Three people enter a room and have a red or blue hat placed on their head. They cannot see their own hat, but can see the other hats.
The color of each hat is purely random. All hats could be red, or blue, or 1 blue and 2 red, or 2 blue and 1 red.
They need to guess their own hat color by writing it on a piece of paper, or they can write "pass."
They cannot communicate with each other in any way once the game starts. But they can have a strategy meeting before the game.
If at least one of them guesses correctly they win $50,000 each, but if anyone guesses incorrectly they all get nothing.
Using optimal strategy, what is the maximal percentage chance of winning that can be achieved?
E.g., if you think the answer is 50 % chance of winning, type in your answer as 50.