This is a problem that I just thought of and could not find online- nor any similar problem.
Suppose we have two different chess piece stationed on opposite corners of a chess board. For this example, let's put a rook on the 'top left' and a knight in the 'bottom right'. The rook randomly moves to one of the legal positions and then the knight moves to a random legal position.
Eventually, one piece is bound to capture the other. What is the probability that the rook is the piece to capture the knight? What is the expected number of moves for this to happen in? Obviously the probability of the knight capturing the rook is just 1-probability of the other way around, but does the expected number of moves change?
I wouldn't really even know how to go about trying to solve this outside of running Monte Carlo simulations to approximate the value (fairly trivial with code).
Any suggestions of how to approach this would be greatly appreciated!