What is a "bad beat"? (A way to avoid tilting?)

[MrGrob]

I lost AA to AA (all in NL pre-flop) the other day. I was talking to a friend about it, and we agreed that this was not a "bad beat", as there is no way that he wasn't supposed to be in the hand. I though about it some more, however, and figured that it might as well be a bad beat, as the chances of LOSING AA to AA is so small.

That takes me to my question...what is a bad beat as you see it? I think that AA to AA is a bad beat, but or a different nature then AA to 57o or something.

I ask this as I was not upset to lose AA to AA, then noticed that I would have been had he had 57o or something...yet, is not his WINNING chances vs AA better then my chance of losing AA to AA?

I now remember this hand when I am about to get upset, and for some strange reason, it works to keep me cool.