### What are bookmakers’ margins and probabilities and How to calculate them?

In two previous articles in this series (Understanding Betting Odds and Betting odds explained), we explained what bookmaker odds are, what odds formats are used, how to calculate winnings and how to convert one odds format to another. Now you need to understand what probabilities and bookmakers’ margins are. Let’s start with the simplest – what is probability?

What is betting generally? It’s the ability to predict the outcome of a certain event. For every event there is a certain number of outcomes, for example, it will be Home win, Draw or Away win in football. Probability refers to how likely the outcome is to occur. In the simplest terms the probability is expressed as a number between 0 and 1, where 0 means absolutely no chance that the outcome will occur and 1 means an event is certain to happen. All other potential outcomes fall somewhere between those points.

So, as we seen from the Figure above, in order to calculate the probability you need to use a simple equation: **Number of favourable outcomes / Number of all possible outcomes**. The best way to explain how to calculate the probability is a coin-toss example. We certainly know that the coin will land on either Heads or Tails so this event has a probability of 1. There are two possible outcomes, so the probability that the coin will land on Heads is 1 / 2 = 0.5, also known as 50% chance (0.5 x 100%). Bookmakers` odds are a representation of probabilities. They use odds to convert a probability into a more usable form in order to offer betting. If bookies take bets on a coin-toss and convert a probability into decimal odds you would see 2.00 – 2.00. So, to calculate decimal odds for the coin being Heads is 1 / 0.5 = 2.00. Let’s imagine a football match with absolutely equal rivals and each of three possible outcomes has the same probability. Accordingly, the probability of each outcome is 1/3 = 0.33. A bookmaker will translate probabilities into odds and we’ll see 3.0 – 3.0 – 3.0. To know how to find the probability is the first step to understand betting odds. Of course, any bettor wants to know how to translate odds into probabilities in order to understand how likely the certain outcome is to happen! This is best explained by a real example.

**How to calculate the betting odds margin? **

Let’s take as an example a real football game with three possible outcomes: Home team to win at 1.80, Away team to win at 3.20 with the Draw set at 4.00. Calculate the possibilities for a three-way market:

**Home Win: 1 / 1.80 x 100% = 55.56%**

**Draw: 1 / 4.00 x 100% = 25.00%**

**Away Win: 1 / 3.20 x 100% = 31.25%**

Now you know that chances of a home team to win is about 55%, but if you try to count in your head, well, then your first words will be ‘What a …?’ Yes, when you sum up all the probabilities, in total you will get 111.81%! How can this be, because the probability of three outcomes is 100%! Where did these 11.81% come from?! The answer is simple – this is the bookmaker’s margin! This is the price a bookmaker charges for offering its services. How to calculate true probabilities? It’s not difficult; you just need to divide the found probability by the margin ratio.

**Home Win: 55.56% / 1.118 = 49.70%**

**Draw: 25.00% / 1.118 = 22.35%**

**Away Win: 31.25% / 1.118 = 27.95%**

TOTAL: 100%

If we return to our example of a coin toss, then as you know in practice you won’t actually see two equally likely outcomes both priced at 2.00 in the betting lines because this situation is called a ‘100% market’ or ‘market with zero margin’. It`s only possible when you bet with your friend on the street. But a bookmaker is someone seeking to make a profit so the market percentage would be greater than 100%, for example 110%. Let’s calculate the odds for this two-way market with 110% percentage:

**Heads & Tails: 2 / Odds = 110% (1.1)**

**Odds = 2 / 1.1 = 1.81**

Betting on a coin toss is a real-life example of how bookmakers make money. Let’s suppose you bet ₤100 on Heads and win, so you get ₤181 and someone loses ₤100. Yes, whatever the outcome will be, a bookmaker still earns ₤19. And now let’s calculate the commission you pay for each bet:

**Commission = (1 – (1 / 1.1) * 100% = 9.1%**

So a bookmaker steals 9.1% of your every bet! When you place ₤100 bet on Heads which has 50% possibility, actually you bet ₤90.9 (₤100 – 9.1%) at odds 2.00 to get ₤181 winnings. So you really have to understand the difference between odds and probabilities if you want to be a winning punter! The betting margin is the dominant weapon of bookmakers in open-ended war against us! How can this weapon kill your bankroll?

And again we return to betting on a coin toss. Let’s say you put 100 stakes on the Heads and won 54 stakes. If you bet with a friend, you will be lucky to win ₤5 400 and lose ₤4 600, your profit will make ₤800. But when you play with a bookmaker everything is different – the margin, figuratively speaking, just eats up your bank! 54 winning bets would bring you only 54 x ₤81 = ₤4 374, that is, the loss would be ₤226 (₤4 374 – ₤4 600)! That’s why in order to get profit in the long run you need to have an advantage over bookmaker odds! How to get it? Read about this in the last article in this series ‘How to beat bookmakers’ odds’.