acalculator

What are the no-vig odds?

Enter the odds of every outcome of one event to strip out the bookmaker’s margin and see the fair odds. The results are mathematics, not betting advice.

Your numbers

Odds format
Outcomes
Row 1
Row 2
Fair probability, outcome 1
57.98%

With the bookmaker’s margin removed, outcome 1 has a fair probability of 57.98% (-138).

Fair American odds, outcome 1
-138
Fair decimal odds, outcome 1
1.7246
Fair probability, outcome 2
42.02%
Fair American odds, outcome 2
+138
Fair decimal odds, outcome 2
2.38
Overround
3.48%
Vig (bookmaker’s margin)
3.36%

Fair probability, outcome 1: 57.98%. With the bookmaker’s margin removed, outcome 1 has a fair probability of 57.98% (-138).

The results are maths only. They are not betting advice or a promise of a return. Bet only what you can afford to lose. For help with gambling, call 1-800-GAMBLER. Terms of use

How to calculate

Removes the bookmaker’s margin (vig) from the odds of every outcome of one event, and gives each outcome’s fair probability and fair odds, with the size of the margin.

Example with the default inputs (Odds format American, Outcomes [Odds -150; Odds +130]): With the bookmaker’s margin removed, outcome 1 has a fair probability of 57.98% (-138).

Method: With decimal odds dᵢ: implied probability pᵢ = 1/dᵢ; book B = Σ pᵢ; fair probability qᵢ = pᵢ ÷ B; fair decimal odds = 1 ÷ qᵢ = dᵢ × B; overround = B − 1; vig = 1 − 1 ÷ B.

  • The margin is removed in proportion to each outcome’s implied probability (the multiplicative or normalization method). Other methods (additive, power, Shin) give slightly different fair odds, most of all for long shots.
  • The odds come from one bookmaker and cover every outcome of the event.
  • Fair odds estimate what the market expects; they are not the true chances.
  • Results are mathematics, not betting advice.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Odds format American, Outcomes -110; -110 gives Fair probability, outcome 1 50%, Fair probability, outcome 2 50%, Fair American odds, outcome 1 +100, Fair decimal odds, outcome 2 2, Overround 4.761905%, Vig (bookmaker’s margin) 4.545455%.Source: hand calculation in content.mdx: 11/21 each, sum 22/21; fair 1/2 each
  2. Odds format American, Outcomes -150; +130 gives Fair probability, outcome 1 57.983193%, Fair probability, outcome 2 42.016807%, Fair American odds, outcome 1 -138, Fair American odds, outcome 2 +138, Fair decimal odds, outcome 1 1.724638.Source: hand calculation in content.mdx: 3/5 ÷ 119/115 = 69/119; 10/23 ÷ 119/115 = 50/119
  3. Odds format Decimal, Outcomes 2.2; 3.4; 3.6 gives Fair probability, outcome 1 44.283647%, Fair decimal odds, outcome 3 3.695187.Source: hand calculation in content.mdx: 5/11 + 5/17 + 5/18 = 3455/3366; fair 1 = 5/11 ÷ 3455/3366 = 306/691

How it works

Each outcome’s odds become decimal odds dᵢ as exact fractions: American +A gives d = 1 + A ÷ 100, American −A gives d = 1 + 100 ÷ A (A ≥ 100), fractional a/b gives d = 1 + a ÷ b.

  • Implied probability pᵢ = 1 ÷ dᵢ.
  • Book B = p₁ + p₂ + … (exact).
  • Fair probability qᵢ = pᵢ ÷ B, shown in percent. The fair probabilities add up to 100%.
  • Fair decimal odds = 1 ÷ qᵢ = dᵢ × B.
  • Fair American odds from the fair decimal odds f: +100 × (f − 1) when f ≥ 2, −100 ÷ (f − 1) when f < 2, rounded to 2 decimals (halves away from 0), trailing zeros dropped.
  • Overround = 100 × (B − 1) percent.
  • Vig = 100 × (1 − 1 ÷ B) percent: what the bookmaker keeps from bets placed so that every outcome pays the same.
  • Note, shown only when B ≤ 1 (the implied probabilities add up to 100% or less): “The implied probabilities add up to 100% or less: the odds may come from different bookmakers, or the outcomes listed may not cover every result.”

