Hello allsop_5, and welcome to the Monastery!

The code as given is imcomplete, as it doesn’t show the declaration and initialization of the variables $string and $shuf_seq. It would be useful if you could provide sample values for these variables, together with the final $score value you expect to generate from these sample values.

One point stands out: in these lines:

$score = scoring($s, $m);
$score += $score;
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you first overwrite the value of the variable $score, then add this new value to itself (thereby doubling it). Neither of these is what you intend. You need something along these lines:

my $score;

foreach (...)
{
    ...
    my $local_score = scoring($s, $m);
    $score += $local_score;
    print $local_score;    # (or did you want to print $score here?)
}
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And BTW: you do begin your script with:

use strict;
use warnings;
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don’t you?

Hope that helps,