Work out implied probability from any odds
Every price a bookmaker shows you is a probability in disguise. This guide shows you how to turn fractional and decimal odds into a percentage, how to add up a whole market to find the bookmaker’s margin, and how to strip that margin out to see a fairer figure. It is written for Irish punters who bet on GAA, racing or football and want to check a price with a sum rather than a hunch. You need nothing more than a calculator on your phone.
What does a price actually tell you?
Implied probability is the chance of an outcome that a price suggests, once you read the odds as a percentage. A horse at 2/1 is being priced as if it wins about one race in three, which is 33.3%.
The sum is simple for both formats. With decimal odds you divide 1 by the price, so 3.50 gives 1 ÷ 3.50, or 28.6%. With fractional odds you take the second number and divide it by the two numbers added together, so 5/2 becomes 2 ÷ 7, which is also 28.6%. The two formats describe the same price, and the answer agrees either way.
Here is the catch, and it is the reason the rest of this guide exists. If you convert every price in a market and add them up, the total comes to more than 100%, because the bookmaker has built a margin into each price. That excess is called the overround, and the percentage on any single selection includes its share of it. So the figure you work out is the bookmaker’s view plus their cut, never a neutral estimate of the true chance, and treating it as neutral will make every favourite look slightly likelier than it is.
That margin is the first number worth knowing.
Converting a football market step by step
We use a made-up three-way football market to show the method: home win 6/4, away win 9/4 and the draw at 11/5. The same steps work for a hurling match or a race card.
- Step 1
Write down every price in the market
List each outcome with its odds. Here that is home 6/4, away 9/4 and draw 11/5. Leave nothing out, or the total in the later steps will come out wrong. - Step 2
Convert each fraction into decimal odds
Divide the first number by the second and add 1. So 6/4 becomes 2.50, 9/4 becomes 3.25 and 11/5 becomes 3.20. Skip this step if your bookmaker already shows decimals. - Step 3
Divide one by each decimal price
1 ÷ 2.50 is 40.0%, 1 ÷ 3.25 is 30.8% and 1 ÷ 3.20 is 31.3%. Each result is the implied probability the bookmaker has given that outcome, margin included. - Step 4
Add the percentages to find overround
40.0 + 30.8 + 31.3 gives roughly 102.0%. The 2% above one hundred is the bookmaker's margin on this market, and it is spread across all three prices. - Step 5
Remove the margin from each outcome
Divide each percentage by the total. The home win becomes 40.0 ÷ 102.0, about 39.2%. Do the same for the away win and the draw, and the three now add to 100%. - Step 6
Compare the fair figure with your view
If your own reasoned estimate for the home win sits well above 39.2%, the price may be generous. If it sits below, the bookmaker rates the team higher than you do.
Fractional or decimal: which is easier to convert?
Irish bookmakers usually show fractional odds by default, especially on racing, while most let you switch to decimals in the account settings. Both lead to the same percentage, but they do not make the sum equally easy.
Fractions are traditional and quick to read for round prices such as evens, 2/1 or 4/1. They become awkward with prices like 8/13 or 15/8, where the division in your head stops being friendly. Decimals already include your stake, so one division gives the answer, and adding up a market is far less fiddly. The comparison below sets the two side by side on the tasks this guide needs.
Our view: switch to decimals while you are learning.
Fractional and decimal odds side by side
Each row takes one job you will do when converting a price and shows how each format handles it.
Fractional odds | Decimal odds |
|---|---|
| Formula: second number ÷ both numbers added | Formula: 1 ÷ the decimal price |
| Evens reads as 1/1, so 50% | Evens reads as 2.00, so 50% |
| Odd prices like 8/13 need care | 8/13 shows as 1.62, about 61.9% |
| Familiar on Irish racecourses and shop boards | Default on exchanges and many apps |
| Profit on the stake is shown directly | Total return including stake is shown |
| Adding a market means converting first | Percentages add up in one pass |
Using implied probability without fooling yourself
A percentage on its own does not tell you whether a bet is good. It only becomes useful when you set it against your own estimate and do the sum.
Take the home win at 6/4 from the steps above, with a fair implied probability of about 39.2%. Suppose your reasoned view is that the team wins 45% of the time. On a €10 stake you win €15 profit 45% of the time and lose €10 the other 55%, so the expected result is (0.45 × 15) – (0.55 × 10), or +€1.25 per bet. If your estimate were 38%, the same sum gives (0.38 × 15) – (0.62 × 10), which is -€0.50, and the bet loses over time.
Free bets change the sum
A free bet returns winnings only, without the stake. A €10 free bet at 6/4 pays €15, not €25, so the price looks the same but the value you can take from it is lower than a cash bet of the same size. The implied probability of the selection does not move; what changes is what you get back when it wins.
Your own estimate is the weak link, and no formula fixes a poor one.
Related Terms
Implied probability questions answered
What is the formula for implied probability with decimal odds?
Divide 1 by the decimal price and multiply by 100. Odds of 4.00 give 1 ÷ 4.00, which is 25%.
How do you convert fractional odds to a percentage?
Divide the second number by the sum of both numbers. For 7/2, that is 2 ÷ 9, or about 22.2%.
Why do the percentages in a market add up to more than 100%?
Each price includes part of the bookmaker’s margin, known as the overround. The amount above 100% is roughly what the bookmaker builds in for itself.
What implied probability does evens represent?
Evens, written as 1/1 or 2.00, represents a 50% implied probability before you account for the bookmaker’s margin on the wider market.
Does a high implied probability mean a safe bet?
No. A 75% favourite still loses one time in four on the bookmaker’s own figures, and the price includes their margin as well.
Does a free bet change the implied probability?
No, the odds and their percentage stay the same. A free bet returns winnings only, without the stake, so the payout is smaller than a cash bet.
More about online casinos
What we check first on any market is step four, because the overround tells you how much the bookmaker keeps before anyone kicks a ball. A two-way tennis or hurling market near 103% is common; a long race card or an outright market can run far higher than that.