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Odds vs Probability

February 26th, 2018 Uncategorised

Odds vs. probability can be a confusing subject. Thankfully, when it comes to betting and matched betting, it needn’t be a issue. The reason for this, is that there are lots of great tools that do all of the hard work for you.

But it’s always a good idea to understand these topics and how they work if you have the time. So with that in mind, we’re going to explore the difference between odds and probability.

What are odds?

In gambling, Odds are either displayed as a fraction or in decimal format. Odds are used to express the probability of an event happening in a way that allows you to understand the stake/payout ratio.

For example, if you have odds of 4/1 the first number is the payout that the bookmaker will make if the selection wins. The second number is the amount that needs to be staked to generate that payout. So with the above example, if you placed a £10 bet, you’d receive a £40 profit.

With events that have a high probability of happening, the odds are flipped and are what’s known as odds on. This is where the smaller number is first and the larger number is second. For example, if the odds were 1/4, 1 still represents the bookmaker payout, and 4 the customer’s stake. You must place £4 on the bet to win £1.

Decimal odds have become more popular since the introduction of internet betting. This is mainly because they are a lot easier to understand. They also allow more precision with prices. Of course most prices can be represented in fractional form, but some of the more precise odds can look more complicated in fractional form.

To work out your winnings for decimal odds, you simply multiply your stake by the odds.

It’s also very easy to convert fractional odds to decimal odds. First you must divide these as low as you possibly can. Fractional odds work with whole numbers which is why you see funny odds such as 11/8. But once you divide 11 by 8, you’re left with odds of 1.38/1. If the fraction already has a 1 as the second number you’re already set.

Then just add the first number to the second number to get your decimal odds. Here’s some more examples:

Fraction Reduced fraction Decimal odds
1/10 0.1/1 1.1
8/15 0.53/1 1.53
5/6 0.83/1 1.83
11/10 1.1/1 2.1
13/8 1.63/1 2.63
10/3 3.33/1 4.33
7/2 3.5/1 4.5
11/2 5.5/1 6.5
10/1 10/1 11.0

What is probability?

Probability in betting is the likelihood of a specified event taking place. This is defined on the scale of 0 and 1 or 0% to 100%.

For instance, if an event is certain to happen, the probability of that event happening is 1. However, if an event is never going to occur, the probability is 0.

For example, the probability of Saturday following Friday is 1, as it’s certain to happen. But meanwhile, the probability of Arsenal winning the Champions League this season is 0, because they’re not in it.

For most other events, the probability of the event occurring sits somewhere in the middle of this scale. A good example of this, would be a coin toss.

There are two sides to a coin, and an equal chance of the coin either landing on heads or tails. Therefore the probability of the coin landing as heads would be expressed as 0.5. While the probability of the coin landing as tails would be 0.5 too.

So if you go one step further and look at the outcome of a Football match and how this is applied by the bookmakers, it becomes more interesting. You have three possible outcomes in a Football match. Home win, Away Win, Draw. If the match is played to conclusion, the probability of one of these outcomes happening is 1.

So the job of the bookmaker is to apply a probability to each of these events happening. They will do this through very thorough statistical models and algorithms.

Eventually they will arrive on a probability of each event happening that may be:

  • Home win – probability of 0.4
  • Draw – probability of 0.3
  • Away win – probability of 0.3

The bookmakers then convert these probabilities to odds. We’ll discuss this in further detail shortly.

What’s the difference between odds and probability?

The relationship between odds vs probability in betting should be becoming more apparent now.

First each event has a probability attached to it. This then allows bookmakers to convert this to odds and display the probability in a more user friendly way that relates to betting.

So to recap – probability is the chances of an event occurring. While odds are the numerical representation of this probability in a way that allows you to understand the stake/payout ratio.

So, there isn’t really much difference between odds and probability in their pure form. They both represent the chances of an event occurring, they’re just displayed in a slightly different format.

However, that becomes a bit blurred when bookmakers become involved as they need to be able to make a profit.

In any true market, the probability of an event occurring is 1 (or 100%) as we’ve already established. But, that won’t make the bookmakers any money.

So to ensure that they make a profit from bets that they take, they have to adjust things slightly.

How do bookmakers use odds and probability?

To understand how and why bookmakers use odds vs probability, lets imagine you are a bookmaker.

You have 6 friends round for a party, and you decide to host a game of dice for them. The dice obviously has 6 sides, so there is a 1 in 6 chance of each number on the dice being rolled.

Below is the probability of each outcome, and the true fractional and decimal representation in the form of betting odds.

Outcome Probability Betting odds
Fractional Decimal
1 0.166 5/1 6.0
2 0.166 5/1 6.0
3 0.166 5/1 6.0
4 0.166 5/1 6.0
5 0.166 5/1 6.0
6 0.166 5/1 6.0

Each of the 6 players choose a number each and put £10 into the betting pot. You then roll the dice…

On each occasion, the £60 in the pot goes to the person who had the correct number. The £60 is their £10 stake multiplied by the decimal odds for their selection, which in this case is 6.0.

However, you may be sat there thinking “Hey, wait a second. This is my game, I’m the bookmaker, yet there is no money here for me”.

So you decide that you should alter the odds to ensure you make money from every game. You change the odds to what you can see below:

Outcome Probability Betting odds
Fractional Decimal
1 0.1667 4/1 5.0
2 0.1667 4/1 5.0
3 0.1667 4/1 5.0
4 0.1667 4/1 5.0
5 0.1667 4/1 5.0
6 0.1667 4/1 5.0

Now, each player still has the same probability of winning the game of dice. However, the odds you offer them aren’t a true representation of the actual probability of each outcome occurring.

When they each put £10 in the pot, the total pot is £60. But, if the outcome was that a 3 was rolled, then the payout would be £50. No matter what number was rolled there would be £10 left in the pot. This is your reward for offering shorter odds to the players.

In basic terms, this is how the bookmakers make money. However, it is obviously a lot more complicated

Firstly, it is a lot easier to calculate the probability of rolling a number on a dice. A Football match for example, has so many variables that make it difficult. They have to consider things like form, home advantage, weather conditions, injuries, the referee etc.

So the bookmaker first calculates what they believe to be the true probability of an event occurring. They then convert it to the true odds which add up to 1, or 100% in terms of probability.

To make money, the bookmakers add what is known as an overround. They give you smaller odds for each selection so that they can guarantee that there is money left in the pot for them once everyone has been paid out.

Real life odds and probability example

To help you understand how this is applied to a real life betting market, let’s take a recent match and the odds that the bookmaker created.

Outcome Tottenham win Draw Man Utd
Fractional odds 5/4 9/4 9/4
Decimal odds 2.25 3.25 3.25

We’ve already told you the odds and probability sum for converting probability to odds. There’s also a simple sum you can use to calculate the implied probability that each of these odds represent:

Implied probability = 1 / decimal odds

So for instance:

  • Tottenham win = 1 / 2.25 = 0.44
  • Draw = 1 / 3.5 = 0.31
  • Man Utd = 1 / 3.5 = 0.31

Now if you add these together, you will get an implied probability of 1.06 or 106%. This extra 6% that the bookmaker adds to the market is the overround we mentioned earlier.

It means that for every £106 the bookmaker takes in bets, they expect to pay out £100. Which is how they make their profit.

As you can see, maths is simply not on your side when you gamble your money with the bookmaker. Bookmaker overround are typically between 5% and 20%. Placing bets at their odds, even if you are a good gambler that uses level stakes, you will lose between 5% and 20% over time.