01How to use the fair odds calculator
- Choose 2-way (for example yes/no, over/under) or 3-way (home/draw/away).
- Enter the odds for every outcome of the market, all from the same bookmaker at the same time. Mixing bookmakers gives you a number, but not a meaningful margin.
- Pick a method. If you're not sure, leave it on Shin.
- Read the fair odds and probabilities. The margin tells you how much the bookmaker is taking on this market.
- Use the fair odds as your estimate in the EV calculator to check prices at other bookmakers.
02How the margin and fair odds are calculated
First turn each price into an implied probability and add them up:
Implied probability = 1 / decimal odds
Booksum = sum of the implied probabilities
Margin % = (booksum - 1) x 100
Payout % = 100 / booksumThen share the margin out. The three methods differ only in how they do that:
Multiplicative: fair p = implied p / booksum
Power: fair p = implied p ^ k, with k chosen so the fair p's add up to 1
Shin: fair p = (sqrt(z^2 + 4(1 - z) x implied p^2 / booksum) - z) / (2(1 - z)),
with z chosen so the fair p's add up to 1
Fair odds = 1 / fair pThe multiplicative method assumes the bookmaker adds margin in proportion to each price. In practice bookmakers tend to take more from long shots, because that's where casual money goes (the favourite-longshot bias). Power and Shin both correct for that. Shin's version comes from a model where the bookmaker is guarding against bettors who know more than it does, and its z is an estimate of how big that risk is. In published comparisons on football odds, Shin's method has generally given more accurate probabilities than the plain multiplicative one. For an evenly balanced market all three methods give the same answer.
03Worked examples
Example
Example 1: a 3-way football market.
Home 2.10, draw 3.40, away 3.60.
- Implied: 1/2.10 = 47.62%, 1/3.40 = 29.41%, 1/3.60 = 27.78%. Booksum 104.81%, so the margin is 4.81%.
- Multiplicative: home = 47.62 / 104.81 = 45.43%, fair odds 2.20. Draw 3.56, away 3.77.
- Shin: home 2.18, draw 3.59, away 3.81. Power: 2.17, 3.60, 3.82.
- The methods agree to within a few hundredths on the favourite and move further apart on the outsiders.
Example
Example 2: an even 2-way market.
Both sides at 1.90.
- Implied 52.63% each, booksum 105.26%, margin 5.26%.
- Fair odds 2.00 on both sides with every method, because there's no long shot to treat differently.
Example
Example 3: a lopsided 2-way market.
1.50 and 2.60, margin 5.13%.
- Fair odds for the outsider: 2.73 multiplicative, 2.79 Shin, 2.81 power. That gap is the reason the method matters most on long shots.
04Frequently asked questions
What are fair odds?
Fair odds are the odds with no margin in them, the price at which a bet would break even in the long run. They're simply 1 divided by the true probability. A 50% chance has fair odds of 2.00.
How do I calculate the bookmaker margin?
Turn each price into a probability with 1 / decimal odds, add them up for the whole market and subtract 1. Odds of 2.10, 3.40 and 3.60 add up to 104.81%, so the margin is 4.81%.
Which method should I use?
If you're not sure, Shin. It's a well-studied method that takes more of the margin from long shots, which matches how bookmakers price. Use multiplicative if you want the simple, common method, for example to match another tool. On evenly balanced markets the choice barely matters.
Why do the methods disagree on long shots?
Because they make different assumptions about where the bookmaker put the margin. Multiplicative spreads it evenly in proportion to each price. Power and Shin assume more of it sits on the outsider, so they give the outsider bigger fair odds.
Why does another site show a different margin?
Some sites quote the margin as 1 - 1/booksum instead of booksum - 1. For a 104.81% book that's 4.59% instead of 4.81%. Both describe the same prices. This calculator shows the overround (booksum - 1) and the payout (100 / booksum).
Can I use this for player props like anytime goalscorer?
Only when the market has every outcome priced, for example a yes/no or over/under line on shots on target. Most goalscorer markets only offer a "yes" price, so there's nothing to balance it against and you need your own estimate of the probability instead. The anytime goalscorer guide explains how.