Universality of critical existence probability for percolation on three-dimensional lattices

Using a histogram Monte Carlo simulation method, we calculate the existence probability E-p for bond percolation on simple cubic (sc) and body-centred cubic (bcc) lattices, and site percolation on sc lattices with free boundary conditions. The R-1 spanning rule considered by Reynolds, Stanley, and Klein is used to define percolating clusters. We find that E-p for such systems has very good finite-size scaling behaviour and the value of E-p at the critical point is universal and is about 0.265 +/- 0.005.