No-Vig Fair Odds: How to Remove the Vig and Find a Fair Price
Related book: The Sports Investing Blueprint by Ethan Cole · Amazon
A fair price is the number a market would post if it charged no margin. Once you can work it out, you have a benchmark for every bet: any posted price can be checked against it in a few seconds. This page walks through the full calculation in four steps, turns the result back into American odds you can read at a glance, does the same for a three-way soccer market, and shows how to tell whether a posted price beats the fair one.
Every price and team on this page is a made-up example. Percentages are rounded to two decimals; the math behind them uses exact fractions.
The four-step fair odds method
- Convert every side to implied probability. For a negative price, drop the minus and call it A: A / (A + 100). For a positive price A: 100 / (A + 100).
- Add the implied probabilities. The total is above 100%. The extra is the overround, the margin built into the market.
- Normalize. Divide each side's implied probability by the total. The results now add to exactly 100%. These are the no-vig probabilities.
- Convert back to fair odds. For a no-vig probability p above 50%: fair price = −100 × p / (1 − p). For p at or below 50%: fair price = +100 × (1 − p) / p. Fair decimal odds are simply 1 / p.
Steps 1 to 3 are covered in more depth, with -110 and three-way tables, in implied probability and the vig. This page focuses on step 4 and on putting the fair price to work.
Worked example: a two-way moneyline
A game is posted Team A -140, Team B +120.
| Side | Posted | Implied | No-vig | Fair American | Fair decimal |
|---|---|---|---|---|---|
| Team A | -140 | 140 / 240 = 58.33% | 77 / 137 = 56.20% | -128.33 | 1.78 |
| Team B | +120 | 100 / 220 = 45.45% | 60 / 137 = 43.80% | +128.33 | 2.28 |
The implied probabilities add to 137 / 132, about 103.79%, so the overround is 3.79 points. Dividing each side by 137 / 132 gives 77 / 137 and 60 / 137, which add to exactly 100%.
Converting back: Team A's fair price is −100 × (77 / 137) / (60 / 137) = −100 × 77 / 60 = -128.33. Team B's is +100 × 77 / 60 = +128.33. In a two-way market the two fair prices mirror each other, which makes a quick sanity check.
So the posted -140 asks you to lay about 11.67 more than the fair -128.33, and the posted +120 pays about 8.33 less than the fair +128.33. That gap is the vig, priced in American odds.
Worked example: a three-way soccer moneyline
A soccer match result has three outcomes. Say it is posted Home +150, Draw +230, Away +190. The method does not change; there is just one more row.
| Result | Posted | Implied | No-vig | Fair American | Fair decimal |
|---|---|---|---|---|---|
| Home | +150 | 40.00% | 38.17% | +161.96 | 2.62 |
| Draw | +230 | 30.30% | 28.92% | +245.79 | 3.46 |
| Away | +190 | 34.48% | 32.91% | +203.88 | 3.04 |
The implied probabilities are 2 / 5, 10 / 33 and 10 / 29. They add to 5,014 / 4,785, about 104.79%, an overround of 4.79 points. Dividing each by that total gives 957 / 2,507, 725 / 2,507 and 825 / 2,507, which add to exactly 100%.
All three no-vig probabilities are below 50%, so each fair price is positive: for the draw, p = 725 / 2,507, so the fair price is +100 × (2,507 − 725) / 725 = +178,200 / 725, about +245.79. Three-way fair prices do not mirror each other, so check them by confirming the no-vig probabilities sum to 100%.
Compare a posted price with the fair price
The fair price is most useful when you hold it up against a price somewhere else. If a posted price pays more than the fair price, its break-even rate is lower than the no-vig probability, and the bet has positive expected value at those chances.
Using the two-way fair line (Team A -128.33, Team B +128.33) as the benchmark:
| Bet | Posted | Break-even | No-vig chance | EV per $100 |
|---|---|---|---|---|
| Team B | +135 | 42.55% | 43.80% | +$2.92 |
| Team B | +128 | 43.86% | 43.80% | −$0.15 |
| Team B | +120 | 45.45% | 43.80% | −$3.65 |
| Team A | -125 | 55.56% | 56.20% | +$1.17 |
| Team A | -130 | 56.52% | 56.20% | −$0.56 |
For Team B at +135: EV = (60 / 137 × $135) − (77 / 137 × $100) = $400 / 137, about +$2.92 per $100. The rule of thumb: a plus price above the fair plus price, or a minus price shorter than the fair minus price, is better than fair.
The same check works on the soccer market. If another book has the draw at +250 against a fair +245.79, the break-even falls to 28.57% against a 28.92% no-vig chance, worth about +$1.22 per $100. The away side at +180 is worse than its fair +203.88 and comes out about −$7.86 per $100.
Which market to use as the benchmark
A fair price is only as good as the market it comes from. A few habits keep the benchmark sharp:
- Use a market with a small overround. Less margin to remove means less room for the removal method to distort the result.
- Use the latest prices. A fair line from hours ago may not reflect news since then.
- Compare like with like: same game, same bet type, same settlement rules.
- The closing price is the most-tested benchmark of all. Closing line value uses this exact no-vig method on the close to grade the prices you took.
This page uses the proportional method, which splits the margin in line with each side's implied probability. It is the simplest method and the one used throughout this site, so the numbers here match the other articles.
Put the fair price to work
Work out the fair line once, then shop for prices that beat it. Line shopping covers how to compare prices across books you are allowed to use, and the free bankroll and line-shopping worksheet gives you a place to record the posted price, the fair price and your stake side by side.
The American odds implied probability table speeds up step 1: look up each posted price, add the rates, divide, and convert back. Keep stakes inside a plan; bankroll management and unit sizing covers that part.
For how fair prices, bankroll and record keeping fit together into one system, see the book.