A Famously Bad Gamble

Man, I am so easily nerd-sniped. First, I can just tell that the wedding profession matcher is going to push me to dig out all sorts of weird, distinctive patterns in the pairings between professionals. But, recently, I found myself idly simulating the answer to another kind of question altogether.

The St. Petersburg Paradox

The St. Petersburg Paradox describes a game with a mathematically “infinite” expected payoff but one that definitely does not feel worth playing. The Wikipedia article is quite good on the subject, but to put it briefly here:

You start the game with two dollars. This is your ‘stake.’ Then, the casino flips a fair coin. If that coin comes up heads, then your stake is doubled. If the coin shows tails, you stop the game and win the stake as is.

Mathematically, the “expected return” of a game of chance or investment is the winnings multiplied by how like you are to win. Here, you can think of a bunch of different “win states:”

• you get tails on the first coin, with a payout of $2 • you get tails on the second coin, with a payout of$4