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Ten coins: one is fair and nine have unknown biases centred on 0.5. You have 100 flips on any coins you like and win one unit per head. How do you choose which coin to flip?

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There are ten coins. The first is fair. Each of the other nine has a heads probability drawn from a roughly normal distribution centred on 0.5 and confined to between 0 and 1. You have 100 flips in total and may choose any coin for each flip. You are paid one unit for every head. How do you choose which coin to flip, and when do you switch?

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