# This takes a player, then determines a valid game pairing.  It 
#returns the opponent's name if there is one, otherwise
# it returns undef.
sub find_paring($white_player){
    my $white_player = $_[0];
    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);
    PAIRING: foreach $black_player (@possible_opponents){
        # Once we have a valid match, we remove the entries from the
        # match hash, and return the pair.
        if (exists $matches_remaining{$black_player}{$white_player}){
            delete $matches_remaining{$white_player}{$black_player};
            delete $matches_remaining{$black_player}{$white_player};
            last PAIRING;
        }
    }

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