Machines numbered 1 to 20 are each real with probability 1/2. A play costs $1, and a real machine x pays x dollars with probability 1/2 per play, at most once. How should you play?
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Twenty machines stand in a row, numbered 1 to 20. Each machine is independently real with probability 1/2 and fake with probability 1/2. Each play of a machine costs $1. A fake machine never pays; a real machine pays out with probability 1/2 on each play, machine number x pays x dollars, and each machine pays out at most once. What playing strategy should you follow?
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