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Probability
The St. Petersburg paradox
Posed by Nicolaus Bernoulli in a 1713 letter; Daniel Bernoulli's resolution appeared in the St. Petersburg Academy's journal in 1738.
A casino offers you this game. A fair coin is tossed until it first lands heads. If heads comes on the first toss, you are paid 2 dollars. If it first comes on the second toss, 4 dollars. On the third, 8 dollars. Every toss that comes up tails before the first heads doubles the prize, with no upper limit, and the casino can always pay.
You play once. The casino asks you to name the most you would pay for a ticket. What is a fair price for one play of this game?