Guide · 6 min read
No-vig fair odds: how to remove the bookmaker margin
Bookmaker odds always contain a margin, so 1 ÷ odds is not the true probability. Removing that margin ("devigging") gives you fair odds, the baseline for expected value, value bets and closing line value. Here are the four common methods, worked through on the same example, and what they mean in practice.
Updated 22 October 2026
Contents
Why odds are not probabilities
Decimal odds imply a probability of 1 ÷ odds (the implied probability). If you add these up for every outcome in a market, you get more than 1. The excess is the bookmaker's margin, also called the overround or vig.
A tennis match: Player A 1.80, Player B 2.10.
1/1.80 = 0.5556 and 1/2.10 = 0.4762. Sum: 1.0318. The margin is about 3.2%.
Together, the implied probabilities come to 103.2%, which is impossible. To get fair probabilities that sum to 100%, you have to take those 3.2% out again. That is where the methods differ. The fair odds are then 1 ÷ fair probability. More on the inputs in implied probability and bookmaker margin and overround.
Multiplicative method (proportional)
The simplest and most common method: divide each implied probability by the sum. The margin is spread in proportion to the probabilities.
fair probability = (1 ÷ odds) ÷ sum, or fair odds = odds × sum
Player A: 0.5556 ÷ 1.0318 = 0.5385, fair odds 1.80 × 1.0318 = 1.857.
Player B: 0.4762 ÷ 1.0318 = 0.4615, fair odds 2.10 × 1.0318 = 2.167.
For two evenly matched sides and a low margin this is usually accurate enough.
Additive, power and Shin methods
- Additive. Subtract the same amount from each implied probability: overround ÷ number of outcomes, here 0.0318 ÷ 2 = 0.0159. With very long outsiders this can produce negative probabilities, so it is unsuitable there.
- Power. Find an exponent k such that (1/odds₁)k + (1/odds₂)k + … = 1. Small probabilities shrink more than large ones, so the outsiders carry more of the margin.
- Shin. A model by Hyun Song Shin (1993) that assumes some bets come from better-informed customers and that the bookmaker protects itself mainly on outsiders. It is solved iteratively. For markets with exactly two outcomes it gives the same result as the additive method (Clarke, Kovalchik and Ingram, 2017).
| Method | Fair odds A (1.80) | Fair odds B (2.10) |
|---|---|---|
| Multiplicative | 1.857 | 2.167 |
| Additive | 1.853 | 2.172 |
| Power (k ≈ 1.047) | 1.851 | 2.175 |
| Shin | 1.853 | 2.172 |
In this close match with a 3.2% margin the methods are only a few thousandths apart. That changes when the margin rises or the odds are far apart.
The favourite-longshot bias
Decades of studies on horse racing and sports betting show that outsiders attract too much money relative to their chances, and their odds are relatively worse than those of favourites. Bookmakers therefore load more margin onto outsiders. The multiplicative method spreads the margin proportionally and so underestimates how overpriced the outsider is.
Fair odds for the outsider: multiplicative 4.20, additive and Shin 4.44, power 4.59. For the favourite: 1.313, 1.290 and 1.278.
If you use the multiplicative method, outsider odds of 4.30 look +EV (4.30 ÷ 4.20 − 1 = +2.4%). With the power method they are −6.4% (4.30 ÷ 4.595 − 1).
Comparative studies such as Štrumbelj (2014) find that Shin-type and power-type methods give slightly more accurate probabilities on average than simple normalisation. For close two-way markets the difference is small; for outsiders and high-margin 1X2 markets it is noticeable.
Which odds make a good reference
The best method is of little use if the input prices are poor. A reference should have two properties: a low margin, so there is little to remove, and a lot of information, meaning high limits and customers who exploit mistakes quickly. Such markets are called sharp; see sharp vs soft bookmakers.
- Sharp bookmakers such as Pinnacle, and betting exchanges, are considered good references. According to our research, residents of Austria cannot open accounts there, and in Slovakia Pinnacle is on the ÚRHH list of prohibited offers. They still work as a price reference only: reading a price does not require an account, and we never suggest them as accounts to Austrian or Slovak users.
- Without a sharp market, the margin-free average of many bookmakers helps.
- A single local bookmaker with a 7 to 10% margin is a weak reference: the more margin you have to remove, the more the result depends on the method.
Also make sure all prices in a market come from the same bookmaker at the same moment.
A 1X2 example to follow
- Note all prices of one market from the same bookmaker, for example 2.30 / 3.30 / 3.20 for home, draw, away.
- Take 1 ÷ odds for each outcome: 0.4348 + 0.3030 + 0.3125 = 1.0503, so a 5.0% margin.
- Choose a method. Multiplicative: fair odds = odds × 1.0503, giving 2.416 / 3.466 / 3.361. Additive or power give about 2.39 / 3.49 / 3.38 here.
- Compare with an offer: if another bookmaker offers 2.50 on the home win, that is 2.50 ÷ 2.416 − 1 = +3.5% against the multiplicative fair price, and 2.50 ÷ 2.392 − 1 = +4.5% against the additive one.
What that percentage means, and why it is still not a certain result, is explained in expected value in betting. Remember that a fee passed on by the bookmaker, such as Austria's 5% Wettgebühr when it is deducted from the payout, lowers your effective odds before you compare. ArbVantage uses margin-free prices internally to sanity-check quotes: a bookmaker more than 10% away from the margin-free median is dropped before sure bets are calculated. Value bets, which rely directly on fair odds, are coming soon.
Frequently asked questions
Which devig method is best?
None is always best. The multiplicative method is simple and usually accurate enough for close two-way markets with a low margin. For markets with a clear favourite and outsider, the power or Shin methods often give slightly better probabilities in studies, because they account for the favourite-longshot bias.
Why do the methods give different results?
Because each method spreads the margin differently across outcomes: in proportion to probability, in equal parts, or more heavily on the outsiders. The higher the margin and the more unequal the odds, the further apart the results.
Does this work for 1X2 bets too?
Yes. Take 1 ÷ odds for all three outcomes, add them up and remove the overround with the method you choose. All three prices must come from the same bookmaker at the same moment.
Do I need an account at a sharp bookmaker to use its odds?
No. You only read the price as a reference. Residents of Austria and Slovakia generally cannot legally open accounts at the best-known sharp bookmakers and exchanges, but their published odds still work as a price reference.
Sources
- Shin (1993): Measuring the Incidence of Insider Trading in a Market for State-Contingent Claims, The Economic Journal 103(420)
- Štrumbelj (2014): On determining probability forecasts from betting odds, International Journal of Forecasting 30(4)
- Clarke, Kovalchik, Ingram (2017): Adjusting Bookmaker's Odds to Allow for Overround, American Journal of Sports Science 5(6)
- Snowberg, Wolfers (2010): Explaining the Favorite-Long Shot Bias, Journal of Political Economy 118(4)
- Úrad pre reguláciu hazardných hier (ÚRHH), Slovakia: licensed operators and list of prohibited offers
As of October 2026. All values rounded to three or four decimal places.
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