### Could there still be new hat puzzles?

Posted:

**Tue Sep 19, 2017 3:17 pm UTC**Here's a hat puzzle inspired by this one.

Seven perfectly rational players stand in a circle.

Everyone gets assigned, randomly and independently, a black hat or a white hat. Nobody can see the color of his own hat but the colors of all other players.

All the players must try to guess the color of their hat simultaneously, without any communication. Let's say they somehow aren't even able to recognize eachother, or they haven't met in person before. They only see hat colors and the relative position of their wearers in the circle.

To win the game, they need a majority (at least 4) of correct guesses.

They can devise a strategy, but it can't be nominative. The player's can't take into account their own identity, the whole strategy has to be exactly the same for all players.

What is the probability that they win the game?

Seven perfectly rational players stand in a circle.

Everyone gets assigned, randomly and independently, a black hat or a white hat. Nobody can see the color of his own hat but the colors of all other players.

All the players must try to guess the color of their hat simultaneously, without any communication. Let's say they somehow aren't even able to recognize eachother, or they haven't met in person before. They only see hat colors and the relative position of their wearers in the circle.

To win the game, they need a majority (at least 4) of correct guesses.

They can devise a strategy, but it can't be nominative. The player's can't take into account their own identity, the whole strategy has to be exactly the same for all players.

What is the probability that they win the game?