The St. Petersburg paradox. Here is an interesting game: You pay a certain amount of money to play. Then you flip a fair coin. If you see tails, you flip again, and the game continues until you see a head, which ends the game.
If you see heads on the first flip, you receive $2. If you see heads on the second flip, you receive $4. If you see heads on the third flip, you get $8, and so forth—the payoff is doubled every time. What is the expected payoff of this game? How much would you pay to play this game? Suppose you pay $1000 to play. What is the probability that you would make money? Why is this game a paradoxical situation given the expected value?
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