[gilly]

I must be missing something. If you are not given the game until after you return from your walk, the info is basically useless. The fact that there is an infinite supply of each color means the probability does not change based on the color hats they are wearing.

Now I do not think you can do better then have me guess (always black, always red or flip a coin) and have the other two always abstain. That will give us a 50% chance of living. However, this is not really plausible. How genius are the other two. Do they know they should abstain so that I can make the guess? If they do not you may all want to guess which means that you live only (1/8) of the time.

I am sure that this makes no sense but what can I say.