How to remove the bookmaker margin from odds to get fair probabilities

Turn every price in one market into an implied probability (1 divided by the decimal odds), add them up, then divide each one by that total. The results sum to exactly 100%. They are margin-free estimates, not the true chances, because the true chances of a sports result cannot be observed.

By BetSmart Kenya Editorial (prepared with AI tools under our editorial policy) · Last updated 2026-10-28

Why prices need cleaning first

The prices in a market add up to more than 100% once you turn them into probabilities. The excess is the margin, which the guide on calculating the bookmaker's margin measures. Removing it means shrinking the probabilities until they add up to exactly 100%, so they can be read as a set of chances.

People searching for how to remove vig from odds usually want one thing: a set of margin-free probabilities for a single market. The method below does that in three steps, and it is simple enough to do on paper.

The rule, stated once

Di is the decimal price of outcome i, and the list must cover every possible outcome of the market. The overround is S − 1. If your prices are fractions or American figures, convert them to decimal first, using the guide on converting betting odds into probability.

Why dividing by S works

Each q_i is divided by the same number, so the ratios between outcomes do not change. If one outcome was twice as likely as another in the prices, it is still twice as likely afterwards. The sum of the new values is (q₁ + ... + q_n) ÷ S = S ÷ S = 1, which is the 100% we wanted.

This is also called the normalisation or proportional method. It takes the margin out in proportion to each probability, so a larger probability loses a larger absolute amount.

Worked example: two outcomes

The margin-free price of each outcome is 1 divided by its new probability, which equals D × S. That gives 1.25 × 1.05 = 1.31 (from 1.3125, rounded to two places) and 4.00 × 1.05 = 4.20.

The margin-free odds are always higher than the offered odds. The difference is the charge you pay on that outcome, which is the same idea as the gap described in the guide on fair odds.

Worked example: three outcomes

Notice that the four-place figures above add to 0.9999, not 1. The exact fractions add to 93/93 = 1. Rounding every value separately is what leaves the small gap, so carry extra decimals through the working.

The margin-free prices are D × S: 1.80 × 1.0333 = 1.86, 3.60 × 1.0333 = 3.72 and 5.00 × 1.0333 = 5.17 (from 5.1667).

Step by step on your own numbers

1. Collect the whole market. Write down the decimal price of every outcome from one market at one moment. The odds converter can handle other formats.
2. Divide 1 by each price. Keep at least five decimal places.
3. Add the results to get S. If S is below 1, an outcome is missing or a price was copied wrongly.
4. Divide each implied probability by S. This is the margin-free probability.
5. Check the total. The values should add up to 1, apart from rounding in the last place.
6. Round at the end. Present percentages to two decimal places and say that they are rounded.

What this does to your money

If the margin-free probabilities were the real chances, every outcome would return the same average amount at the offered price. That amount is p × D = (1 ÷ (D × S)) × D = 1 ÷ S. In the three-way example it is 30/31, or 96.77 per 100 staked.

On KES 1,000 staked that is an average return of about KES 968 and an average cost of about KES 32. Removing the margin from the numbers on your screen does not remove it from the bet. The link between S and the payout rate is set out in the guide on bookmaker payout percentage.

One convention among several

Dividing by S is a choice, not a law of nature. It assumes the margin is taken from each outcome in proportion to its probability. A bookmaker can load margin differently, and the prices alone do not reveal how.

A second simple convention subtracts an equal share of the overround from each implied probability: p_i = q_i − (S − 1) ÷ n. The next table applies it to the three-way example. The equal share is 0.0333 ÷ 3 = 0.0111.

The two columns disagree by up to about 0.7 percentage points in this example, and neither can be shown to be correct. The subtraction method can also give a value at or below zero when an outcome has a very small implied probability and the overround is large. Other methods exist, but this guide does not work through them.

What the result does not tell you

• Not the true chance. The true probability of a match result is not knowable, and no calculation on prices can reveal it.
• Not a forecast. A margin-free 23.81% outcome still fails about three times in four.
• Not a signal to bet. Whether a price is high or low against a margin-free estimate says nothing about whether a bet is wise. How averages are weighed against results is covered in the guide on the expected value of a bet.

Where the prices come from

Regulation 23(1) of the Gambling Control (Conduct of Gambling Operations) Regulations, 2026 requires a licensee to clearly display betting odds, rules and terms applicable to each bet. The prices you need for this sum should therefore be visible before you stake. The regulation as read for this guide does not state a maximum margin.

Use the numbers to understand what a bet costs, then decide a limit you can afford to lose before you start and keep to it. Gambling is addictive, so play responsibly or not at all.