Crossing probabilities in one, two or three directions for percolation on a cubic lattice

The probabilities of crossing in exactly one, two or three directions have been investigated using Monte Carlo simulations of percolation on cubic lattices with free boundary conditions. The crossing probability in exactly one given direction shows the least influence of finite-size effects and is best suited to obtain the percolation threshold (p(c)). Finite-size effects are most important for simultaneous crossing in three directions. Crossing probabilities at p(c) for large lattices are the same for site and bond percolation. The crossing probability in a given direction regardless of crossing in other directions, R1, is 0.28. Exact results for small lattices agree with simulation results.