An interesting probability problem

[doormat]

You are one of three prisoners. You cannot communicate with your compatriots in any way, but may assume that the other two are brilliant, i.e. they will do the right thing. You are each outfitted with a hat - which you cannot see. The warders have an infinite supply of red and black hats, so you know your hat must be one of those two colors. The three of you are led to a courtyard, to view each other's hats (sort of like that poker game where everyone holds a card to their own forehead). You are led back to your cells, and asked to state what color hat you are wearing. You may choose red, black, or "abstain." Warning, if all three abstain you will all be killed. Also, if any one of you guesses your color incorrectly, you will all be killed. You do not know beforehand the purpose of going to the courtyard, and you are all questioned simultaneously while separated from one another. What is the best strategy?

doormat