Three Helmets, One Bold Guess
Three cyclists on a team each have a sticker — gold or silver — slapped on their helmet, decided by three independent fair coin flips. Each rider sees the other two stickers but not their own. On a signal, all three simultaneously either guess their own sticker color or stay silent. The team wins a sponsorship if at least one rider guesses and every rider who guesses is correct. No communication is allowed after the stickers are placed, but the team plans beforehand. What strategy maximizes the win probability, and what is that probability?
Answer
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