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A fair coin is tossed 100 times to create a sequence of heads and tails. A participant is allowed to ask 1 yes or no question (e.g. was the first coin flip heads?), then plays a game where he tries to guess all 100 coins. The participant is awarded $1 for every coin guessed correctly, and loses $1 for each incorrect guess. Find and prove an optimal strategy.
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Quantitative Researcher

Interviewed at G-Research

3.7★
Jun 25, 2021

A fair coin is tossed 100 times to create a sequence of heads and tails. A participant is allowed to ask 1 yes or no question (e.g. was the first coin flip heads?), then plays a game where he tries to guess all 100 coins. The participant is awarded $1 for every coin guessed correctly, and loses $1 for each incorrect guess. Find and prove an optimal strategy.

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