Fair odds are the prices a market would show with the bookmaker’s margin taken out. In other words, they are an estimate of the true chance of each outcome, written as odds. Once you have them, you can see whether the best price on offer is longer than it should be.
This guide shows you how to remove the margin from a 2-way and a 3-way market. It also explains how to compare the result with the best price you can find.
Read the transcript
Every price includes the bookmaker's margin. Here's how to take it out.
Here's a match. Home two point one, draw three point four, away three point six. As percentages, that's forty-seven point six, twenty-nine point four, and twenty-seven point eight.
Together they make a hundred and four point eight per cent. The extra four point eight is the margin.
To remove it, divide each percentage by the total. Home becomes forty-five point four, the draw twenty-eight point one, and away twenty-six point five. Now they add up to one hundred.
Turn those back into odds, and you get the fair prices. Two point two, three point five six, and three point seven seven.
If you find a price above the fair odds, it's worth a closer look. Our fair odds calculator does the sums for you.
Please bet responsibly.
The short version
- First, turn each price into an implied probability and add them up.
- Next, divide each probability by that total. The results now add up to 100%.
- Then 1 ÷ each new probability gives you the fair odds.
- Finally, a best price above the fair price suggests value on paper, but it is only an estimate.
Why fair odds matter
First of all, every bookmaker builds a margin into its prices. As a result, the implied chances in a market add up to more than 100%. So the raw odds overstate how likely each outcome is, and you can’t use them as they stand. To see how this margin compares with a casino game, read bookmaker margin vs house edge.
Therefore, taking the margin out gives you a cleaner benchmark. That benchmark is the core of value betting, because you need a fair price before you can spot a generous one. If you need a refresher on the first step, read our guide to turning odds into percentages.
How to find fair odds in a 2-way market
A 2-way market has two outcomes, such as over or under 2.5 goals. Here is the simple proportional method, step by step.
Worked example
Say over 2.5 goals is 1.80 and under 2.5 goals is 2.05.
- Over: 1 ÷ 1.80 = 55.56%. Under: 1 ÷ 2.05 = 48.78%.
- Total: 55.56% + 48.78% = 104.34%. So the margin is 4.34%.
- Over: 55.56 ÷ 104.34 = 53.25%. Under: 48.78 ÷ 104.34 = 46.75%.
- Fair odds: over 1 ÷ 0.5325 = 1.88, under 1 ÷ 0.4675 = 2.14.
Notice that both fair prices are a little longer than the quoted ones. That is because the margin has been handed back. Also, the fair chances now add up to exactly 100%, so you can use them as a clean estimate of each outcome.
Fair odds in a 3-way market
Next, a football match result, or 1X2 market, has three outcomes: home, draw and away. The method is the same. However, there are more numbers to keep track of, so a table helps.
Worked example
The prices are 2.10 home, 3.40 draw and 3.60 away. Together they add up to 104.81%, so roughly 105%.
| Outcome | Odds | Implied % | Scaled % | Fair odds |
|---|---|---|---|---|
| Home | 2.10 | 47.62% | 45.43% | 2.20 |
| Draw | 3.40 | 29.41% | 28.06% | 3.56 |
| Away | 3.60 | 27.78% | 26.50% | 3.77 |
| Total | 104.81% | 100.00% |
In this case, each scaled figure is the implied % divided by 1.0481. Then each fair price is 1 ÷ the scaled figure.
Use the calculator below to do this for any 2-way or 3-way market. Simply enter the prices, and then it shows the margin and the fair odds.
Fair odds and margin calculator
Other ways to remove the margin
The proportional method is simple, so it is a good place to start. Even so, it assumes the margin is spread evenly across every outcome, and that may not be true.
For example, research on the favourite-longshot bias suggests longshots are often priced shorter than their true chance. In that case, more of the margin sits on the outsiders. Other methods, such as the power method, the log method or Shin’s method, try to allow for this. Compared with the proportional method, they usually give the favourite a slightly higher fair chance and the longshot a slightly lower one.
In practice, the gap between methods is small in most markets. Typically, it might move a fair price by a few hundredths. But it can matter more for big outsiders. For a clear technical comparison, see the vignette for the implied R package, which sets the methods side by side.
How to compare fair odds with the best price
Once you have a fair price, the next step is to look for the best price at any bookmaker. Then divide the best price by the fair price and take away 1. That gives a rough edge.
Worked example
From the table, the fair price for the home win is 2.20. Say the best price you can find is 2.30.
So 2.30 ÷ 2.20 − 1 = 0.045, an edge of about 4.5% on paper. By contrast, a best price of 2.15 would be below fair, so it would have a negative edge.
A few cautions apply. First, your fair price is only as good as the market you started from. That is why a sharp, busy market gives a better benchmark than a single soft bookmaker. Second, small edges can vanish if you estimate badly, so check your inputs. You can check the sum with our guide to expected value. Shopping around also helps, as our page on odds shopping explains.
Lastly, a positive edge on paper does not promise a profit.
Related guides
- Bookmaker margin vs house edge
- Implied probability explained
- Using exchange prices as a benchmark
- Sharp bookmakers
- Value betting explained
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