Bets and decisions · Coin game · difficulty 3 of 5
Heads, squared
You flip a coin that lands heads with probability 0.5, independently each time, and keep flipping until the first tails. Let H be the number of heads you saw before that tails (it can be 0). You're paid H² dollars. What is the fair price to play, in dollars, meaning the expected payout?
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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