Lionel Roubeyrie

With the Champions League heading to it’s quarterfinals, I thought it would be a good idea to talk about the hobby that most people get into during this period of the year: betting. Now, I’m not a betting guru, and my student bank account can prove that, but, some microeconomic studies do theorize on how to bet efficiently. And, since I don’t have a nephew, such as our great columnist Sander Onderstal has, I will have to make use of an economic narrative to better explain what this theory is about.

I have a friend called Christoph, which, I must say, quite enjoys betting in football. Don’t get me wrong, he doesn’t watch all Champions League games and check all the teams’ stats to make precise bets, he actually just asks for another friends’ guess. And not a specific one as well, just any friend that is randomly close to him. And even though I’m not a betting guru, I thought this was the most irrational way of betting I had ever seen. But as it turns out, Christoph actually had an efficient decision making process.

According to microeconomic theory, Christoph has one thing on his mind, while choosing a bet: his wealth. The risks he will be willing to take in any bet decision he makes ,will depend mainly on his wealth. So, if he just received his wages after 1 week of pure hard work, he will be leaning towards betting; if he is one day away of getting his wages, which for most students means you have cents in your account, he would be leaning towards not betting.

mike1.1

This would be a graphical representation of what Christoph has in mind when making his choices: as his wealth increases, his utility increases as well. So in the graph on the left, Y would be his utility, and X would be his wealth.

Imagine it’s Champions League day. Christoph goes to university, meets up with us and decides who he is going to bet on. He presents his options: he can bet on Arsenal’s win against Bayern Munich, and the payoff is 4.5* (amount of initial

gambling-utilityHis betting option can be translated into the graph we used above, by comparing his initial level of wealth to the levels of wealth he would derive from winning or losing the bet. What will make him decide whether or not to bet, will be the total expected utility he would get from the bet.

Most of you should be familiar with the concept of utility, but it basically represents how well off he would feel by making that bet.

Theoretically, he would make that bet if the expected utility of the bet is higher than the utility of not betting at all. His expected utility will be an average of the utility he gets in either scenario, with the probability of it happening. So, let’s say he is willing to bet for 10 euros. The probability of Arsenal winning the game is low, and if you follow the Champions League, you might know why. Let’s say this chance is 20%. That would result in the following expected utility equation:

EU= 0.2*U(wealth+payoff) + (1-0.2)*U(wealth-loss)

So, we assigned a utility for each of the scenarios possible for Christoph, if he decides to make the bet. It is important to remember that he will only take the bet if the value of his expected utility is higher than the utility level he obtains without making the bet. Christoph loves the rush of betting, the adrenaline, and everything that comes with it. He is, what we call in microeconomics, a risk lover. This means that his utility while betting works in a different way than, for example, my utility while betting. He will have an increasing utility, read benefit, towards betting, whereas I will have a decreasing one. This means I would prefer taking a safe bet with a lower payoff rather than a risky bet with a higher payoff. On the other hand, Christoph’s utility gain when winning the bet is higher than his utility loss when he loses that bet.

Even though I believe betting on Arsenal to win any game at all is simply ludicrous, Christoph made his decision of betting on them, and after understanding why he made that decision, I couldn’t really disagree with it. And the most beautiful part of economics is that even though all decision making processes are rational and efficient, it could all go south. And it did. Because in the end, who the hell bets on Arsenal against Bayern Munich?