Following on from the latest puzzle from +Mike McLoughlin
This is one of my favourites, but perhaps a bit more "mathematical" than "logical". Whatever the case... I'm a nerd.
Two people have 3 hats stacked on each of their heads. Each hat is either black or white, and you can assume each hat was drawn from an infinite pool of black and white hats (or to put it another way, a coin flip determines the colour of each hat). So it is possible that each person could have 3 black hats on their head. Each person can see the other person's hats, but not their own.
The game: each person silently and simultaneously points to a hat on their own head (lowest, middle or top). The round is "won" if each person points to a white hat.
Now, if each person was to just randomly point at any hat on their head, it would seem the odds of winning each round would be 25%. The question: is there any predetermined strategy that can improve these odds?
(Any form of communicating what hats are on the other person's head is not allowed.)