Bets and decisions · Casino
The St. Petersburg casino
A casino offers a game. It flips a fair coin until the first heads. If heads first appears on flip k, you win $2ᵏ: $2 if the first flip is heads, $4 if it's the second, $8 for the third, and so on. But the casino only has $1,024 in total, so it can never pay more than that. What is the game's expected payout, in dollars?
Answer with an expected value. First lock in a gut guess with an 80% range, then solve it properly, then watch a simulation settle on the truth.
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