profit.
Betting is for adults only (18+). Only stake money you can afford to lose, set limits before you start, and stop if it stops being fun. If gambling is causing you problems, contact a local support organisation.