Note that there are two variables for running the simulation:
t - duration of simulation for each individual particle
N - number of simulated particles
I believe if you leave t fixed, and then increase the size of the grid, then yeah, the number of simulated particles you need probably increase exponentially (or worse) for finding one that reaches the exit.
But you probably want to increase t with the grid size as well, and I think that would mitigate this to be less bad than exponential. This is basically diffusion, and characteristic distance travelled by diffusion is proportional to sqrt(t).
t - duration of simulation for each individual particle
N - number of simulated particles
I believe if you leave t fixed, and then increase the size of the grid, then yeah, the number of simulated particles you need probably increase exponentially (or worse) for finding one that reaches the exit.
But you probably want to increase t with the grid size as well, and I think that would mitigate this to be less bad than exponential. This is basically diffusion, and characteristic distance travelled by diffusion is proportional to sqrt(t).