Odds Betting

The bookmakers quote odds which can be translated into probabilities (see Table Of Odds for a listing).

To translate odds into probabilities, take the right hand side of the odds and divide it into the right and left added together.

Take 4/1 as an example.

Right hand = 1

Right and left added together = 4+1 = 5

Right / (Right and left) = 1/5 = 0.2 which is the probability

Imagine a horse race with 5 runners and every horse is considered to have an equal chance. Each horse has a 1 in 5 chance of winning, so, if you keep running the same race over and over again, any selected horse would be expected to win an average of 1 out of 5 races. Think of that as 4 losses and 1 win, so you have the odds of 4/1.

The bookmakers need to build in a profit margin to make it worth their while. Let’s be a miserly bookmaker and quote each horse at odds of 3/1. If I backed every horse with a £1 stake my outlay would be £5. Only 1 of them can win and, when it does, the return will be just £4, so my outlay is £5 but my return only £4.

This is where the probability allows you to calculate the margin in the bookmaker’s favour. Each horse is quoted at 3/1 and we now know that equates to a probability of 0.25 because

Right / (Right + Left) = 1 / 4 = 0.25.

There are 5 horses, so the ‘book’ is 5 * 0.25 = 1.25.

A golden rule of probabilities is that for any event they will add up to 1, so something has been added in, that something being the bookie’s margin, giving what can also be called a 125% book.

Generally, the higher % probability the greater the bookie’s margin and the lower % probability the lower the bookie’s margin.

Arbing or arbitraging is a situation where you can take advantage of different bookie prices by backing all the outcomes and locking in a profit. To achieve this the % book will need to be less than 100% i.e. in the punter’s favour.

It sounds easy but there are plenty of pitfalls with this. The main issue is that the bookies usually realise quickly that they have opened themselves up to easy money and so change the prices. Unless you can fill the trades at exactly the same time there is no guarantee of locking in a profit and you could end up with a position you don’t want.

The other main problem is that they don’t like this sort of practice. There is an argument that they are just glorified arbers themselves but if they spot one of these ‘pariahs’ they will restrict them pretty smartish.

A major plus about sports betting is that it can be quite subjective. Each bookmaker will quote their own odds for certain events often leading to a significant difference of opinions. For this reason most serious punters will open accounts with as many different bookmakers as possible as they always want to be able to get the best price for their selections.