So if you want to say I can't beat a UFAI at a game, you aren't trying to tell me something about the UFAI---you are trying to tell me something about the game.

I like this line, and I agree with it. I'm not sure how much more difficult this becomes when the game we're playing is to figure out what game we're playing.

I realize that this is the point of your earlier box argument---to set in stone the rules of the game, and make sure that it's one we can analyze. This, I think is a good idea, but I suspect most here (I'm not sure if I include myself) think that you still don't know which game you're playing with the AI.