PETERSBURG PARADOX


Play single Game Start all over

You win Dollars Your total Dollars
The bank wins Dollars Bank total Dollars
You entered in the Petersburg casino. Your entrance fee is 20 dollars in each game. In one game, a coin is thrown repetively until it shows no more head. You get 2n-20 Dollars, if n times Head appeared, the bank gets in each game 20-2n dollars.
You will experience that with this entrance fee, you are loosing money. In reality, it is a mathematical fact that you are expected to win: you win with probability 2-n the amount of 2n Dollars. Summing over all n gives an infinite expectation value for your win. Whatever entrance fee you would pay, you would win. The paradox is that this disagrees with your experience to loose.

Oliver Knill, Demo