OK, I guess I understand your argument that the mugger can construct an algorithm producing very high utility using only N bits. Or that I can construct a whole whack of similar algorithms in response. And end up unable to do anything because of the forest of low-probability high-utility choices. Which are known to be present if only you spend enough time looking for them. So that's why you suggest limiting not (only) the number of states, but (also) the number of steps. I wonder what Eliezer and others think about that.