Play single Game Start over

You win Dollars Your total Dollars
The bank wins Dollars Bank total Dollars
You enter the Petersburg casino. In each game, your entrance fee is $20. During such a game, a coin is thrown repeatedly until it stops showing "head". You win 2n-20 dollars, if n times "head" appears. The bank makes 20-2n dollars.
You will experience that with this entrance fee of 20 dollars you are losing 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 win expectation. Whatever entrance fee you would pay, you would be still be in an advantage. The paradox is that this mathematical finding disagrees with your experience.

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