A warden is playing a game with three prisoners. He says he will place a hat on every prisoner, either black or white. He flips a fair coin to decide on the color of every hat, independent of other choices. Every prisoner can see the hats of the other two prisoners, but not his own. Then, every prisoner recieves a piece of paper, and writes either "Black", "White" or "Forfeit" on the piece of paper; and hand it in to the warden (without having seen what other prisoners write).
If at least one of the prisoners guesses his color right, and the rest forfeit, the prisoners win and they go out free. Otherwise - if at least one prisoner guesses wrong, or all of them forfeit - they lose and die.
The prisoners are allowed to form a strategy before the game starts. If the strategy was "write black or white, randomly" for everybody, then the probability for being saved would be 1/8. If the strategy was two players write "forfeit" and the third writes black or white randomly, then the saving probability would go up to 1/2. Can you improve on that number?