To get things rolling here is a strategy to win

2 out of 3 times.

in the two player case. This serves as a lower bound for the 8 player scenario. because we can "neutralise" any even number of excess players by pairing them up and have each player choose what they can read on their partner's hat.

The two player strategy is to choose

what loses to what's on the other player's hat.

If the players happen to have the same thing on their hats they will lose 0:2. If what's on their hats is different then one will draw, the other will win, so the team will win. As the second scenario is twice as likely as the first the claimed collective win rate is achieved.

To get things rolling here is a strategy to win

2 out of 3 times.

in the two player case. This serves as a lower bound for the 8 player scenario because we can "neutralise" any even number of excess players by pairing them up and have each player choose what they can read on their partner's hat.

The two player strategy is to choose

what loses to what's on the other player's hat.

If the players happen to have the same thing on their hats they will lose 0:2. If what's on their hats is different then one will draw, the other will win, so the team will win. As the second scenario is twice as likely as the first the claimed collective win rate is achieved.

To get things rolling here is a strategy to win

2 out of 3 times.

in the two player case. This serves as a lower bound for the 8 player scenario. because we can "neutralise" any even number of players by pairing them up and have each player choose what they can read on their partner's hat.

The two player strategy is to choose

what loses to what's on the other player's hat.

If the players happen to have the same thing on their hats they will lose 0:2. If what's on their hats is different then one will draw, the other will win, so the team will win. As the second scenario is twice as likely as the first the claimed collective win rate is achieved.

To get things rolling here is a strategy to win

2 out of 3 times.

in the two player case. This serves as a lower bound for the 8 player scenario. because we can "neutralise" any even number of excess players by pairing them up and have each player choose what they can read on their partner's hat.

The two player strategy is to choose

what loses to what's on the other player's hat.

If the players happen to have the same thing on their hats they will lose 0:2. If what's on their hats is different then one will draw, the other will win, so the team will win. As the second scenario is twice as likely as the first the claimed collective win rate is achieved.