# Betting Odds Explained - Convert to probability

Let’s use an example of a football match between Barcelona and Real Madrid where there are three outcomes, a win for the home team, a draw or a win for the away team. We will assume fractional odds of 4/6 on Barcelona, 11/4 on the draw and Real Madrid at 4/1 for the following examples and from this information you can see the percentages that the bookmakers have played on the probability of each outcome.

## Basic Odds Understanding

The first thing you need to understand is what basic betting odds mean. Let’s take odds of 2/1. This means that you need to bet one unit to win two back. Odds of 4/1 means that you bet one unit to win four back. Then you have odds-on prices such as 1/2. In this scenario, you would need to bet two units to win one back. So a £1 win on odds of 2/1 lands you £2 profit while a £1 win at 1/2 odds-on lands you £0.50 profit. So there is the risk/reward factor of betting.The longer odds of 2/1 have less of a chance of winning, while the 1/2 odds-on price is more likely to happen but you would have to risk twice as much to get the same return as if the longer price won. There is no difference between decimal and fractional odds, only that when looking at decimal odds it includes the stake return.

For example fractional odds of 3/1 and a £1 stake would be calculated as £3 profit, but you then add back your £1 stake for a £4 return. Fractional odds of 3/1 convert to 4.00 decimal odds and so your £1 stake on 4.00 is easy to see that you would get back £4 because the decimal odds contain both the stake and profit. Same thing either way, just a preference of how you like looking at odds. For many, decimal is preferable.

## Convert Fractional odds to Decimal Odds

There is no difference between decimal and fractional odds, but if you want to convert from fractional to decimal there is an easy way to do that. You use a simple formula of x/y + 1 and you have converted to decimal!So for the 4/6 odds for Barcelona, that is 4 divided by 6 + 1 which works out at 0.67 + 1 = 1.67 decimal odds.

Conversion Formula from Fractional to Decimal on X/Y odds

x/y + 1

x/y + 1

## Convert betting odds to probability

Now we want to see what those odds mean in terms of probability. There is another simple formula that takes the numbers in a fractional odds presentation, adds them together and then divides that total by the second number to give a probability factor.So for Barcelona at 4/6 that is 4+6=10 and then 10 divided by 6 = 1.6 then multiply that by 100 = 60%. So Barcelona have a 60% chance of winning the match according to the bookmakers at a quote of 4/6.

Fractional odds to probability conversion formula

(x + y) / y x 100 = z

e.g. 4/6 odds turns to (4 + 6) / 6 x 100 = 60%

(x + y) / y x 100 = z

e.g. 4/6 odds turns to (4 + 6) / 6 x 100 = 60%

Carrying on in this scenario lets look at the 11/4 odds on the draw. 4 divided by 15 (11 + 4) = .026 multiplied by 100 = 26.6% chance of a draw. For Real Madrid at 4/1 it would be 1 divided 5 (1 + 4) = 0.25 multiplied by 100 = 25%. So there are the probability outcomes for the match.

But wait, a 60% chance for Barcelona plus a 26% chance of a draw plus a 25% chance on Real Madrid winning adds up to 111% not 100%. Why? Because the bookmakers margins are worked into the percentage so that they can make their money. See below for more details.

Note: The easy way to convert decimal odds to probability is just a simple formula of 100% divided by the decimal odds quote. For this example lets use 100 divided by 2.50 decimal odds = 40% probability.

## Understanding Probability

All sports betting comes down to chance. Of course Barcelona may have an off day and Real Madrid land the win at big 4/1 odds, doing a few punters and a bookmaker a nice favour. The probability percentages are a guideline for the bookmaker to gauge profit. Let’s look at the 4/6 odds on Barcelona which converts to a 60% chance of winning. Stop for a moment and look at it the other way around, they have a 40% chance losing so you aren’t too far away from a 50/50 shot which then makes the odds-on price on Barcelona perhaps not so appealing.But Real Madrid have a 75% chance of losing which has a bigger probability of happening so you have less chance of hitting profit from hoping for a Real Madrid victory at the bigger odds. There is the dilemma and how much would you be prepared to risk in either scenario?

Incidentally, the draw is known as the bookmakers friend because punters generally throw big money at a winner and when a draw occurs, bookmakers land a huge payday. Bookmakers have banks of traders and analysts figuring out the probability of outcomes and then they set the odds from there.

With a little practice, you can learn to recognise the probability of an outcome from the odds presented. Just remember an Even Money price is a 50% chance of an outcome happening. Anything on the odds-on side of that and you are increasing probability percentages. Anything longer than Even Money is decreasing the probability percentage of an outcome happening.

## How to calculate bookmaker margin

There is a thing called bookmaker margins. This is where a bookmaker makes their profit and you can see it in action. In a football match where there are three outcomes, you can add up the odds to just how the bookmaker makes their money. On an event with two outcomes, say a tennis match, one player is trading at 1.9 and the other at 2.0. The formula for calculating a bookmaker margin is this 1/odds*100 + 1/odds *100. In this case it is 1/1.9 *100 + 1/2.0 *100. So it is 52.63 + 50 = 102.6 and that means the bookmaker would be running a margin of 102.6% on the bets.If for example this was a coin toss where would always be a 50% even chance. If the punter won five times out of ten, the bookmaker would be even at the end of the day, with no profit. However, if the bookmaker was making money on the coin toss by putting odds which total to a percentage of more than 100% (in the above case 102.6) they would have made a profit from five equal flips of the coin. This is known as the ‘juice’ or the ‘vigorish’ or ‘edge’. If the punter played £10 on each of the ten coin tosses and won five at odds of 1.9 they would have made a £9 profit from each bet for a total of £45.

From the five lost tosses performed by the punter, the bookmaker would earn £55. So even if the outcome of number of coin tosses was equal, the bookmaker wins because they are shaving off how much the punter gets for winning. Just to compare, if things were at 50/50 with the bookmaker not making a profit by offering odds of 2.0 on both Heads and Tails, then the punter would obviously have won £10 for each bet.

## What US Odds means and how to convert them

Now and again you may come across US odds or a Moneyline which may look a bit confusing. You will see something like -150 or +150 on a market selection. This simply means that the negative number is how much you need to place as a wager to earn $100. So here you would have to bet $150 to win $100 (which the equivalent of 1.67 decimal odds). Of course, you don’t have to bet the full $100. The positive number in US odds is how much profit you would pick up if you staked $100. So for that $100 stake you would have $150 profit. +150 US odds converts to 2.50 decimal odds.Out of interest if you want to convert US odds to decimal odds, when it is a negative figure in this example -150, divide 100 by the quote and then add one. So it is 100 divided by 150 (don’t use the negative!) + 1 = 1.67 decimal odds.

To convert a positive moneyline figure to decimal, divide the figure by 100 and add one. So for a +150 quote, you would do 150 divided by 100 + 1 = 2.50.