A Tale Of My Hat!
Now a hat chosen at random is placed on each of their heads, such that you can see the color of others hats but not your own. You can't talk to each other or communicate in any way, but you see that the others can't deduce the color of their hats or are unwilling to guess.
Can you show them that you are better than them by deducing the color of you hat?
Don't guess; you may use any mathematical probability, statistic, or induction to solve the problem. Be sure to share your reasoning in the solutions.