sub n_sides {6}
sub attack  {3}
sub defend  {2}

sub loss {
    my ($att, $def) = @_;
    return (($att->[0] <= $def->[0]) + ($att->[1] <= $def->[1]));
}

sub pair_prob {
    my ($K, $pair) = @_;
    my ($i, $j) = @{$pair};
    
    return (((($i < $j) 
            ? ($K * $i ** ($K-1))
            : ($i ** $K - ($i-1) ** $K))
            - $K * ($i-1) ** ($K-1)) / (n_sides() ** $K));
}

my @pairs = map {my $j = $_; map {[$_,$j]} (1..$j) } (1..n_sides());
my @losses;

foreach my $att (@pairs) {
    foreach my $def (@pairs) {
        $losses[loss($att,$def)] += 
            pair_prob(attack(), $att) *
            pair_prob(defend(), $def);
    }
}
print "P(loss = $_) = ", $losses[$_], "\n" for (0..@losses-1);