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The fraction of samples spanning a lattice at its percolation threshold is found via simulations of bond and site-bond percolation to have a universal value of about 0.42 in three dimensions. The ratio of shift (of the finite to infinite size threshold) to width of the threshold distribution is also compatible with universality. Lattices with up to 1001 3 sites and/or very good statistics were needed to obtain clear results in these Monte Carlo tests; preliminary studies with smaller lattices were inconclusive.
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Stauffer et al. (1994) studied this question.
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