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How Do Bookmakers Work?

Betting at the bookmakers, or bookies, is a popular form of gambling: in some places, such as the UK, it is even more common than gambling at casinos. Bookmakers are entities that create odds on real-world events, which people can then place bets on. The most popular thing to bet on is often sports, however bets can be placed on anything from Oscar winners to the outcome of an election.

Betting on the bookies can be fun, but it is undoubtedly confusing to beginners. How do bookmakers work? What do the odds mean? How do they profit? We are going to look into the mathematics of bookmaking to understand how the system works and how to play it to your advantage.

Mathematics of Bookmaking: The Basics

Perhaps the most confusing part of betting at a bookmaker’s for many beginners is making sense of the odds. Particularly if you are used to odds being expressed in percentages (e.g: 75%), the format primarily used by bookmakers can seem strange.

First of all, there are three common ways in which odds are expressed in bookmakers around the world: fractional (preferred in the UK), decimal (Europe, Canada, Australia, New Zealand), and moneyline (U.S). To simplify the mathematics of bookmaking, we are going to focus on the fractional format for now.

A standard fractional odds looks like this: 5/7. A simple way to read that for a beginner is that the first number is how much you will win if you bet the second number (not including your profit): bet £7, get £5. You will recognise that as a relatively low-risk, low-return bet, and it is known as an Odds-On selection: these occur when there is a strong favourite to win something.

If you are used to working with statistics, it can be useful to convert these odds to percentages, which is done with the calculation b/(a+b), which in this case means 7/(5+7)=0.58, or 58%. Seeing it like this, beginners can get a much better idea of how likely the outcome they are betting on is.

So, how do bookmakers work in terms of payouts? The calculation is once again quite simple. To know what your potential payout is for a given bet, assuming a £21 stake ‘s’, you do: ((s/b) x a) + s = (21/7 x 5) + 21 = 15+21 = £36.

Note: Converting fractional odds to decimal odds is easy: the decimal odds are the decimal value of the fraction, plus one. In our example, this means the decimal odds for 5/7 are (5/7)+1= 1.71. The reverse is slightly more complicated, as fractional odds should always be represented as integers, and you will have to round up or down.

How Do Bookmakers Work?

Just like casino games always have a house edge, bookmakers always calculate a margin, or overround, into their odds. Once they calculate the true odds of something happening, a certain percentage is added on and the bookmakers present these odds to customers for betting. By accepting bets for each outcome in the correct proportion, a bookmaker can consistently make profit.

To understand this better, let’s get back into the mathematics of bookmaking. There are two routes to calculating the margin of any given bet, depending on whether you use fractional or decimal odds.

Say a football game is being listed at a bookmakers as having the following odds:

Draw: 9/4 (Decimal: 3.25 ; Percentage: 31%)

Team A: 3/1 (Decimal: 4 ; Percentage: 25%)

Team B: 10/11 (Decimal: 1.91 ; Percentage: 52.3%)

If you are using fractional odds, all you have to do is convert them to percentages using the formula we explained above, and add those percentages up. Straight away, you can see that adding those percentages equals 108.3: if you remember anything about statistics from school, you should remember that all the probabilities for the possible outcomes for an event should add up to 100%. The overround is obvious when you look at it that way: the margin here is 8.3%.

However, if you are using decimal odds, the formula below amounts to the same calculation:

[((1/Decimal Odds option A) + (1/Decimal Odds option B)…) x 100] – 100 = Margin

[((1/3.25) + (1/4) + (1/1.91)] x 100 = (0.31+0.25+0.52)) x 100] – 100 = 8.3%

How do bookmakers know what the odds are?

It is a fair question, and one that most people have asked themselves at some point. How do bookmakers effectively predict the future using statistics and probability, and how do they reduce an outcome to such a specific number?

Well, this works in a similar way to the stock exchange: a team of dedicated Risk Analysts, sometimes called Traders or Odds Compilers, are responsible for analysing all the available data to arrive at a statistical probability for every possible event.

This incorporates hundreds of variables: in a football match alone, elements that can influence the game include health of the players, team morale, fan support, weather, quality of turf, and whether a team is playing at home or away. Advanced computer systems help track all the variables, and a precise probability for literally anything happening can be calculated.

At this point, bookmakers have found the true odds of the event. The margin we have looked at is added on afterwards, and makes up the final number which we as customers see listed.

How do I choose a bookmakers?

The next logical step, now that you know how bookmakers work, is selecting the best one. Understanding the mathematics of bookmaking will help you make a decision and know what service to use for your bet. If you don’t feel like doing manual calculations for every bookmakers, there are comparison services online that will tell you who is offering the best odds for a given bet.

It is important to note how traditional bookmakers differ from exchanges: exchanges, such as Betfair, connect gamblers who want to play opposing bets with each other. This eliminates the need for a margin, so the odds represented on exchanges tend to be truer. However, exchange websites take a commission on every bet.

Depending on the website and bookmakers, you may find that the commission charged is less than the margin. Our example above was taken directly from a leading bookmaker’s website, and had an 8.3% margin; exchange commissions can sometimes be as low as 2%.