The St Petersberg paradox illustrates the differences between mathematical theory and street-level practice.
Suppose you are offered a bet where you toss a coin. The first time you get heads, you get $2. The second time you get heads, you get $4. This keeps doubling until you get a tail. Then the game ends, and you keep your winnings. So the payoff is 2 to the power of (consecutive heads+1).
The question is, how much will you pay for
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