Bookmaker margin calculator: how to work out the overround from decimal odds

Every price a bookmaker posts carries a small, built-in charge. You never see it as a line item, but you can calculate it in under a minute from the decimal odds, and once you can, you can compare books on the one number that decides how much betting costs you over hundreds of bets. This guide is a bookmaker margin calculator in written form: the formula, worked two-way and three-way examples, a comparison table you can rebuild in any spreadsheet, and the arithmetic that shows why margin outweighs a welcome bonus.

What is the bookmaker margin, or overround?

Decimal odds convert straight into an implied probability: divide 1 by the odds. Odds of 2.00 imply 50%, odds of 1.25 imply 80%.

In a fair market, the implied probabilities of every possible outcome would add up to exactly 100%. Bookmakers price each outcome slightly shorter than fair, so the total comes to more than 100%. The excess is the overround, also called the margin, vig or juice.

There are two common ways to express it, and books and comparison sites mix them up:

• Overround = sum of implied probabilities - 1. This is how much the book's prices exceed 100%.
• Hold = 1 - 1 / sum of implied probabilities. This is the share of total stakes the book expects to keep if money is spread across outcomes in line with the true chances.

Hold is always slightly smaller than overround. Both are useful; the important thing is to use one consistently when comparing books.

How do you calculate the overround from decimal odds?

1. Write down the decimal odds for every outcome in the market.
2. Divide 1 by each one.
3. Add the results.
4. Subtract 1. That is the overround.

In a spreadsheet with the odds in cells B2, C2 and D2, the formula is =1/B2+1/C2+1/D2-1. For a two-way market, drop the third term.

Worked example: a two-way market

Two-way markets cover tennis matches, basketball and esports moneylines, point spreads, totals and Asian handicaps. Take a basketball point spread priced at 1.91 on both sides:

Overround: 4.71%. Hold: 1 - 1 / 1.0471 = 4.50%. If each side is a true 50%, the fair price is 2.00, and 1.91 is the book's discount on it.

The odds do not have to be equal. A tennis match at 1.65 and 2.30:

• 1 / 1.65 = 60.61%
• 1 / 2.30 = 43.48%
• Total = 104.08%, overround 4.08%

That book charges slightly less than the 1.91 / 1.91 spread, even though neither price looks especially generous.

Worked example: a three-way football market

A football match result market has three outcomes: home, draw and away. Suppose the prices are 2.40, 3.30 and 3.10:

Overround: 4.23%. With three outcomes there are more places to hide margin, which is one reason three-way markets often carry a higher overround than the two-way markets on the same match, such as draw no bet or Asian handicap.

How do you remove the margin to find fair odds?

The simplest method, often called the proportional or multiplicative method, divides each implied probability by the total:

Now you have a baseline. If another book offers the home side at 2.55, that price is longer than the no-margin estimate of 2.50 from this book.

A caution: the proportional method assumes the margin is spread evenly. Betting research has long documented a favourite-longshot bias, where longshots tend to be priced with a larger share of the margin than favourites. For outcomes priced at 2.00 to 4.00 the proportional method is a reasonable approximation; for long shots at 15.00 or more it will tend to overstate the true chance.

How do you compare bookmaker margins across sites?

Line up the same market at several books, calculate each overround, then build a combined row from the best price on each outcome:

Three things stand out. Book C is the cheapest overall. Book B, the most expensive, still has the best away price. And by taking the best price on each outcome, a bettor with accounts at all three cuts the effective margin from about 4% to about 1%.

If the best-price row ever totals less than 100%, the market is an arbitrage: stakes split in proportion across the three books would return a profit whichever outcome happens. These gaps are rare, close quickly, and books often limit accounts that take them repeatedly.

Repeat the table across a dozen matches and the leagues and markets you bet most, and you will know which book is cheapest for your style of betting. That is more useful than any single headline price.

Converting American and fractional odds first

The method needs decimal odds. Convert first:

• American positive (+150): 1 + 150 / 100 = 2.50
• American negative (-110): 1 + 100 / 110 = 1.909
• Fractional (5/2): 1 + 5 / 2 = 3.50; (10/11): 1 + 10 / 11 = 1.909

The classic US price of -110 on both sides is the same 1.91 / 1.91 market as above: a 4.71% overround.

Why does margin matter more than bonuses over time?

A bonus is paid once; the margin is paid on every bet. The maths makes the point.

If a book's prices are fair apart from a proportional margin, your expected return per unit staked is 1 / (sum of implied probabilities) - 1. At a 7% overround that is about -6.54%; at 3% it is about -2.91%.

Suppose you stake $500 a week, every week, for a year: $26,000 of turnover.

Now compare a typical welcome offer: a $100 free bet where the stake is not returned. Placed on a 50/50 market at 1.91, its expected value is 0.5 x $91 = $45.50. Even a generous deposit match is usually locked behind a wagering requirement that consumes much of its value at the book's own margin. The bonus on the expensive book does not come close to closing a $944 gap.

This is why price deserves more weight than promotions when you choose where to bet. A bonus is easy to advertise; a lower margin is not, and it is worth more to anyone who bets regularly.

Where are bookmaker margins usually wider?

Margins are not uniform across a book. They are typically widest in:

• Player props and specials, where the book has less competition and less data.
• Lower leagues and niche sports, where a mistake costs the book less.
• Live markets, where prices move fast and the book adds a buffer.
• Parlays, where margins compound. Three legs at a 5% overround each produce a combined overround of 1.05 x 1.05 x 1.05 - 1 = 15.8%, and an expected return of about -13.6% against -4.8% for a single.

Run the formula on a few markets you actually bet before deciding where to stake. Apply it to the books on our crypto sportsbooks list for the markets you bet, and use our bankroll management guide explains how to track what you are actually paying.

Betting within your limits

Knowing the margin tells you the cost of betting; it does not make betting profitable. Treat every stake as money you can afford to lose, set a deposit limit before you start, and use self-exclusion if betting stops being something you control. Our responsible gambling page has support contacts for many countries.