Quote Originally Posted by Kalirren View Post
Well, but then the random walk is biased. I thought that any given state (including 0, or the state corresponding to any finite number for that matter) is only guaranteed to be recurrent if the random walk is unbiased, and is transient otherwise. So our first proof that the chain of attacks marches off to infinity would be correct...right?

Actually, I've got my hands on a proof that it's guaranteed to terminate even in the biased case. Very very clever maths, and very complicated, but works. If you're on a uni connection, you may have free access, otherwise, it's pay to view.