Odds that add up to more than 100%
In a perfectly fair market, the probabilities of all possible outcomes would add up to exactly 100%, because one of them has to happen. A fair coin priced at 2.00 on heads and 2.00 on tails shows this: 50% plus 50% is 100%.
Bookmakers do not quote fair prices. They shade every price a little so that the implied probabilities sum to more than 100%. The amount above 100% is the overround, and it is the usual way of describing the bookmaker margin. The same idea appears in any odds format, which is why the calculation is easiest in decimal.
A worked example
Take a three-way market on a football-style match, with made-up decimal prices. The numbers are an illustration, not real odds.
| Outcome | Decimal odds | Implied probability (1 / odds) |
|---|---|---|
| Home win | 2.50 | 40.00% |
| Draw | 3.20 | 31.25% |
| Away win | 2.90 | 34.48% |
| Total | 105.73% |
The sum is 105.73%, so the overround is about 5.73 percentage points. A fair book would show exactly 100%.
What the extra 5.73% does
One way to see its effect is a thought experiment in which someone covers every outcome. To receive the same amount whatever happens, the stakes would have to be proportional to the implied probabilities: about 0.4000 on the home win, 0.3125 on the draw and 0.3448 on the away win. Each of those returns about 1 if it wins, but the stakes total 1.0573.
So the person spends about 1.0573 to get back about 1, a loss of roughly 0.0573, or about 5.4% of the total staked. Put another way, the payout ratio is 1 / 1.0573, or about 94.6%. This is not a strategy; it simply shows that the margin is baked into the prices, so there is a built-in shortfall whichever result occurs.
Estimating fairer probabilities
If you want to strip out the margin to estimate what the bookmaker’s own view might be, a common simple approach is to divide each implied probability by the total.
- Home win: 40.00 / 1.0573 = about 37.83%
- Draw: 31.25 / 1.0573 = about 29.56%
- Away win: 34.48 / 1.0573 = about 32.61%
These add to 100%. The method assumes that the margin is spread across outcomes in proportion to their probabilities. In practice, bookmakers may load more of the margin onto some outcomes, often the less likely ones, so the adjusted figures are estimates rather than the true chances. Other adjustment methods exist and give slightly different answers.
How the margin differs between markets
The size of the overround is not fixed. It often varies between bookmakers, between sports, and between types of market. Markets with many possible outcomes, such as picking a winner from a large field, typically carry a larger total margin than a simple two-way line, though that is a general tendency rather than a rule. Prices can also change over time as bookmakers adjust.
It is also worth separating two ideas that sound similar. The overround is measured against the sum of probabilities, while a casino game’s house edge is measured as an expected loss per unit staked. In the example above, the overround is 5.73%, but the expected loss from covering every outcome is about 5.4% of the stake. The two figures are related but not identical, so comparing them directly is misleading.
What the margin means for a bettor
Because every outcome is priced a little short, the average bet in a market carries negative expectation. If a bettor’s estimates were exactly the same as the fair probabilities, the expected value of each bet would be below zero by roughly the size of the margin. Single results can still go either way, but over many bets the margin tends to show up, in line with the law of large numbers.
This does not mean a bettor can never be right about a price, only that a bettor needs to be right by more than the margin before an average gain is even possible, and that is hard to know in advance. No arrangement of stakes removes the margin.
If you bet at all, treat it as entertainment with a cost. Setting spending limits before you start is a basic part of responsible play, and anyone concerned about their gambling can contact a local support service.