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sub _max_throw {
    my ($throws) = @_;

    my $max_throw = reduce { 
        my $a_1 = ( ref $a eq 'ARRAY' ? max(@$a) : $a );
        my $b_1 = ( ref $b eq 'ARRAY' ? max(@$b) : $b );
        $a_1 >= $b_1 ? $a_1 : $b_1;
    } @$throws;

    # if our pattern is a 1-length multiplex pattern, 
    # reduce returns the first element, so correct for
    # that here
    $max_throw = max(@$max_throw) if ref $max_throw eq 'ARRAY';

    return $max_throw;
}

# extend the pattern by the number of throws equal to the biggest
# throw in the pattern, to ensure that every throw in the pattern
# lands at least once.