  A new method to simulate probability distributions in regions where the
events are VERY unlikely (e.g. p ~ 10^{-40}) is presented. The basic idea is to
represent the underlying probability space by the phase space of a physical
system. The system is held at a temperature T, which is chosen such that the
system preferably generates configurations which originally have low
probabilities. Since the distribution of such a physical system is know from
statistical physics, the original unbiased distribution can be obtained.
  As an application, local alignment of protein sequences based on BLOSUM62
substitution scores with (12,1) affine gap costs are considered The
distribution of optimum sequence-alignment scores S is studied numerically over
a large range of scores.
  The deviation of p(S) from the extreme-value (or Gumbel) distribution is
quantified. This deviation decreases with growing sequence length.
