  The problem of determining the correct order of fluctuation of the optimal
alignment score of two random strings of length $n$ has been open for several
decades. It is known that the biased expected effect of a random letter-change
on the optimal score implies an order of fluctuation linear in $\sqrt{n}$.
However, in many situations where such a biased effect is observed empirically,
it has been impossible to prove analytically. The main result of this paper
shows that when the rescaled-limit of the optimal alignment score increases in
a certain direction, then the biased effect exists. On the basis of this result
one can quantify a confidence level for the existence of such a biased effect
and hence of an order $\sqrt{n}$ fluctuation based on simulation of optimal
alignments scores.This is an important step forward, as the correct order of
fluctuation was previously known only for certain special distributions. To
illustrate the usefulness of our new methodology, we apply it to optimal
alignments of strings written in the DNA-alphabet. As scoring function, we use
the BLASTZ default-substitution matrix together with a realistic gap penalty.
BLASTZ is one of the most widely used sequence alignment methodologies in
bioinformatics. For this DNA-setting, we show that with a high level of
confidence, the fluctuation of the optimal alignment score is of order
$\Theta(\sqrt{n})$. An important special case of optimal alignment score is the
Longest Common Subsequence (LCS) of random strings. For binary sequences with
equiprobable symbols, the question of the fluctuation of the LCS remains open.
The symmetry in that case does not allow for our method. On the other hand, in
real-life DNA sequences, it is not the case that all letters occur with the
same frequency. Thus, for many real life situations, our method allows to
determine the order of the fluctuation up to a high confidence level.
