Tool No. 1
Odds format converter
Type a price into any one field — American (-110, +150), decimal (1.91) or fractional (10/11) — and the other two formats and the implied probability update as you type.
- Implied probability
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- Break-even record
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- Profit on $100
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Tool No. 2
Two-way no-vig calculator
Enter the American odds on both sides of a two-way market (a spread, a total, or a two-way moneyline). The calculator shows the total market percentage, the book’s hold, and the no-vig fair probability and fair price for each side.
- Total market
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- Vig (hold)
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- Fair — Side A
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- Fair — Side B
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Quick reference: American to decimal to probability
The table below is exact, not rounded off a chart someone else made. Decimal odds are the total return per unit staked; implied probability is the break-even win rate the price charges you.
| American | Decimal | Implied probability |
|---|---|---|
| -200 | 1.50 | 66.67% |
| -150 | 1.667 | 60.00% |
| -120 | 1.833 | 54.55% |
| -110 | 1.909 | 52.38% |
| -105 | 1.952 | 51.22% |
| +100 | 2.00 | 50.00% |
| +110 | 2.10 | 47.62% |
| +120 | 2.20 | 45.45% |
| +150 | 2.50 | 40.00% |
| +200 | 3.00 | 33.33% |
| +250 | 3.50 | 28.57% |
| +300 | 4.00 | 25.00% |
The math the converter is doing
All three formats encode one number: the price of the outcome. Conversion is just re-arranging it.
- Negative American odds (say −A): implied probability = A ÷ (A + 100). Decimal odds = 1 + 100 ÷ A.
- Positive American odds (+A): implied probability = 100 ÷ (A + 100). Decimal odds = 1 + A ÷ 100.
- Decimal odds d: implied probability = 1 ÷ d. To go back to American: if d ≥ 2, American = +(d − 1) × 100; if d < 2, American = −100 ÷ (d − 1).
- Fractional odds n/d: decimal = 1 + n ÷ d, and implied probability = d ÷ (n + d).
Worked example: −110
At −110 you risk 110 to win 100. Implied probability = 110 ÷ 210 =52.38%. Decimal = 1 + 100/110 = 1.909. In fractional terms that is 10/11. The reading that matters: you must win more than 52.38% of these bets over time just to break even. Our primer on how to read betting odds goes through each format from scratch.
Worked example: +150
At +150 you win 150 per 100 risked. Implied probability = 100 ÷ 250 =40%. Decimal = 2.50, fractional 3/2. The price is telling you the book has this outcome at four chances in ten — before its margin. What you do with that number is covered in our guide to implied probability.
Removing the vig, step by step
A two-way market priced −110 / −110 implies 52.38% on each side. Together: 104.76%. Reality only has 100% to hand out, so the extra 4.76 points are the vig — the fee baked into the prices. As a share of all money the book handles on the market, its hold is 4.76 ÷ 104.76 = 4.55%.
To find the fair line, normalize: divide each side’s implied probability by the total. Here, 52.38 ÷ 104.76 = 50% for each side, which converts back to fair odds of +100 (decimal 2.00). That is the number to compare your own estimate against when you are hunting for positive expected value — not the shaded price on the board.
The same procedure works on lopsided lines. Take −200 / +170: the favorite implies 66.67%, the underdog 37.04%, total 103.70%. Fair probabilities are 64.29% and 35.71% — fair odds of about −180 and +180. More on where books put the margin, and why it varies by market, in our market mechanics section and the odds pieces in odds & probability.
Frequently asked questions
How do you convert American odds to decimal odds?
For negative American odds, decimal = 1 + 100 ÷ |odds|. So −110 becomes 1 + 100/110 = 1.909. For positive American odds, decimal = 1 + odds ÷ 100, so +150 becomes 1 + 150/100 = 2.50. The decimal number is your total return per unit staked, including the stake.
How do you calculate implied probability from betting odds?
Convert to decimal and take the reciprocal: implied probability = 1 ÷ decimal odds. Equivalently, for negative American odds it is |odds| ÷ (|odds| + 100), and for positive American odds it is 100 ÷ (odds + 100). At −110 that is 110/210 = 52.38%; at +150 it is 100/250 = 40%.
What is the vig on a −110 / −110 line?
Each −110 side implies 52.38%, so the two sides sum to 104.76% — an overround of 4.76 percentage points. As a share of the total money handled, the book’s hold is 4.76 ÷ 104.76 = 4.55%. After normalizing, the no-vig fair probability of each side is exactly 50%, i.e. fair odds of +100 (decimal 2.00).
What are no-vig (fair) odds?
No-vig odds are what the market would pay if the sportsbook took no margin. You compute them by dividing each side’s implied probability by the sum of both sides’ implied probabilities, then converting those normalized probabilities back into odds. They are the cleanest estimate of what the market actually thinks the probabilities are.
Why do implied probabilities add up to more than 100%?
Because every price is shaded against you. The excess over 100% is the overround — the sportsbook’s built-in margin. If two outcomes were priced with no margin at 50% each, both would be +100. Price them both at −110 instead and each implies 52.38%, which is where the extra 4.76% comes from.
How do you convert fractional odds like 10/11 to a probability?
A fraction n/d pays n profit per d staked, so the decimal odds are 1 + n/d and the implied probability is d ÷ (n + d). For 10/11: decimal 1.909, implied probability 11/21 = 52.38% — exactly the same price as American −110.