I am working on a controller that plays Ms. Pac-Man using a minimax algorithm. The controller has a limited time amount in which it can choose a move on each round, otherwise when the time runs out the system chooses a random action instead.
My goal is to select a value for the depth that is large enough to consent Ms.Pac-Man to achieve a decent score, but not so large to cause a lot of timeouts. Leaving the number of timeouts aside, basically I did the most intuitive thing: I increased the depth until I noticed a drop on the score values, but that drop could have occurred casually.
Is there a more scientific/statistical way to do that (that ideally addresses both the score e the timeout issues)?
(I fantasized about performing repeated hypothesis testing, but I quickly learned how silly that idea was when I heard about multiple testing problem).