Three Hats Puzzle
The color of each hat is purely random. All hats could be green, or blue, or 1 blue and 2 green, or 2 blue and 1 green.
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 guess incorrectly they all get nothing.
What strategy would give the best chance of success?
(Hint: 100% chance of success is not possible.)
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