Probability distribution P(s) for gapped sequence alignment using BLOSUM62 matrices and affine gap costs with α = 12, β = 1 for two sequences lengths L = M = 40. The results for other lengths are summarized in additional file 1. Strong deviations from the Gumbel distribution become visible in the tail. The dotted lines show the original Gumbel distribution, when fitted to the region of high probability. The inset shows the same data with linear ordinate.