This fair odds calculator takes the bookmaker's margin out of a market and shows what each price would be without it. The same tool is also called a no vig, devig or true odds calculator, vig being the US word for the margin. Type every selection's decimal odds and pick one of four de-vig methods: the fair price appears beside each selection, and a price you have been offered is shown as an edge against it.
A fair price is an estimate worked back from prices somebody else set, never the real chance of anything. How betting odds work covers where the margin comes from, and removing the bookmaker margin compares the methods.
How to use the fair odds calculator
Three inputs, and only the first is needed.
- Market odds: every selection in one market at one bookmaker, in decimal odds. The tool opens with two boxes: press Add a selection for each extra one, up to 30, and Remove to drop one. Prices in fractional or American odds go through the odds converter first.
- Method: multiplicative, additive, power or Shin. The fair prices change with it.
- Price offered: optional, one per selection. Type the price you can actually get and its edge appears with it.
Prices read from $1.01 to $10,001, and a blank box leaves that selection out rather than refusing the market, so a half-typed price is never an error. Fair prices show to the cent and percentages to one decimal place, or two below 1%, rounded once, at the end.
The formula each method uses
Two lines come first:
implied probability = 1 / decimal odds
market percentage = the sum of every selection's implied probability
A market with no margin adds to exactly 100%, and anything above that is the margin. The bookmaker margin calculator measures it; this one hands it back. Below, the market percentage is a plain number, so 103.2% is 1.032.
- Multiplicative: fair probability = (1 / odds) / market percentage. Every chance shrinks by the same proportion, so fair odds = decimal odds x market percentage.
- Additive: fair probability = (1 / odds) - (market percentage - 1) / number of selections.
- Power: fair probability = (1 / odds) raised to the power k, the one power that makes the fair probabilities add to 1.
- Shin: fair probability = (the square root of (z x z + 4 x (1 - z) x (1 / odds) x (1 / odds) / market percentage) - z) / (2 x (1 - z)), where z is the share of money treated as better informed.
Fair odds are then 1 / fair probability, and the calculator searches for k and z. The power method and the Shin method cover what each assumes.
A two way market, de-vigged
With illustrative prices of $1.80 and $2.10: 1 / 1.80 = 0.55556, or 55.6%, and 1 / 2.10 = 0.47619, or 47.6%. The market percentage is 0.55556 + 0.47619 = 1.03175, or 103.2%.
Multiplicative: 0.55556 / 1.03175 = 0.53846, a fair price of 1 / 0.53846 = $1.86, and 0.47619 / 1.03175 = 0.46154, which is $2.17.
Additive: the margin is 0.03175, so 0.01588 comes off each side. 0.55556 - 0.01588 = 0.53968, which is $1.85, and 0.47619 - 0.01588 = 0.46031, which is $2.17.
| Method | Fair chance, $1.80 side | Fair price | Fair chance, $2.10 side | Fair price |
|---|---|---|---|---|
| Multiplicative | 53.8% | $1.86 | 46.2% | $2.17 |
| Additive | 54.0% | $1.85 | 46.0% | $2.17 |
The power and Shin answers land on the same $1.85 and within a cent of the same $2.17, because these two prices sit close together.
A short favourite pulls the methods apart even with two outcomes. With illustrative prices of $1.20 and $4.50, the market is 1 / 1.20 + 1 / 4.50 = 1.0556, so on the multiplicative method the outsider is 4.50 x 1.0556 = $4.75. The additive method takes 0.0556 / 2 = 0.0278 off the outsider's chance, leaving 0.2222 - 0.0278 = 0.1944, which is 1 / 0.1944 = $5.14. Shin gives the same $5.14 and power $5.41, 66 cents longer than the multiplicative price.
