My guess is that you'd model the troll as a 2D simple symmetric random walk with the rabbits and black holes stationary and distributed randomly with some densi

My guess is that you'd model the troll as a 2D simple symmetric random walk with the rabbits and black holes stationary and distributed randomly with some densities R and B. As a first go I'd assume that the topology was that of a torus, so as to not deal with the boundary. Now, as the exact definition of a "round" wasn't specified, I'll just assume the troll can walk forever. Now, it's been proven that a simple symmetric random walk on a 2D lattice has probability 1 of reaching any given point as the number of steps goes to infinity. So, ignoring the teleporting, the closed form answer for the number of rabbits eaten is mnR. With teleporting, I'd guess the Markov chain would mix better. So, the closed form answer would again be mnR.