# Arbitrage in Sports Betting

There are lots of ways of doing arbitrage betting and we are going to show how it works in typical events where we look at it as only two outcomes.

This article goes through arbitrage betting while both backing and laying an event. It is possible to do this in different ways, but we will mainly go through how it is done using a betting exchange, as well as through Asian handicap. Check out this article to be able to understand how to do it with three outcomes.

Let us start with the definition of arbitrage as Wikipedia defines it:

“In economics and finance, arbitrage is the practice of taking advantage of a price difference between two or more markets: striking a combination of matching deals that capitalise upon the imbalance, the profit being the difference between the market prices at which the unit is traded.”

Typically, this would mean that you will be doing arbitrage if you buy gold in Spain for $1000 (whatever amount) and selling it in the USA for$1200 (the same amount). This is because you buy and sell it in two different markets, while making money off the price difference, in this case $200. Keep this in mind while we go back to our crossbar challenge between Andrew and Bobby. Andrew hits the crossbar 4 out of 5 times, which correspond to odds of 1.25 for hitting, and 5 for missing. Bobby now offers Andrew odds of 1.3, because he gets a downgrade in IQ again. Andrew now has the odds of 1.3 while Bobby still has the odds of 5. As we know from the article about odds, this will mean that Bobby will lose in the long term. Andrew and Bobby have a friend named Charlie who comes to watch. Charlie watches while they bet, and because he is smart, he sees arbitrage opportunity. To compare this with the definition of arbitrage: Andrew and Bobby both provide a betting market that is on the same event. Compared to the usual bookmaker, the probability stick is now smaller than 1 as shown in the image below. You should really study the image with the probability stick because this shows the mechanisms that is underlying for arbitrage opportunities in betting markets. It is important to notice that it is the total difference in odds (giving total probability stick less than 1) which is the reason for the arbitrage opportunity. Here we can differentiate between a value bet and an arbitrage bet because we can have a value bet without having an arbitrage bet, but an arbitrage bet always means that one of the sides you bet on is a value bet. Let us show you what this means by example with the crossbar challenge: We have four different possible cases: 1. Value in both sides as well as an arbitrage bet Say we have the odds of 1.3 for hit and 6 for miss, we have value on both sides (1.3 > 1.25 and 6 > 5) and we have an arbitrage bet (1/1.3 + 1/6 = 0.936). 1. Value on only one side, but still an arbitrage bet Say we have the odds of 1.22 for hit and 6 for miss, we have value on one side (1.22 < 1.25 and 6 > 5) but we have an arbitrage bet (1/1.22 + 1/6 = 0.986). 1. Value on only one side, but not an arbitrage bet Say we have the odds of 1.05 for hit and 6 for miss, we have value on one side (1.05 < 1.25 and 6 > 5) but we do not have an arbitrage bet (1/1.05 + 6 = 1.12). 1. No value and no arbitrage bet Say we have odds of 1.2 for hit and 4 for miss, we have no value on either of the outcomes (1.2 < 1.25 and 4 < 5) and we do not have an arbitrage bet (1/1.2 + 1/4 = 1.0833). It is worth noting that these cases go from less likely to most likely from top to bottom. 1/1.3 + 1/5 = 0.969 (1) → Given odds While 1/1.2 + 1/5 = 1 (2) → True odds 1-1/1.3 = 0.231 1/0.231 = 4.33 would be the right odds for it not to happen if 1.3 were the right odds. 1-1/5 = 0.8 1/0.8 = 1.25 would be the real odds for it to happen if 5 where the right odds. As we can see, the important part to understand is that they are overvalued compared to each other, either way we look at it. These odds imply that there is 1-0.969 = 0.031 or 3.1% chance that something else is to happen. In this scenario it is not possible for something else to happen because Andrew and Bobby have defined the event as either hit or miss. Hence, the odds are overvalued compared to each other making the probability stick equalling less than 1. There are still only two things that can happen: Andrew hitting the crossbar or Andrew missing the crossbar. Notice that the total probability of all the outcomes of an event cannot be anything else than 1 in theory, but in this case, it is less than 1 as reflected in the odds. Charlie can use this to his advantage, winning a small amount of money regardless of the outcome. Let us show you how Charlie thinks: Firstly, we know that there is value here, but we want to know how much we should bet on each side of the event to get the same (or maximal) amount of profits regardless of the outcome. So, Charlie knows that he wants to give Andrew$100, but we need to find out what Charlie needs to lay (or give to Bobby for him to bet). We set up the profits on each side to be the same:

Andrew’s side profits if hit – Bobby’s side profits if miss

(1.3*100 – 100) – X = 5*X – X – 100

30 - X = 4*X – 100

130 = 5*X

X = 26

So, if Charlie now gives $100 to Andrew with 1.3 odds and gives$26 to Bobby, betting on Andrew missing with 5 odds.

100*1.3 = 130 → 130 -100 (stake1) – 26 (stake2) = 4 dollars

26*5 = 130 → 130 – 26 (stake2) – 100 (stake1) = 4 dollars

As you can see, Charlie would win $4 regardless of the outcome. This is how arbitrage works. But these opportunities are quite rare in the real world and as a thought experiment, think of what would happen in the first scenario, where the odds are 1.1 and 5. You might expect that you would lose a small amount of your money for every bet, and you are right. Above there is an image to clarify how Charlie looks at the situation to make it possible for him to make risk-free money off of it. Notice that Charlie would in practice give$100 to Andrew for him to place a bet in Bobby’s market with the odds of 1.3 for hit and give \$26 to Bobby for him to place a bet in Andrew’s market with the odds of 5 for a miss.

### ARBITRAGE IN PRACTICE

You might have noticed that you can not always bet on two sides of the same bet at the bookies. There are some ways to do this: either play on the events of two outcomes (over/under or money line for example) or you can play the Asian lines.

If you are playing on a match between Liverpool and Manchester United at Anfield, you would bet on Liverpool home win as well as Manchester United away win + 0.5 (Asian handicap).

This is the same as playing on a Home win and not a Home win because Manchester United +0.5 (Asian handicap) means that if it’s a draw or a win to Man Utd, you win.

Another way is to use betting exchanges which gives you the opportunity to back and lay every bet they have.

### KEY TAKEAWAY

This article is here to show you how the theoretical basics works when it comes to arbitrage in sports betting. You should now be able to understand how and when these opportunities arise and hopefully you will be able to make some money off it!