Why the methods disagree on a long shot
Five illustrative win prices in one race: $2.00, $4.00, $6.25, $8.00 and $20.00. They imply 50%, 25%, 16%, 12.5% and 5%, which add to 108.5%.
| Price | Multiplicative fair price | Additive fair price |
|---|---|---|
| $2.00 | $2.17 | $2.07 |
| $4.00 | $4.34 | $4.29 |
| $6.25 | $6.78 | $6.99 |
| $8.00 | $8.68 | $9.26 |
| $20.00 | $21.70 | $30.30 |
Multiplicative multiplies every price by 1.085. Additive takes 8.5 / 5 = 1.7 points of chance off each selection, so the outsider falls from 5% to 3.3%, which is 1 / 0.033 = $30.30. Against the multiplicative column that leaves the favourite's fair price 10 cents shorter and the outsider's $8.60 longer.
Shin sits between the two columns on every line. Power does not: it raises each price to the power k, here about 1.064, so the outsider becomes 20.00 raised to the power 1.064 = $24.23, nearer the multiplicative end. But 4.00 raised to that same power is $4.37 and 6.25 is $7.03, longer than either column.
Note: No method knows how a bookmaker spread its margin across a market. Each is an assumption about that, which is why outsiders are where they differ.
Reading the edge on a price you were offered
edge = offered price / fair price - 1
Take the two way market above, on the multiplicative method: a fair price of $1.86 against an offered $1.95 is 1.95 / 1.857 - 1 = 0.050, an edge of 5.0%. On the additive or Shin method the fair price is $1.85, and the same $1.95 is 1.95 / 1.853 - 1 = 5.2%. The calculator works from the unrounded fair price behind the $1.86 on screen, so it shows 5.0% where the rounded figure gives 4.8%. A negative edge, the usual answer, means the offered price is shorter than the fair estimate.
An edge is only as good as the market behind it, and how to calculate fair odds covers which market to start from.
Risk: Betting involves risk. A fair price is an estimate, so a price with an edge against it can still lose, and often does, and there is no guarantee of profit. See responsible gambling for limits and support.
What the calculator refuses to answer
- A price outside $1.01 to $10,001, or anything that is not a decimal number: that box turns red and is left out. A box part-way to a price, such as 1. on the way to 1.80, is left out quietly instead.
- Fewer than two prices, because one price is not a market.
- The additive method, where it would take more chance off a selection than it has. Add a $71.00 outsider to the five prices above: the market reads 109.9%, so additive would take a sixth of those 9.9 points off everything, about 1.7 points, while the outsider's whole chance is 1.4 points. Its fair chance would land below zero, so the calculator refuses rather than print a negative price.
- A market so lopsided that a method's own arithmetic runs out, such as 29 prices at $1.01 beside one at $10,001. The fair price would come back as nothing a reader could use, so that method refuses too.
- Nothing under 100%: a market that adds to less is flagged instead, not refused.
Mistakes that cost money
| Mistake | What it costs | The fix |
|---|---|---|
| Mixing prices from two bookmakers | The market can add to under 100% and the fair prices come back too short | Use one bookmaker's market |
| Leaving a selection out | On the multiplicative method, dropping the $20.00 above reads the market as 103.5%, so the $2.00 fair price becomes 2.00 x 1.035 = $2.07, and an offered $2.10 looks like a 2.10 / 2.07 - 1 = 1.4% edge when, with every selection in, it is 2.10 / 2.17 - 1 = minus 3.2% | Type every selection and check the Prices read tile against the field |
| Typing a place market | With three places paid its fair chances should add to 300%, but the calculator scales every market to 100%, so on the multiplicative method each fair place price comes back about three times too long | De-vig win and head to head markets only, where one selection wins |
Where the screeners fit
B337's +EV screener repeats this sum across sports markets: the margin comes out of prices across the market, the results are combined into one fair price per selection, and the bookmaker prices above it are ranked by edge. The arbitrage and middles screeners beside it look for something else: prices across bookmakers that add to under 100%, and gaps between two lines on the same total or handicap. All three come with Terminal Pro and Full Automation, or as the Screeners plan, and a free account sees the live counts with the rows locked. You place every bet yourself, and positive expected value betting covers what an edge against an estimate is worth.
Risk: Betting involves risk. An edge measured against an estimate is an estimate too, and an arbitrage or a middle only works if every bet is accepted at the price shown. Many bookmakers restrict or prohibit automated betting, third-party access and multiple accounts in their terms, and a bookmaker can limit your stakes, void bets or close your account; that risk is yours.