The St. Petersburg paradox, in a nutshell, is: why would you refuse to play a game with an unlimited expected payout? Shouldn't you be willing to pay any finite price to play, since your expected return is infinite?
This simulation explores what the Stanford Encyclopedia refers to as the "Average Win" explanation, that:
Expected value is in effect average payback in the long run.... [I]f you're going to play St. Petersburg with a substantial fee per game, you're likely to have to play a very very long time before you come out with a positive net payoff. Ordinary practical considerations thus apply... You may have to play a very long time before winning once. But worse: in a series of losses, the amount needed for the next bet rises. How much bankroll would you need to guarantee success...? Whatever bankroll you take into the casino, there's a chance that this will not be enough.