St. Petersburg paradox
The St. Petersburg Paradox is a problem about probability. Imagine that you are offered a chance to play a game where you have a 50/50 chance of winning 2 dollars, or nothing. The game will be played many times, and the amount of money you get from the game is doubled each time you win. So if you win the first time you play, you get 2 dollars. The second time you play and win, you get 4 dollars. The third time, you get 8 dollars. This continues forever.
It might seem like it would be a good game to play, because each time you win, you get twice as much money. But the problem is that the payoffs increase so quickly that the expected value (what you are likely to get in the end) is actually infinite - meaning there is no amount of money that you could pay that would make the game worth it!
So the St. Petersburg Paradox tells us that even though a game can look like it's a good deal at first, it can turn out to be worthless if the payoffs increase too quickly.
It might seem like it would be a good game to play, because each time you win, you get twice as much money. But the problem is that the payoffs increase so quickly that the expected value (what you are likely to get in the end) is actually infinite - meaning there is no amount of money that you could pay that would make the game worth it!
So the St. Petersburg Paradox tells us that even though a game can look like it's a good deal at first, it can turn out to be worthless if the payoffs increase too quickly.