I have 3 persons which either wear a white or a black cap. They can only see the color of the other caps, but not their own. White and black caps are eqally likely. As a team, they play a game of guessing their own cap color. If they will win, all of them have to guess correctly their own cap color. Once the game begins, they cannot communicate the color of the other two caps.
Now my interesting question: What is a good strategy for the 3 persons such that with 75% probability all answer correctly? (if the strategy should be made before the caps are donned)
The hard thing is that the players cannot communicate anything with each other once the have the caps.