This is being a little picky, but I noted you used:

sub find_pairing($white_player){ ... }
[download]

in the code snippet. This prototype will work, but isn't strictly correct. It would be better to say:

sub find_pairing($) { ... }
[download]

I also noted that some of the replies used:

sub find_pairing() {
    my $white_player = shift;
    ...
}
[download]

This is bad. If you call this method after this declaration, then a call like find_pairing("Bob") will fail because the prototype will accept no arguments. It would be better to say nothing about the signature of the subroutine like:

sub find_pairing { ... }
[download]

Anyway, you're all probably aware of this, but I wanted to make sure the casual browser, who might not, knows the difference between these slight variations. I look forward to Perl 6, where this cruft will be cleaned up.