From 2 to 10 outcomes are allowed. When the sum is below 100% (odds from different bookmakers), the overround and vig are negative and the fair probabilities scale up.

What you can type: spaces are ignored and − reads as -. Each format has its own shape, so odds typed in another format are never read as this one: the page says which format they are in and gives the same price in the chosen format. American odds have a + or − sign and a size of at least 100 (+150, -110, +1,000; commas are thousands commas). Decimal odds are a plain number above 1 with no sign (2.5); a single comma with no point is a decimal comma (2,5 is 2.5) unless exactly 3 digits follow it (1,000 is 1000), and any other comma is a thousands comma. Fractional odds are a/b, a:b, a-b or a to b with a and b above 0, or evens, even or evs (any letter case, to too); a bare number is not fractional odds. A number with no sign typed as American odds (100 or more), a whole number typed as fractional odds, or a number below 100 typed as a probability gets a message saying what to add (+150, 4/1, 40%). Decimal odds above 1,000,001 (American +100,000,000) give no answer.

Assumptions

  • The margin is spread in proportion to each outcome’s implied probability.
  • The outcomes cover every way the event can end.
  • Fair odds are the market’s estimate without the margin, not the true chances.

Worked examples by hand

−110 / −110. Each pᵢ = 11/21, B = 22/21. Fair probability = (11/21) ÷ (22/21) = 50% each, fair decimal odds 2, fair American +100. Overround 1/21 = 4.76%, vig 1 − 21/22 = 4.55%.

−150 / +130. p₁ = 3/5 and p₂ = 10/23, so B = 119/115. q₁ = (3/5) × (115/119) = 69/119 = 57.98%; q₂ = 50/119 = 42.02%. Fair decimal odds are 119/69 = 1.7246 and 119/50 = 2.38; in American format, −100 ÷ (50/69) = −138 and +100 × 1.38 = +138.

Decimal 2.2 / 3.4 / 3.6 (a three-way market). p = 5/11, 5/17 and 5/18. Over the common denominator 3366 they are 1530, 990 and 935, so B = 3455/3366 (102.64%). q₁ = 1530/3455 = 306/691 = 44.28%. The third outcome’s fair decimal odds are 3.6 × 3455/3366 = 691/187 = 3.6952.

A note on betting

These results are mathematics, not advice. Fair odds are an estimate, and every bet can lose. If gambling is causing problems for you or someone you know, the US National Problem Gambling Helpline is 1-800-MY-RESET (call or text).

Other questions people ask

What is the vig?

The vig (vigorish, juice or margin) is the bookmaker’s built-in edge. It makes the implied probabilities of all outcomes add up to more than 100%. At −110 on both sides they add up to 104.76%.

How do I remove the vig from odds?

Turn each outcome’s odds into an implied probability (1 ÷ decimal odds), add them up, and divide each one by the sum. For −150 / +130, the implied probabilities 60% and 43.48% add up to 103.48%, so the fair probabilities are 57.98% and 42.02%.

What are the fair odds of −110 / −110?

Each side implies 52.38%. Divided by the 104.76% sum, each is 50%, which is +100 (decimal 2.0) in fair odds.

What is the difference between the overround and the vig?

Both measure the same margin. The overround is how far the implied probabilities add up past 100% (4.76% at −110 / −110). The vig here is the share of the money staked that the bookmaker keeps when every outcome pays the same (1/22 = 4.55%).

Which method does this calculator use?

The proportional (multiplicative) method: every implied probability is scaled by the same factor. It is the most common method. Others (additive, power, Shin) remove more margin from long shots, so their fair odds for long shots differ.