How to calculate fair odds and check for value: a guide to the fair odds calculator

Fair odds and the margin in two sentences

Betting odds are the inverse of a probability: odds of 2.00 mean 50%, odds of 4.00 mean 25%. At a bookmaker the probabilities of all the outcomes of one market add up to more than 100%, and the excess is the margin, the bookmaker's earnings built into the prices.

An example on the 1X2 market:

The margin of this market is 5.32%. Fair odds are the odds with that excess removed: the price at which neither you nor the bookmaker has an edge. The whole question is how to split those 5.32% across the three outcomes, and that is what the methods of removing the margin answer. How the margin gets into the prices is covered in how bookmakers make money.

How to use the calculator step by step

1. Choose the number of outcomes under Outcomes: 3 (1X2) for markets with a draw or 2 for two-way markets such as over/under, Asian handicap, BTTS, draw no bet or a tennis match.
2. Enter the reference odds: the full set of odds of one market from one bookmaker. The calculator works out the fair odds from them.
3. Optionally enter the odds to assess: the offer you want to check, for example at another bookmaker. One outcome is enough; you do not have to enter the whole market.
4. Read the result: the margin of the market, the range of fair odds for each outcome, the value check with EV and the table comparing the methods.

A decimal point and a decimal comma both work in the odds, and the number of outcomes is remembered in your browser.

Which market to use as the benchmark?

Fair odds are only as good as the market you work them out from. A good reference market:

• comes from one bookmaker: a margin only makes sense within one offer, and by mixing the best prices from several places you create a market nobody has priced,
• has a low margin: the calculator grades it as Low margin (up to 3%), Medium margin (up to 6%) or High margin (above 6%), and the lower it is, the less guesswork goes into splitting it,
• is liquid: the main markets (1X2, 2.5 goals, the main handicap line) in popular leagues are priced more accurately than side markets or lower leagues,
• is current: a price from an hour ago does not reflect the line-up news the market already knows (more in when odds stop moving).

The best benchmark is a low-margin bookmaker that takes big stakes and moves its prices quickly (a so-called sharp bookmaker). If you only have access to soft bookmakers, pick the one with the lowest margin on the market in question and treat the result with more caution.

If the sum of the probabilities comes out below 100%, the odds form a surebet. There is then no margin to remove, and the calculator offers you the surebet calculator, where you can split the stakes.

Five ways to remove the margin

The methods differ in how they split the margin between the favourite and the underdog:

• Multiplicative (normalisation): divides each probability by the sum, so it spreads the margin in proportion. The simplest and most popular, but it usually overstates the underdogs' chances.
• Margin proportional to odds (Joseph Buchdahl's method): takes the same share of probability off every outcome, so the underdog carries most of the margin. With very high odds it has no solution.
• Odds ratio: scales the odds of every outcome, p/(1−p), by one common factor.
• Logarithmic: raises the probabilities to one power, which corrects the underdogs harder.
• Shin: assumes that the bookmaker uses the margin to protect itself against better-informed bettors. It only works for markets with a margin above 0.

Why does it matter? Bookmakers usually put more margin into the underdogs' odds than into the favourites' (the so-called favourite-longshot bias, which shows clearly in our data on tennis favourites). In an even match the methods give almost the same answer, but with a clear favourite the differences are large:

Depending on the method, the underdog's fair odds run from 11.49 to 13.16. That is why the calculator gives you a range rather than one number. With two equal prices (such as 1.90 and 1.90) every method gives exactly 2.00, so the range collapses.

Example: does this offer have value?

The reference odds are the ones from the table at the start of the article: 3.75 / 4.45 / 1.78 (a 5.32% margin). The calculator works out these fair odds ranges from them:

Another bookmaker pays 4.20 / 4.80 / 1.95. The value check looks like this:

• 1 at 4.20: Value, EV from +4.3% to +6.3%. The price is above the whole fair range.
• X at 4.80: Unclear, EV from −0.6% to +2.4%. The price falls inside the range, so the methods disagree.
• 2 at 1.95: Value, EV from +4.0% to +6.2%.

Two of the three prices beat the fair odds by every method, so on the home and the away win the other bookmaker pays more than the reference market says those results are worth. That is the gap the calculator is there to find. On the draw the edge depends on the method, and that is too little to rely on.

EV (expected value) is the average result per £1 staked over the long run: an EV of +5% means an average profit of £5 for every £100 staked on such bets. A single bet still either wins or loses, so EV only makes sense over a large number of bets.

The margin: how far below fair odds a usual price sits

The margin pushes every bookmaker's price below its fair odds. With the margin spread evenly (the multiplicative method in reverse: fair odds ÷ (1 + margin)), a market with a 3% or a 6% margin, the calculator's limits for a low and a medium margin, prices outcomes like this:

For a bet to have value, its price has to be above the fair odds, so it has to beat the bookmaker's usual price by about as much as the margin: 2.00 or more instead of 1.94 or 1.89. Since bookmakers load more of the margin onto underdogs, the gap on a long shot is usually bigger than the table shows. A difference like that between a price and the market's valuation comes up mainly with promotions: odds boosts and special prices. That is why the fair odds calculator is most useful for assessing a boost: enter the reference market, then the boosted price as the odds to assess, and you see straight away whether the promotion is worth anything.

How to read the result in the calculator

• The margin strip: the Margin, the Sum of probabilities and the grade of the market (Low margin, Medium margin, High margin), with a short hint on whether the market works as a benchmark.
• The fair odds cards (Fair odds): the range of fair odds and probabilities for each outcome. On the plot the dots are the methods and the vertical tick is the odds with margin, and once you enter odds to assess you also see where they sit against the range.
• The value check: Value (the odds are above the whole fair range), Unclear (inside the range) or No value (below it), with the EV from the most cautious to the most generous method.
• The comparison of methods (Methods compared): a table of the probabilities and fair odds from each method, and a With margin row with the original odds. A method without a solution for the given odds is marked, and the others carry on.

Treat Unclear as "not enough of an edge to be sure". If the odds to assess are on an underdog, the methods that correct it harder (margin proportional to odds, logarithmic, Shin) are usually more reliable than the multiplicative one.

What the calculator will not do

• It does not know the match: it works from the odds alone. If the reference market is wrong, the fair odds are wrong with it.
• It does not link markets: fair odds on 1X2 will not turn into a handicap or goals by themselves.
• It does not see odds movements: the result applies to the odds you entered. If the reference moves, calculate again.

If you want a benchmark for football matches that does not depend on a bookmaker, try the Elo calculator, which works out 1X2 chances from our club Elo ratings and also compares them with a bookmaker's odds. Why even a good model rarely beats the market is explained in why a betting model is not enough.

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