Odds converter
One price in — decimal, fractional and implied probability out, both directions. The full conversion table is below, along with the thing most converters skip: implied probability is not the real chance of something happening.
Implied probability — how often a bet at −110 must win to break even.
Decimal odds — your total return per $1 staked, stake included.
Fractional odds — profit relative to stake, the way racebooks quote prices.
The four formats, and what each is for
- American — the US standard. A minus number is what you stake to win $100; a plus number is what $100 wins. +100 is even money.
- Decimal — the total multiplier on your stake, stake included. Easiest for working out returns: $50 at 2.50 returns $125. Standard across Europe and on exchanges.
- Fractional — profit over stake, reduced. 10/11 means winning ten for every eleven risked. Traditional in UK racing.
- Implied probability — the win rate the price needs to break even. The one to use when comparing a price against your own view rather than working out a payout.
The conversion formulas
- American to decimal — plus price: 1 + odds ÷ 100. Minus price: 1 + 100 ÷ |odds|.
- Decimal to implied probability: 1 ÷ decimal.
- American to implied — minus: |odds| ÷ (|odds| + 100). Plus: 100 ÷ (odds + 100). Both agree with 1 ÷ decimal.
- Probability back to American — above 50%: −(100 × p) ÷ (1 − p). Below 50%: 100 × (1 − p) ÷ p.
- American to fractional: profit over stake, reduced. −110 is 100/110, which reduces to 10/11.
Implied probability is not the real chance
This is the part that matters and the part most converters leave out. A single price's implied probability includes the book's margin, so it overstates the chance of the outcome.
Take a market at −110 both ways. Each side implies 52.38%. Added together that is 104.76% — but two outcomes cannot together be more than certain. The excess 4.76% is the book's margin, and the hold it keeps is 4.55%.
Strip that out proportionally and each side is 50.0% — the market's actual view. So when you convert a single price, treat the result as the break-even rate you need, not as an estimate of the truth. Getting from one to the other takes both sides of the market, which is what the devig calculator does.
Odds conversion table
Every common price in all four formats.
| American | Decimal | Fractional | Implied |
|---|---|---|---|
| −1000 | 1.100 | 1/10 | 90.9% |
| −500 | 1.200 | 1/5 | 83.3% |
| −300 | 1.333 | 1/3 | 75.0% |
| −250 | 1.400 | 2/5 | 71.4% |
| −200 | 1.500 | 1/2 | 66.7% |
| −150 | 1.667 | 2/3 | 60.0% |
| −125 | 1.800 | 4/5 | 55.6% |
| −110 | 1.909 | 10/11 | 52.4% |
| −105 | 1.952 | 20/21 | 51.2% |
| +100 | 2.000 | 1/1 | 50.0% |
| +105 | 2.050 | 21/20 | 48.8% |
| +110 | 2.100 | 11/10 | 47.6% |
| +125 | 2.250 | 5/4 | 44.4% |
| +150 | 2.500 | 3/2 | 40.0% |
| +200 | 3.000 | 2/1 | 33.3% |
| +250 | 3.500 | 5/2 | 28.6% |
| +300 | 4.000 | 3/1 | 25.0% |
| +500 | 6.000 | 5/1 | 16.7% |
| +1000 | 11.000 | 10/1 | 9.1% |
Worked example
A book lists a prop at +120. Decimal is 1 + 120 ÷ 100 = 2.200, so $10 returns $22.00 in total. Fractional is 120/100, reduced to 6/5 — six won for every five risked. Implied probability is 100 ÷ 220 = 45.5%.
That last figure is the useful one: the bet has to land more than 45.5% of the time to be worth taking. And if the other side is priced −140, the pair implies 103.79% in total, so the fair chance on your side is nearer 43.8%.
Why converting matters when you compare books
American odds are hard to compare by eye. The gap between −105 and −115 looks trivial and is worth about 9% of your profit. In decimal it is 1.952 against 1.870, which is obvious immediately. If you are shopping the same bet across books, convert first and the better price stops hiding.
Related tools
- Bet calculator — a converted price plus a stake gives profit and total return.
- Devig calculator — remove the margin from both sides for the true probability.
- EV calculator — compare a price against your own probability estimate.
- Parlay calculator — where decimal conversion does the real work, because legs multiply.
Questions
What are American odds?
American odds quote prices relative to $100. A negative number like −110 is the amount you must stake to win $100; a positive number like +150 is the profit on a $100 stake. Favourites are negative, underdogs positive, and +100 is even money.
How do you convert American odds to decimal?
For positive odds, decimal = 1 + odds/100, so +150 becomes 2.50. For negative odds, decimal = 1 + 100/|odds|, so −150 becomes 1.667. Decimal odds multiply directly by your stake to give the total return, stake included.
How do you calculate implied probability from odds?
For negative odds it is |odds| ÷ (|odds| + 100); for positive odds it is 100 ÷ (odds + 100). Both give the same answer as 1 ÷ decimal odds. So −110 implies 52.38% and +150 implies 40.0%.
Is implied probability the same as the real chance of winning?
No, and it is the most common misunderstanding about odds. A single price includes the book’s margin, so its implied probability is inflated. Both sides of a −110/−110 market imply 52.38%, totalling 104.76% — the excess is the hold. Strip it out and each side is actually 50%.
How do I convert a probability back into odds?
Above 50%, American odds = −(100 × p) ÷ (1 − p). Below 50%, they are 100 × (1 − p) ÷ p. A 60% chance is −150; a 40% chance is +150.
Why does −110 show as 10/11 in fractional odds?
Fractional odds quote profit over stake. Risking $110 to profit $100 is 100/110, which reduces to 10/11. Same price, written the way racing books quote it.
Which odds format should I use?
Whichever your book shows — they are the same number. Decimal is easiest for working out returns because it multiplies straight into your stake. American is standard in US sportsbooks, fractional is traditional in UK racing, and implied probability is the one to use when comparing a price against your own view.
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