21.One Coin Back
★★★expected valueJane Street
Four fair coins are tossed and you are paid per head. After seeing the result you may pick exactly one coin and toss it again, keeping whatever it then shows. Playing optimally, what is the expected payout?
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You would only ever re-toss a tail, and only if there is one. Work out what a single re-toss is worth and how often the option is usable.
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