Remember the hat problem? It goes like this: A team of n people are put into a room together. A hat, either black or white, is placed on each. You can't see the color of your own hat, only the colors of the other n - 1 people's hats. No communication is allowed among teammates once they get their hats. After seeing the other hats, the three of you are separated and each is asked "What is the color of your hat?" You can answer "black" or "white", or you can abstain from replying. If at least one person on the team guesses the right answer and nobody guesses wrong, then your team wins. What is the optimal strategy to maximize the chance of winning?
As you know you can do as good as 75% for n = 3. But what about n = 7? It turns that you increase the chance of winning to 87.5%. Did you know that?
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Remember the hat problem? It goes like this: A team of n people are put into a room together. A hat, either black or white, is placed on each. You can't see the color of your own hat, only the colors of the other n - 1 people's hats. No communication is allowed among teammates once they get their hats. After seeing the other hats, the three of you are separated and each is asked "What is the color of your hat?" You can answer "black" or "white", or you can abstain from replying. If at least one person on the team guesses the right answer and nobody guesses wrong, then your team wins.
What is the optimal strategy to maximize the chance of winning?
As you know you can do as good as 75% for n = 3. But what about n = 7? It turns that you increase the chance of winning to 87.5%. Did you know that?
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