sub find_paring()
{
    my $white_player = shift;
    my $black_player = "none";

    # Get a list of players still in the running
    my @possible_opponents =
        keys %{$matches_remaining{$white_player}};

    # Shuffle the list to add some randomness, then find the first
    # avaliable opponent.
    &shuffle(\@possible_opponents);
    foreach (@possible_opponents)
    {
        # Once we have a valid match, we remove the entries from the
        # match hash, and return the pair.
        if (exists $matches_remaining{$_}{$white_player}){
            $black_player = $_;
            delete $matches_remaining{$white_player}{$_};
            delete $matches_remaining{$_}{$white_player};
            last;
        }
    }

    # Return the info we have
    return ($white_player, $black_player);
}