# No-vig odds

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Canonical: https://novigapi.com/learn/no-vig-odds

No-vig odds are the prices a market would show with the bookmaker margin removed, so the implied probabilities of all outcomes add to exactly 100%.

```
no_vig_decimal_i = sum(q) / q_i, where q_i is the implied probability of outcome i
```

No-vig odds are what a market's prices would be if the book charged nothing. They are the output of devigging, written back as odds instead of probabilities. A coin flip with no vig is +100 on both sides; a -150 favorite against a +130 underdog becomes roughly -138 and +138 once the margin is gone. No-vig odds are the cleanest way to compare a price at one book to the consensus at another.

## How it works

Convert every outcome to an implied probability, add them up, and divide each probability by the total. The result is a set of fair probabilities that sum to 100%. Convert each one back to odds: decimal odds are 1 / p; American odds are -(p / (1 - p)) x 100 when p is above 50% and +((1 - p) / p) x 100 when it is below. On a two-way market the two no-vig American prices are always mirror images, such as -138 and +138.

## Worked example: a three-way soccer market

Three-way markets carry more margin than two-way markets, which makes the no-vig price more useful. Take Home +150, Draw +240 and Away +190.

No-vig odds on a three-way market (multiplicative method)

| Outcome | Book odds | Implied | No-vig probability | No-vig American | No-vig decimal |
| --- | --- | --- | --- | --- | --- |
| Home | +150 | 40.000% | 38.501% | +159.7 | 2.597 |
| Draw | +240 | 29.412% | 28.309% | +253.2 | 3.532 |
| Away | +190 | 34.483% | 33.190% | +201.3 | 3.013 |
| Total |  | 103.895% | 100.000% |  |  |


The book's margin is 3.895% above 100%. Any other book offering Home at better than +159.7 is beating this market's fair price. You can reproduce the table, or try the additive, power and Shin methods, in the [no-vig calculator](https://novigapi.com/no-vig-calculator).

## On Novig

Novig prices are already close to no-vig odds, because an exchange has no house margin. The remaining gap is the spread between the best bid and the implied ask. When the book shows a Yes bid of 55% and a No bid of 42%, the midpoint fair price is 56.5% for Yes and 43.5% for No, or -129.9 and +129.9 in American odds. That midpoint is a no-vig price built from traders' own orders. Our `/fair-price` endpoint publishes it for every two-sided market, and the [Novig odds converter](https://novigapi.com/novig-odds-converter) handles the conversion.

## Common mistakes

- Using no-vig odds from a thin or stale market. A wide spread or an old quote makes the midpoint unreliable.
- Forgetting that the method matters on long shots. Multiplicative and Shin can differ by a full point on a +1000 price.
- Treating no-vig odds as the price you can bet. They are a benchmark, not an offer.

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