Many look at betting as being a game of tennis or a football match. We enhance the tension, excitement and not knowing the outcome by placing a sports wager. It’s entertainment.

How does a bookmaker look at it? Well, we’ll guide you through a process by which bookmakers calculate their odds and make a sports book.

They are a business after all and need to turn a profit. It is not fun and not emotional. Bookies calculate a series of probabilities that they measure and can make a profit from.

Let’s get into numbers mode. We out looking at the numbers with a level head, you’ll never beat the bookie at their own game. A methodical approach is needed when assessing chance, odds, and probability.

#### Common sense

#### Birthday Cake Anyone

### A common sense approach

Rolling a dice. Six sides and a one in five chance that either will end up on top. That’s true odds of 5/1. That is easy to work out and helpful if you have a bookmaker offering odds of 4/1 for rolling a six.

How can we decide if an event has been priced properly?

Comparing odds to the ‘true’ probability of something happening is a good way to start. This is the Birthday cake example.

### What’s this got to do with birthday cake?

At my nieces birthday party she has a birthday cake. With 10 pieces of cake up for grabs the kids are getting hungry. Six pieces of cake have blue icing on top and 4 have pink icing. I decide to run a book so as to make a little money from the unsuspecting parents.

What is my niece’s chance of getting a blue piece of cake. There are 10 opportunities to get a piece of cake, 6 with blue and 4 with pink icing. Subtract the number of chances of getting a blue piece of cake and we are left with the top figure of our odds; 4.

The bottom figure is the number of times that the outcome could happen. The cake has 6 blue pieces, you’ve guessed it, our bottom figure is 6.

That’s true odds of my niece getting a blue piece of cake of 4/6. Imagine my niece is second in line to get cake because a greedy friend has already nabbed another piece. Repeating the process you would end up with odds of 4/5.

As I want to make some money at this birthday party I need to factor in my profit margin into the odds. So lets take back that piece of cake of the greedy chappy who stole my nieces first piece and start over.

So how do I make some money at this birthday party? I can’t offer odds of 4/6 or 4/5 because I would not make any money. Instead I offer the ‘shorter’ odds of 8/13 (the next available). Now if my niece does end up with a blue piece of cake I won’t have to pay out as much money as the true odds would have dictated. I’ve build myself a profit margin over the real odds.

Okay what about the parents at the party who want to bet my niece won’t get a piece of blue cake? If the true odds of my niece getting a blue piece of cake are 4/6, it means that the true odds of her not getting one are the reverse, 6/4. This works with any price in all situations.

So I need to change the price of my niece not getting the blue piece of cake to guarantee me a profit. I get my bookmaking manual and recall the basics. My book must balance and the odds I provide always come in pairs. The price for something happening is paired with the price of something not happening. In a two horse race backing the out lying horse is the same as betting the favourite will not win.

### Do true probabilities exist in sports?

Think of almost any sport and consider how many factors contribute to the outcome of the event. One occasion I can think of is the coin toss at a cricket match. It’s been known for bookmakers to hood wink the public offering heads or tails at 5/6. This results in a profit of 4.55%!

Think about the job of an odds compiler. The price conjured up by the person producing the odds at the bookmakers can never be anything other than an educated opinion. We are pitting our wits against these folk. They can never be right 100% of the time.

The percentage profit on each event must match. The percentage profit is the amount by which the odds I offer differ from the true odds. In my example, there is a margin of 1.9% if my niece gets it. I price not getting it at odds of 6/5 producing a margin of 5.45% (the amount it varies from the true odds of 6/4). My book is unbalanced and I’m not going to make much money here, whether my poor niece ever gets a piece of cake or not.

So I need to shorten my odds for getting the piece of cake and lengthen my odds for not getting it. I move the 8/13 price to the next shortest price which is 4/7, This means I pay out less if she gets the blue piece making me more money. The outsider odds (of getting pink piece – as there are less of them) are moved to 5/4. That’s a margin of 3.63% for getting it and a margin of 4.44% of not getting it.

Okay. Great, the book is now balanced. Are we satisfied now? The answer is no. Any bookmaker wants his biggest profit on the most likely outcome, because this is where most of the money will go. My niece is most likely to get the blue piece of cake because there is more of them. I want a wider profit margin on this outcome, so, I shorten the price on the most likely outcome. This makes sense, because I am cutting my risk of losing money on the most likely result. This is how bookmakers fix the odds in their favour.

Taking the odds on favourite, getting blue cake, I can increase the profitability by shortening the odds. The next lowest odds are 8/15 giving a profit over the true probability of 5.21%. Adjusting the price of ‘no she doesn’t get it’ to 11/8 makes a margin of 3.64%. Now I’m satisfied because the book is balanced in my favour. I expect the most money to go on the favourite where I’ll make the most profit. Using the cake example you can see how bookmakers aspire to have their cake and eat it!