Re percolation probabilities: If we're talking about about site percolation on the hexagonal lattice in the plane -- i.e., each site is surrounded by 6 others -- then the critical probability = 1/2. For the square lattice, bond percolation (i.e., a unit edge of the square tiling is present with a given probability) also has critical probability = 1/2 (of having an infinite component made of these edges). --Dan