How to use the implied probability calculator
The implied probability calculator works on a whole market, not just one price. Type the odds for each selection in any format (9/4, 3.25 or +225). Use Add a selection for more runners and the cross to remove one. Each row shows the chance its price implies and its fair odds; the results show the book percentage and the bookmaker margin.
The margin and fair odds only mean something when every runner in the race is listed. The three prices the calculator opens with add up to 90.8%, under 100%, because the rest of the field is missing. For a single price, the return and its implied chance, the odds calculator is quicker.
Book percentage and bookmaker margin
Each price implies a chance of 1 / decimal odds. Add those chances up across every runner and you get the book percentage. A fair book would total exactly 100%; a bookmaker's totals more, and the amount over 100% is the overround, or bookmaker margin.
Take a two-horse match at 1.90 each. Each price implies 52.6%, so the book is 105.26% and the margin is 5.26%. If the bookmaker takes £100 on each horse, it holds £200 and pays out £190 whichever wins: £10 kept, which is 5% of the money staked.
The lower the book percentage, the less you give away, so it is worth comparing before you bet. If a full field ever adds up to less than 100%, usually only by taking the best price on each runner from different bookmakers, backing every runner in proportion returns more than the total stake.
Worked example: a five-runner race
A five-runner race priced 6/4, 9/4, 4/1, 8/1 and 12/1. The implied chances add up to 109.57%, a margin of 9.57%. To get fair odds, the calculator divides each implied chance by the book percentage so the chances total 100%, then turns them back into odds.
| Price | Decimal | Implied | Fair chance | Fair odds |
|---|---|---|---|---|
| 6/4 | 2.50 | 40.0% | 36.5% | 2.74 |
| 9/4 | 3.25 | 30.8% | 28.1% | 3.56 |
| 4/1 | 5.00 | 20.0% | 18.3% | 5.48 |
| 8/1 | 9.00 | 11.1% | 10.1% | 9.86 |
| 12/1 | 13.00 | 7.7% | 7.0% | 14.24 |
| Total | 109.6% | 100% |
Fair odds rarely land on a traditional fraction, so read them as decimals; the odds converter turns any of them into fractional or American odds.
Fair odds and turning a probability into odds
To go the other way, from a chance to odds, divide 1 by the probability for decimal odds, or work out (1 - p) / p for fractional odds. A 25% chance is 4.0, or 3/1; a 20% chance is 5.0, or 4/1.
Sharing the margin out in proportion to each implied chance is the simplest way to strip it, but it is one method of several. Others spread the margin differently between favourites and outsiders, and none of them reveals the true chances, so treat fair odds as an estimate. Compare them with your own view of a horse to judge value, size a bet with the Kelly criterion calculator, or split a stake across several runners with the dutching calculator.