Implied probability and bookmaker margin: how to find the fair odds

Every price a bookmaker offers is really a probability in disguise. Turn the odds into a percentage and you can see how likely the bookmaker thinks each outcome is, how much margin it has built in, and what the fair price would be without it.

Short version: implied probability = 1 ÷ decimal odds. Add up all the sides of a market: the amount over 100% is the bookmaker's margin. Scale the percentages back down to 100% and you have the fair chances and fair odds.

Calculator

Enter the prices for each side of a market. The calculator shows the implied chance of each, the bookmaker's margin, and the fair chance and fair odds with the margin removed. Add the odds you took to see their expected value against the fair price.

What is implied probability?

Implied probability is the chance of an outcome that the odds represent. For decimal odds:

implied probability = 1 ÷ odds

Decimal odds	Implied probability
1.50	66.7%
1.80	55.6%
2.00	50.0%
2.50	40.0%
3.00	33.3%
4.00	25.0%
6.00	16.7%
10.00	10.0%

Odds of 2.00 mean the outcome is priced as a 50% chance: if it happened exactly half the time, betting it at 2.00 would break even.

Other odds formats

Fractional (UK): add 1 to the fraction to get decimal odds. 6/4 = 1.5 + 1 = 2.50; 1/2 = 0.5 + 1 = 1.50.
American (moneyline): for positive numbers, divide by 100 and add 1: +150 = 2.50. For negative numbers, divide 100 by the number (ignoring the minus) and add 1: −200 = 100 ÷ 200 + 1 = 1.50.

Then use 1 ÷ decimal odds as above.

What is the bookmaker's margin?

If the odds were perfectly fair, the implied probabilities of all outcomes in a market would add up to exactly 100%. Bookmakers price every side slightly short, so the total comes to more than 100%. The extra is the margin, also called the overround or vig.

Example, 1X2: home 2.10, draw 3.50, away 3.60.

1 ÷ 2.10 = 47.6%
1 ÷ 3.50 = 28.6%
1 ÷ 3.60 = 27.8%
Total = 104.0%, so the margin is 4.0%

Example, Asian handicap: home −0.5 at 1.93, away +0.5 at 1.97.

51.8% + 50.8% = 102.6%, a margin of 2.6%

The margin is the bookmaker's built-in edge: on average, bettors get back less than they stake. Sharp bookmakers such as Pinnacle run small margins on their main lines, often in the low single digits; many recreational bookmakers charge noticeably more, especially on 1X2 and smaller markets.

How to remove the margin: fair odds

To find the fair probabilities, scale the implied probabilities down so they add up to 100%:

fair probability = implied probability ÷ total of all implied probabilities

fair odds = 1 ÷ fair probability

Using the 1X2 example above (total 104.0%):

Outcome	Odds	Implied	Fair chance	Fair odds
Home	2.10	47.6%	45.8%	2.183
Draw	3.50	28.6%	27.5%	3.639
Away	3.60	27.8%	26.7%	3.743

This is the proportional method, the simplest and most widely used. It is what the calculator above uses.

Other ways to remove the margin

Bookmakers don't always spread their margin evenly. There is a well-known tendency, the favourite-longshot bias, for longshots to carry more of the margin than favourites. Methods such as the power method and Shin's method try to account for that, and give slightly different fair odds, mainly for big outsiders.

For two-way markets priced near even, such as a main Asian handicap or over/under line, the methods agree almost exactly, so the proportional method is fine. The differences matter more for 1X2 markets with a heavy favourite and a long-priced underdog.

Using fair odds

Once you have a fair price, you can judge any other price against it:

expected value = your odds × fair probability − 1

If Pinnacle's main line is home 1.93 / away 1.97, the fair home price is about 1.980. A bookmaker offering home at 2.05 is then worth about +3.6% of your stake in expected value; a bookmaker offering 1.90 is worth about −4.0%.

Using the closing Pinnacle price as the fair price is how bettors measure closing line value, the most reliable test of whether a betting method works. Odds History shows Pinnacle's opening and closing prices for every line, so you can look up the fair price for any match you bet on. See opening vs closing odds.

FAQ

How do I convert odds to a probability?
Divide 1 by the decimal odds. Odds of 2.50 are 1 ÷ 2.50 = 40%.

How do I calculate the bookmaker's margin?
Add the implied probabilities of every outcome in the market and subtract 100%. Odds of 1.90 and 1.90 give 52.6% + 52.6% = 105.3%, a margin of 5.3%.

What is the overround?
Another name for the bookmaker's margin: the amount by which the implied probabilities add up to more than 100%.

What are fair odds?
The odds with the bookmaker's margin removed, so the probabilities add up to exactly 100%. They are the best estimate of the true price, especially when taken from a sharp bookmaker's closing line.

What is a good margin?
Lower is better for the bettor. Sharp bookmakers' main Asian handicap and over/under lines usually carry the smallest margins in football.