When not at work with students, I spend my time in my room either reading, calculating something using pen and paper, or using a computer. I read almost anything: from the pornographic to the profound, although my main interests are mathematics and physics. "When I get a little money I buy books; and if any is left I buy food and clothes." -Erasmus

Monday, June 8, 2015

Unfair wagers

I've been reading a few books with a decidedly behavioral economics theme. The two most recent ones were Dan Ariely's Predictably Irrational, and Belsky and Gilovich's Why Smart People Make Big Money Mistakes -- And How To Correct Them. I've had a lot of time for all this since I'm currently out of work, and waiting for a government funded writing project. I'm also seriously considering becoming self-employed, since I much prefer doing something self-directed. My main expected headache, though,  is how to deal with taxes if I do take that route.

From my recent reading, I encountered the following problem: Assume that you have a fair coin (equal likelihood for heads and tails), and you were asked if you were willing to make the following wager: USD 150 for you if it's heads, and USD100 for the house if it's tails. Would you be willing to take that wager?

A simple calculation shows that the expected payoff if you do take the wager is USD 25, which is obtained in the following way: Expected payoff $=(150)(0.5)+(-100)*(0.5)$ =USD 25. So if you were the rational man of classical economics, you should take the wager.

Unfortunately, there is something that's really wrong with the rational man. If your total net worth is USD 100, then if you were unlucky, then you may be faced with ruin at a single toss of the coin. That's certainly not a good outcome. And if you have a net worth, for example, USD 200, then the odds of getting both tails would be 0.25. Again, if you were unlucky, you could face ruin after two tosses with probability $\frac{1}{4}$.

The only realistic way that you could play this game is if you had a margin of safety, if the bets you make were small compared to your net worth. I'm not sure, for example, if the bank would be willing to extend credit while you take the losses while you undergo large number of bad runs. Given how hard it is to raise additional capital, even unfair wagers where you have the advantage may be a bad idea.