Implied probability is the chance of an outcome that a set of betting odds suggests. In fact, every price you see is really a percentage in disguise. So once you can turn odds into a percentage, you can start to judge whether a price is short or generous.
This guide shows you how to convert decimal, fractional and American odds. It also explains why the percentages in a market always add up to more than 100%.
Read the transcript
Here's how to turn any odds into a percentage, in sixty seconds.
With decimal odds, divide one by the odds. One divided by two point five is zero point four. That's forty per cent.
With fractional odds, divide the right-hand number by the two numbers added together. Six to four is four divided by ten. Forty per cent again.
Evens is fifty per cent. Two to one is thirty-three. One to two is sixty-seven. And four to one is twenty.
Add up every outcome in a market and you'll get more than one hundred per cent. The extra is the bookmaker's margin.
Use our free odds converter to check any price. Please bet responsibly.
The short version
- Implied probability = 1 ÷ decimal odds. So 2.50 means 40%.
- For fractional odds a/b, first work out a ÷ b + 1 to get decimal odds.
- The percentages in a market add up to more than 100%, because the extra is the bookmaker’s margin.
- However, the odds tell you what the price assumes, not what will happen.
What implied probability means
First, odds tell you how much you get back if a bet wins. However, they also hide a second number: the chance the price assumes. That chance is the implied probability.
For example, think of a fair coin. It lands heads half the time, so the fair price is 2.00 (evens). So if you stake £10 and win, you get £20 back. As a result, over many flips you would break even. In short, 2.00 and 50% are the same idea written two ways.
This matters because value betting is about comparing two numbers. First, you need the chance the odds imply. Then you need your own honest estimate of the real chance. Our value betting guide also explains how those fit together.
How to work out implied probability from decimal odds
Decimal odds are the easiest to use, because you simply divide 1 by the odds, then multiply by 100 to get a percentage.
Worked example
For example, a team is 2.50 to win. Then 1 ÷ 2.50 = 0.40, so the implied probability is 40%.
Next, say a horse is 6.00. Then 1 ÷ 6.00 = 0.1667, so the price suggests a 16.7% chance.
You can also go the other way, for example from a chance to a price. If you think a chance is 25%, then 1 ÷ 0.25 = 4.00. So 4.00 is the break-even price for a 25% chance.
Fractional and American odds to percentages
Fractional odds such as 5/2 show your profit for each unit staked, so they need one extra step. To convert them, divide the first number by the second, then add 1. For example, 5/2 becomes 5 ÷ 2 + 1 = 3.50. Next, 1 ÷ 3.50 gives 28.6%.
Similarly, odds-on prices work the same way. So 4/6 becomes 4 ÷ 6 + 1 = 1.67, and 1 ÷ 1.67 is 60%.
Meanwhile, American odds use a plus or minus sign. A plus price such as +150 shows the profit on a $100 stake. The implied probability is 100 ÷ (150 + 100) = 40%. On the other hand, a minus price such as −200 shows what you must stake to win $100. In that case, the sum is 200 ÷ (200 + 100) = 66.7%.
Implied probability conversion table
Below are some common prices with their implied probability. The decimal figures are rounded to two places.
| Fractional | Decimal | American | Implied % |
|---|---|---|---|
| 1/4 | 1.25 | −400 | 80.0% |
| 1/2 | 1.50 | −200 | 66.7% |
| 4/6 | 1.67 | −150 | 60.0% |
| 10/11 | 1.91 | −110 | 52.4% |
| Evens | 2.00 | +100 | 50.0% |
| 6/4 | 2.50 | +150 | 40.0% |
| 2/1 | 3.00 | +200 | 33.3% |
| 5/2 | 3.50 | +250 | 28.6% |
| 3/1 | 4.00 | +300 | 25.0% |
| 4/1 | 5.00 | +400 | 20.0% |
| 5/1 | 6.00 | +500 | 16.7% |
| 10/1 | 11.00 | +1000 | 9.1% |
Use the calculator below to convert any price between formats and see its implied chance.
Odds converter
Why the book adds up to more than 100%
First, add up the implied probability of every outcome in a market. In a fair world, the total would be exactly 100%, because one of the outcomes must happen. However, bookmakers build in a margin, so the total is always higher.
Worked example
A football match is priced at 2.10 home, 3.40 draw and 3.60 away.
- Home: 1 ÷ 2.10 = 47.6%
- Draw: 1 ÷ 3.40 = 29.4%
- Away: 1 ÷ 3.60 = 27.8%
The total is 104.8%. In other words, that extra 4.8% is the overround, the bookmaker’s built-in edge.
In practice, the overround means each price is a little shorter than the fair odds. As a result, the implied probability of each outcome is slightly too high. To find a cleaner estimate, you strip the margin out. Our guide to removing the margin to find a true price shows the steps. For more on how this differs from a casino’s edge, see bookmaker margin vs house edge.
What implied probability can and can’t tell you
In short, the odds show what the market assumes. They don’t tell you what will happen. After all, a 40% chance still loses 6 times in 10, so a single result proves very little.
Also, the market can be wrong, but it is often right. In fact, prices from busy markets tend to be sharp, because lots of money and information shape them. So if your own estimate differs a lot, check your reasoning before you trust it. Next, compare the number with the odds using expected value. That shows whether a price has a positive edge on paper.
Finally, keep in mind that value betting is a way to judge prices. It does not promise a profit. Most bettors lose over time, and even a real edge brings long losing runs.
Related guides
- Value betting explained
- Fair odds: how to remove the margin
- Expected value betting with worked examples
- Odds shopping
- Glossary of betting terms
For background on odds formats and the maths behind them, see the Wikipedia entry on odds.
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.