While a graduate student at the University of Chicago, I taught an introductory statistics class, mostly to economics majors. The most memorable and long-lasting lesson of that class came during a lecture on the St. Petersburg paradox.

We play the following game. Toss a fair coin indefinitely. The amount I owe you starts at $1 and doubles every time a head occurs. The game ends, and I pay what I owe, after the first tail occurs. For example, if the outcomes are heads, heads, heads, tails, then I’ll owe you 2 x 2 x 2 = $8. If the first outcome is a tail then I owe you $1. And so on. How much would you pay to play this game? (More on this question below.)