Particle movements in Monte Carlo should be random (as random as the algorithm allows), resulting in more or less probable configurations which are then sampled to give a weighted average. There's no way to predict the actual location of a particle for the next simulation step unless the thermodynamic properties of the system and thus the probabilities of given configurations occuring are known beforehand (which would make the simulation unnecessary).
It is not possible to predict the exact location of a particle since Monte calro simulation is implemented by random numbers. What we can know is only the distribution function of the particle location.
The transport of a particle in a medium is usually stochastic. Then, you could only determine the expected value of the quantities used to describe the particle state. This is the case of the position of the particle (also its energy, direction, etc.). You may do a simulation of your particular problem and determine the probability to find a particle in a given region.
Like everything else in life, it depends on the fundamental properties of your "particles" (what are they?) as well as your constraints / boundary conditions. Even if movement is random, for instance, completely solid particles cannot penetrate completely solid walls
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