How do bookmakers guarantee their profit?

Learn about book balancing, a strategy used by bookmakers to ensure their profit regardless of the actual outcome of sport events.

Summary

• Bookmakers ensure their profits by balancing odds
• A bookmaker margin is the percentage by which a book’s overround exceeds 1
• Betting odds are dynamically adjusted by bookmakers to shape the distribution of wagers across different outcomes

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The Book Maker

The work of a bookmaker is to formulate and assign betting odds to the possible outcomes of an event so that he will get a profit regardless of the final result. In jargon this procedure is called “making a book“, and despite it may sounds counterintuitive, some familiarity with betting odds and implied probabilities it’s all it takes to grasp this tactic (see Do you speak Betting Odds?).

How do bookmakers formulate odds? And how do they adjust them in order to profit regardless of the actual outcomes? Let’s make a book for the fight “Striker VS Grappler”.

Fair Books and how to hack them

For the sake of simplicity we assume that a draw is not admitted and that hat the chance of winning for Striker and Grappler are 50% and 50%. A book where odds are faithfully representing the underlying probabilities, would look like this:

Player	Outcome	Odds
Striker	Win	2
Grappler	Win	2

If we convert the decimal odds reported in Book 1 into probabilities, we see they add up to 1. This is what is called a Fair Book.

Player	Outcome	Odds	Implied Probability
Striker	Win	2	0.5
Grappler	Win	2	0.5
			1

From the bookmaker’s perspective, the most important aspect of a Fair Book is that…it does not guarantee him a profit!!!

Given Book1, what happens if a punter bets $10 on each outcome? The bookmaker takes $20 but regardless of the outcome he will payout $20 to the punter. The Fair Book is ensuring the bookmaker a profit of $0 when the bets are distributed according to the odds’ implied probabilities! Even worse, the bookmaker will lose money in case the bets get distributed unevenly in favor of the actual final outcome!

From the bookie’s perspective this is a recipe for disaster. In order to guard themselves from losing money, bookmakers have to balance their books.

Overround Books and positive margins

To turn the book into a profitable one, the bookmaker has to tweak the odds he is offering. For example he could come up with the following book:

Player	Outcome	Odds	Implied Probability
Striker	Win	1.85	0.54
Grappler	Win	1.85	0.54
			1.08

Indeed, by changing the odds of each result from 2 to 1.85, the implied probabilities changed as well. Notice that the implied probabilities for the event now add up to 1.08. Mathematically it doesn’t make any sense to have probabilities bigger than 1, however in our case this is a reflection of how unfair the odds have become in order to ensure a profit for the bookmaker. This is now an overround book, that is a book where the sum of the implied probabilities is bigger than 1.

An Overround Book is a book where the sum of the implied probabilities for all possible mutually exclusive outcomes is bigger than 1.

With this book at hand, what would happen if each result attracted a total amount of $10? The bookmaker would take $20 and payout only $18.5 regardless of the actual result. This book has a built-in positive margin of 8% for the bookmaker. A bookmaker margin is defined as the percentage by which the actual book’s overround exceeds 1. In our example, Book 2 has a margin of 8% given by (1.08 – 1) * 100.

Dynamic odds balancing

The overround is a necessary but not sufficient condition for a book to have a positive margin. In order to profit from the positive margin generated by the overround, bookmakers balance the odds in relation to the distribution of wagers across outcomes. Let’s make an example:

Player	Outcome	Odds	Implied Probability
Striker	Win	2.3	0.43
Grappler	Win	1.54	0.65
			1.08

Book 3 is overround, the odds reflect the fact that Striker is considered underdog while Grappler is favorite. Consider this distribution of wagers are distributed on Book 3:

Player	Outcome	Odds	Implied Probability	Total Wagers
Striker	Win	2.3	0.43	$135K
Grappler	Win	1.54	0.65	$65K
			1.08	$300K

The total wagers on this book are $300K, but if Striker wins, the total payout would be $310.5K for a bookmaker’s loss of $10.5K. This book is unbalanced, despite the overround this book does not lock in the profit for the bookmaker. In order to avoid this risk, the bookmaker must balance the odds based on the flow of wagers.

The Overround isn’t a sufficient condition for a book to have a positive margin. In order to preserve a positive margin, bookmakers balance the book in relation to the distribution of wagers.

In Book 4 below the bookmaker adjusted the odds as the money were flowing in and preserved his profit.

Player	Outcome	Odds	Implied Probability	Total Wagers
Striker	Win	2.1	0.48	$135K
Grappler	Win	1.67	0.60	$65K
			1.08	$300K

The total wagers on this book are still $300K as for Book 3. However, with these odds the bookmaker has a profit of $16.5K if Striker wins and $191.45K if Grappler wins. The odds of Book 4 are now balanced to ensure the bookmaker’s profit regardless of the fight outcome (even though there is still room to improve this book profitability).

This type of mechanism is the reason why you see odds changing over time as the Fight Night approaches.

To sum up

• Bookmakers ensure their profits by balancing odds
• A bookmaker margin is defined as the percentage by which a book’s overround exceeds 1
• Betting odds are dynamically adjusted by bookmakers to shape the distribution of wagers across different outcomes

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