How should I use Monte Carlo method to simulate some police cars that keep patroling in a tile based map? I have a tile map (isometric) and I have some police cars that they patrol all the time on the map, there is some building and other cars in map too so they are considered as constraints in my shortest path algorithm (below). I use to randomly select some target for each police car and use A algorithm to find the path to the randomly selected destination tile and this cycles over and over. because cars should move all the time! (except those that gamer should control) The problem is police cars routes are correlated and they do not just traverse the area randomly, for instance, they do not usually cover a same area or they do not repeat their own route so my implementation based on some random destination point wasn t a good idea and the result was not satisfying. Take a look at the following picture, it shows how randomly selecting the destinations worked for me, obviously, it is a dumb patroling for sure, even a cockroache could do better! Suddenly, I remembered Monte Carlo Method and I thought it would solve my problem, because it exactly does what I wanted to do, However may be I should use Zobrist Hashing since it is tile base in nature. Does anyone has any idea how should I use this kind of methods? Question in Brief How can I use Zobrist Hashing or Monte Carlo method to set destinations points for my patroling car (like police car)? If anyone knows another way to implement a patrolling method, he she is very welcome to post an answer, I am not sure if Zobrist Hashing is the best and worth to implement. First Edit (added following paragraph) I need to distribute the cars and their destination points in a homogeneous manner. Every kind of solution that get me close to a good pattern could be my answer, of course there is a lot of methods to do so, but I dont have any clue.