Here I present an extension to the famous ant on a cube question:
Two ants, A and B, are placed on diametrically opposite corners of a cube. With every step, each ants move from one vertex to an adjacent vertex (with 1/3 probability of moving along each of the joining edges). What is i) the probability that A and B collide before either ant reaches the diametrically opposite corner; and ii) the expected number of steps before they collide?
I fully understand how the law of iterated expectations work for a single ant reaching the diametrically opposite corner, however I am unsure of how to extend it for this case. I read in a separate question (lost the link sadly, please edit if you find it) about two players meeting on a random walk, and how characteristic functions were involved, but I did not really understand it. Could someone provide some insight? Cheers!
Edit: second part makes more sense after drawing the Markov chain, could someone prod me in the right direction for constructing the Markov chain for the first part?