The one formula worth knowing
Expected value, or EV, is the average profit a bet would make if you could place it over and over. The formula is simple: EV equals the chance of winning times the profit, minus the chance of losing times the stake. It weighs what you stand to gain against what you stand to lose, each scaled by how likely it is, and boils the whole thing down to a single pounds-and-pence figure.
That figure is what separates a good bet from a bad one before any result is known. A positive EV means the bet makes money on average; a negative EV means it bleeds money on average. The result of any single bet is luck, but the EV is the truth about the bet.
A worked example
Suppose you put $10 on a selection at decimal odds of 3.00, and you estimate its true chance at 40%. The profit if it wins is $20 (3.00 means $30 back, minus your $10 stake). Plug the numbers in: EV equals 0.40 times $20, minus 0.60 times $10. That is $8 minus $6, which comes to plus $2. On average this bet earns you $2 every time you place it, even though on any given night it either wins $20 or loses $10.
Positive EV is worth taking, and negative EV bleeds money even when it sometimes wins. A bet can win four times out of ten and still be superb, or win six times out of ten and still be a slow leak, depending entirely on the price. The number tells you which is which.
How sensitive EV is to your estimate
The uncomfortable truth is that EV is only as reliable as the probability you put into it, and it is very sensitive to that input. Keep the same $10 bet at 3.00, but drop your estimate from 40% to 33%, and the sum becomes 0.33 times $20 minus 0.67 times $10. That is $6.60 minus $6.70, roughly break-even. A seven-point shift in your opinion turned a clear winner into a coin flip.
The table shows the same $10 bet at 3.00 across a range of estimated chances. Watch how quickly the EV crosses from positive to negative as the probability falls. This is why disciplined bettors are conservative with their estimates and why a small error in judging a chance can quietly wipe out an edge you thought you had.
| Estimated chance | Win profit | Lose stake | Expected value |
|---|---|---|---|
| 45% | $20 | $10 | +$3.50 |
| 40% | $20 | $10 | +$2.00 |
| 33% | $20 | $10 | ≈ $0.00 |
| 30% | $20 | $10 | −$1.00 |
| 25% | $20 | $10 | −$2.50 |
EV and value are the same idea
Value and expected value are two views of one thing. A value price, by definition, is one longer than the true chance deserves, and a value price always carries positive EV. When you say a bet has value you are really saying its EV is above zero; when you calculate EV you are measuring exactly how much value in cash terms. The percentage edge and the pounds of EV rise and fall together.
That link is useful because it lets you cross-check yourself. If a price looks like value but the EV comes out negative, your probability estimate and your instinct disagree, and one of them needs revisiting before you stake.
Living with variance
Positive EV does not promise a profit tonight, this week, or even this month. Variance, the natural swing of short-run results around the average, can bury a real edge for a long stretch. A bet with plus $2 of EV still loses its $10 stake 60% of the time. Only volume lets the average assert itself, which is why bankroll discipline and consistent staking matter as much as finding the edge in the first place.
While you wait for variance to settle, track your closing line value. CLV tells you whether your prices were ahead of the market well before your profit and loss confirms it. Positive EV at the point of betting, backed by consistent CLV, is about as much certainty as betting ever offers.