### What is the expected value of the game

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Question: St. Petersburg Paradox. Consider the following game that you have been invited to play by an acquaintance who always pays his debts. Your acquaintance will flip a fair coin. If it comes up heads, you win \$2. If it comes up tails, he flips the coin again. If heads occurs on the second toss, you win \$4. If tails, he flips again. If heads occurs on the third toss, you win \$8, and if tails, he flips again, and so on. Your payoff is an uncertain amount with the following probabilities:

This is a good game to play because you are bound to come out ahead. There is no possible outcome from which you can lose. How much would you pay to play this game? \$10? \$20? What is the expected value of the game? Would you be indifferent between playing the game and having the expected value for sure?

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