A price is not a fact. It is the bookmaker's probability estimate, expressed as a number with a margin built in. Expected value asks a different question from "will this bet win?" It asks whether your own probability estimate, compared honestly with that price, suggests the bet will pay off on average. That is a statement about the price, not a prediction about the event.
The formula
EV per dollar staked = (your probability × profit if it wins) − (1 − your probability)
At 2.20 decimal, a $1 stake profits $1.20 if it wins. Rate the true probability at 50%:
- Market's implied probability — 45.5%
- Your edge - +4.5 percentage points
- EV per dollar - +10.0%
- Fair odds at your probability — 2.00
You believe the fair price should be 2.00. The market is offering 2.20. That 0.20 difference, expressed as a probability difference rather than a price difference, is the edge. It is only a real edge if your 50% estimate is a better assessment of what actually happens than the market's 45.5%, rather than simply being a different estimate.
Same price, no edge
Run the same 2.20 price with your probability estimate set to exactly the market's implied number, 45.45%:
- Your edge — 0.0 percentage points
- EV per dollar — 0.0%
- Fair odds at your probability — 2.20, identical to the market price
Nothing about the price changed. What changed is whether your opinion adds anything to it. A price with no difference between your estimate and the market's is not necessarily a bad bet. It is simply fairly priced, and a fairly priced bet has an expected value of exactly zero before costs, regardless of the odds.
Positive EV is a statement about averages, not this bet
A +9% edge does not mean this specific bet is 109% likely to be worth having placed. It means that if you could place the same decision a large number of times, the average return across those bets would be positive.
Any single bet can still win or lose, just as a fair bet can. The important word in expected value is "expected". It describes the average of a distribution, not the result of one individual outcome.
A string of losses on genuinely positive-EV bets is not evidence that the edge was fake. Variance can dominate small samples whether or not there is a real edge underneath, which is why it is important to consider how many bets it actually takes for an edge to become visible.
Stake size changes the dollars, not the edge
EV per dollar staked is a rate, not an amount. It does not change whether the stake is $10 or $1,000. What changes is the dollar value it produces, along with the variance that comes with it.
The same +9.1% edge produces $0.91 of expected value on a $10 stake and $91 on a $1,000 stake. The range of actual outcomes around that expectation also becomes wider by the same multiple.
Sizing a stake is a separate decision from deciding whether a bet has value. One asks whether the price is worth taking. The other asks how much of your bankroll that answer is worth risking. Mixing the two is how a correctly identified edge can turn into an oversized and uncomfortable position.
Estimating your own probability without fooling yourself
The formula completely trusts whatever probability you put into it, which is also its main weakness. It has no way to distinguish a carefully reasoned 55% estimate from a hopeful guess that happens to use the same number.
Round numbers deserve particular attention. An estimate that repeatedly lands on tidy figures such as 50%, 55% or 60% may be reflecting a habit of rounding rather than a genuinely precise assessment of the event. Rounding upward, especially towards the side that already looks appealing, can create an edge that was never really there.
The useful question is not whether the calculation is correct after you choose the probability. It almost always is. The more important question is whether the estimate itself would still look reasonable if you had written it down before seeing the available price.
Where the estimate itself gets checked
The difficult part of this formula is not the arithmetic. It is knowing whether your probability estimate is actually better than the market's.
One widely used, although imperfect, signal is closing line value. If the price you bet consistently moves in your direction before the market closes, meaning the price becomes shorter after you back it more often than chance alone would suggest, that is evidence that your estimates may be leading the market rather than following it.
It is not proof on any individual bet, and it does not tell you whether a specific bet will win. But when tracked over a large enough sample, it is one of the more practical ways to assess whether the edge you are calculating is genuine or simply the result of optimistic estimates.
Run your own price and probability estimate through the expected value calculator. It shows the fair odds implied by your own probability alongside the market's price, so the difference between them is the first thing you see rather than something you have to calculate separately.