Expected value betting: how to work out EV

Expected value betting means judging a bet by its average result, not by whether it wins. In other words, you ask what the bet would return per £1 if you could place it thousands of times. If that average is above zero, the price is in your favour on paper.

This guide gives you the formula, some worked examples and the honest limits. Above all, it explains why one bet tells you almost nothing.

Expected value, worked out A step-by-step expected value example: £10 at odds of 2.30 on a 47% chance, and what +8.1% really means.
Read the transcript

Expected value tells you what a bet is worth on average. Let's work one out.
Say you think a team has a forty-seven per cent chance of winning, and the best price is two point three. You stake ten pounds.
If it wins, you get twenty-three pounds back. That's thirteen pounds profit, forty-seven times in a hundred. If it loses, you're down ten pounds, fifty-three times in a hundred.
Forty-seven per cent of thirteen pounds is six pounds eleven. Fifty-three per cent of ten pounds is five pounds thirty. The difference is plus eighty-one pence.
That's an expected value of plus eight point one per cent of your stake. It's an average over many similar bets, not what happens on this one.
And it's only as good as your forty-seven per cent. Below forty-three and a half per cent, the edge disappears.
Please bet responsibly.

The short version

  • EV per £1 staked = your probability × decimal odds − 1.
  • So £10 at 2.30 on a 47% chance has an EV of +£0.81.
  • A positive EV is only as good as your probability estimate.
  • However, EV only shows up over hundreds of bets, and losing runs are normal.

What expected value betting is

Every bet has two possible results: it wins or it loses. Expected value (EV) blends them into one number. To do that, you weight each result by how likely it is.

So the key input is your own estimate of the chance. First, you turn the odds into an implied probability. Then you compare it with the chance you believe is real. If your chance is higher than the price suggests, the EV is positive.

That idea sits at the heart of our value betting guide. In short, you judge the price, not the team.

The EV formula

There are two ways to write it, and both give the same answer.

  • Short form: EV per £1 = p × decimal odds − 1
  • Long form: EV = (p × profit if it wins) − ((1 − p) × stake)

Here p is your probability as a decimal, so 47% becomes 0.47. To get the EV in pounds, multiply the short form by your stake.

Worked example

You stake £10 at 2.30 (13/10). You think the real chance is 47%.

  • Short form: 0.47 × 2.30 − 1 = 0.081. Then 0.081 × £10 = +£0.81.
  • Long form: a win pays £13 profit, so 0.47 × £13 = £6.11. A loss costs £10, so 0.53 × £10 = £5.30. Finally, £6.11 − £5.30 = +£0.81.

On average, this bet is worth 81p to you. However, you will never actually win 81p. Each time, you either win £13 or lose £10.

Use the calculator below to enter your own stake, odds and probability. It shows the EV in pounds and as a % edge.

Expected value calculator

Negative EV examples

Most bets have a negative EV, because the bookmaker’s margin is built into the odds. So it helps to see what a poor price looks like.

Worked example

  • A coin-flip chance (50%) priced at 1.80: 0.50 × 1.80 − 1 = −0.10. So £10 has an EV of −£1.00.
  • A 15% chance priced at 6.00 (5/1): 0.15 × 6.00 − 1 = −0.10. Again, £10 has an EV of −£1.00.
  • A 45% chance priced at 2.10 (11/10): 0.45 × 2.10 − 1 = −0.055. That is −55p per £10.

Notice the last one. The odds look generous, yet the bet still has a negative EV. That is because the price only pays enough for a 47.6% chance, while your estimate is lower.

Expected value betting as a % edge

The short form already gives you a percentage. For example, 0.081 is an edge of 8.1%. That means you expect to get back £1.081 for every £1 staked, on average, over a long run.

There is also a quick shortcut. Divide the odds by your fair odds, then take away 1. In the example, your fair price for a 47% chance is 1 ÷ 0.47 = 2.13. Then 2.30 ÷ 2.13 − 1 is roughly 8%, the same edge.

Real edges tend to be small. A figure of 2% to 5% is far more typical than 8%. So if your sums show a huge edge, check your probability first. Often the estimate is too keen, not the price too big. Our page on fair odds without the margin gives you a cleaner starting point.

Why EV only shows over many bets

EV is an average, and averages need lots of results to settle. In the short run, luck swamps any edge.

Worked example

Take the same bet again: £10 at 2.30 with a true 47% chance. Suppose you could place it many times.

  • After 100 bets, you expect to be up £81. But the spread of results is wide, about ±£115 for one standard deviation. As a result, you still finish behind roughly 1 time in 4.
  • After 1,000 bets, you expect to be up £810. Even so, there is still about a 1% chance of a loss.

These figures assume your 47% is exactly right. In real life it won’t be.

That is why a bet with positive EV can lose, and a bad bet can win. For the same reason, you should judge your process by your records over time. Our guide to betting variance shows how long losing runs can last.

The limits of expected value betting

EV is a tool for judging prices, not a promise of profit. Most bettors lose over time. Also, an edge is only real if your probability is better than the market’s, and that is hard.

A good test is whether you beat the closing price. Read about closing line value to learn how. Then, if you do bet, decide your stake before you start, and never chase losses.

For the maths behind it, the Wikipedia article on expected value covers the formal definition.

Related guides

18+ only. Betting should be fun, and every bet can lose. Set a budget you can afford to lose and stick to it. For free, confidential support, visit BeGambleAware.org or call the National Gambling Helpline on 0808 8020 133.

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