I originally posted the following on August 13, 2009, but if you are unfamiliar with it, have some fun this weekend thinking about it. (That post is long enough ago that I bet even if you saw it, you can’t immediately remember how to think this through.)
Suppose everyone in your town selects a real number between 0 and 100, inclusive (i.e. 0 and 100 are both possible choices, as is any other number between). The winner is the individual (or individuals) who selects the number closest to 2/3 of the average of numbers chosen. What number do you choose? Why?
Just to be clear, suppose there are three players who select the numbers 10, 20, and 30. The average is 20, and 2/3 of the average is 13.333… . Therefore, the winner is the individual who selected 10 because it is closest to 2/3 of the average.
Yes, you can find out all about this problem on the internet. If that’s how you want to go about this, then just read my analysis and application to speculative bubbles in financial markets. But, do yourself a favor and think about the problem, talk it over with your colleagues, family, and friends (even play it with them). I bet you’ll have some fun, or 2/3 of the average of fun, or something.