Three people, A,B,C, participate in this game. The host has 2 kind of caps, white and black. He chooses uniformly at random and places a cap on each of the peoples heads. The trick is, each person can see the other two people's cap but cannot see her own cap....
They are strictly prohibited from communicating with each other (ofcourse, before the game, they can agree on a scheme). The host gives them each a piece of paper. Each participant has to guess her own cap. They can write "White", "Black" or "Pass" on their paper. They cannot see each other's papers.
The group wins the game if at least one participant guesses correctly and no other participant guesses it wrong. For example if A guesses it correctly, and B,C write "Pass" they win. But if A guesses correctly and B guesses her own cap wrong, they lose.
What are the best odds of winning this game ?
Posted from above to keep the reference correctly ...
one can easily get 75% of saving by:
Simple strategy, if you see other two of the same color, guess yours opposite, else pass. One looses only when all three caps are the same color.