Card Game Puzzle

[drummerlsu]

Whether he looked at one card or both cards made a huge difference

First of all, I intended it to be obvious that he looked at both cards from the problem statement; I apologize that it wasn't.

Still, we have no reason to rule out the possibility that he looked at both cards. So when calculating the probability of him having AA, we can only rule out hands with no A. All other hands remain viable possibilities. Since there wasn't any specific information given about how many cards he looked at to determine he had at least one A, it's still logical to assume each possible hand is of equal probability.

The only possible way it would come into play is if you assume there is a chance that your friend would have looked at only one card and answered "I don't know" when you asked him whether he had an ace. But I didn't forsee anyone considering that as a possible circumstance. I'll be more clear next time.