How to use it
- Choose the format you have – decimal, fractional, American, probability, Hong Kong, Indonesian or Malay – and type the odds.
- The headline shows the implied probability; the rows list the same price in every format, with the payout for your stake underneath.
- Switching the format converts the value you typed instead of clearing it, so you can compare notations quickly.
- To measure a bookmaker’s margin, enter the odds of all two or three outcomes of one market in the Overround panel.
Example
Decimal 2.50: profit per unit is 2.50 − 1 = 1.5 = 3/2; because the price is 2.00 or more the American form is +(1.5 × 100) = +150; the implied probability is 1 ÷ 2.50 = 40 %. A 100 stake returns 250. For an odds-on price such as 1.50: profit 0.5 = 1/2, American −100 ÷ 0.5 = −200, probability 66.7 %. A two-way market at 1.91 / 1.91 has implied probabilities of 52.36 % each, a 104.7 % book, a 4.7 % overround and fair odds of 2.00 on both sides.
Formulas
d = decimal odds (total return per 1 staked), d > 1
fractional = (d − 1) written as a fraction 2.50 → 3/2
American = +(d − 1) × 100 if d ≥ 2 2.50 → +150
= −100 ÷ (d − 1) if d < 2 1.50 → −200
probability = 1 ÷ d 2.50 → 40 %
Hong Kong = d − 1 2.50 → 1.50
Indonesian = d − 1 if d ≥ 2, else −1 ÷ (d − 1) 1.50 → −2.00
Malay = d − 1 if d ≤ 2, else −1 ÷ (d − 1) 2.50 → −0.667
payout: profit = stake × (d − 1), total return = stake × d
overround = Σ (1 ÷ dᵢ) − 1; margin = 1 − 1 ÷ Σ (1 ÷ dᵢ); fair odds = dᵢ × Σ (1 ÷ dᵢ)Fractional odds are shown with the smallest denominator (up to 100) that reproduces the price, so 1.909 becomes the familiar 10/11 while 1.91 stays 91/100. American odds are rounded to whole numbers as bookmakers quote them. Probability input accepts 40, 40% or 0.4. All conversions are exact arithmetic; small differences between formats come only from the rounding bookmakers apply when quoting a price.
Conversion table
| Decimal | Fractional | American | Probability | Hong Kong | Indonesian | Malay |
|---|---|---|---|---|---|---|
| 1.10 | 1/10 | -1000 | 90.91% | 0.10 | -10.00 | +0.100 |
| 1.25 | 1/4 | -400 | 80% | 0.25 | -4.00 | +0.250 |
| 1.50 | 1/2 | -200 | 66.67% | 0.50 | -2.00 | +0.500 |
| 1.91 | 91/100 | -110 | 52.36% | 0.91 | -1.10 | +0.910 |
| 2.00 | 1/1 | +100 | 50% | 1.00 | +1.00 | +1.000 |
| 2.50 | 3/2 | +150 | 40% | 1.50 | +1.50 | -0.667 |
| 3.00 | 2/1 | +200 | 33.33% | 2.00 | +2.00 | -0.500 |
| 4.00 | 3/1 | +300 | 25% | 3.00 | +3.00 | -0.333 |
| 5.00 | 4/1 | +400 | 20% | 4.00 | +4.00 | -0.250 |
| 11.00 | 10/1 | +1000 | 9.09% | 10.00 | +10.00 | -0.100 |
| 101.00 | 100/1 | +10000 | 0.99% | 100.00 | +100.00 | -0.010 |
Sources: Wikipedia – Odds (gambling odds formats), Wikipedia – Mathematics of bookmaking (overround).
Reading the overround
If every outcome were priced fairly the implied probabilities would sum to exactly 100 %. Bookmakers shorten each price so the sum is higher – a 1.91/1.91 coin flip sums to 104.7 %. The overround is that excess; the margin (4.5 % here) is the share of total stakes the book expects to keep when bets are balanced. Fair odds remove the margin proportionally, which is a common first step when comparing prices across bookmakers or against your own probability estimate.
Questions
- What do odds of +150 mean?
- A bet of 100 wins 150 profit (250 back in total). It equals 2.50 decimal, 3/2 fractional and a 40 % implied probability. Positive American odds always describe a price of 2.00 or longer.
- How do I convert fractional odds to decimal?
- Divide the top number by the bottom and add 1: 5/2 → 2.5 + 1 = 3.50; 4/6 → 0.667 + 1 = 1.67. Evens is 2.00.
- Why do the implied probabilities add up to more than 100 %?
- Because the bookmaker builds in a margin. Two prices of 1.91 each imply 52.4 % – together 104.7 %. The extra 4.7 % is the overround; the fair price without it would be 2.00 on each side.
- What are Hong Kong, Indonesian and Malay odds?
- Asian formats that quote the profit per unit staked (Hong Kong: 1.50 for decimal 2.50). Indonesian odds switch to a negative “stake to win 1” form below evens (−2.00 for decimal 1.50); Malay odds do the reverse and go negative above evens (−0.667 for decimal 2.50).