I had fun playing with it, and generalized it to this. Not particularly different from the others, nor extensively tested.

If anyone has the general formula, I'd be curious to see it.

#!/your/perl/here

# DND dice stats
# give expected value for $dice_num, with $dice_sides, dropping the lo
+west $dice_drop die.

use strict;
use warnings;

our $dice_num  = ( shift or 4 );
our $dice_side = ( shift or 6 );
our $dice_drop = ( @ARGV ? shift : 1 );

our $total;
our $count;

foreach my $index ( 0 .. ( $dice_side**$dice_num ) - 1 )
{
    use integer;
    
    my @digits;
    foreach my $digit ( 0 .. $dice_num - 1 )
    {
        $digits[$digit] = ( $index / ( $dice_side ** $digit ) ) % $dic
+e_side + 1;
    }
    
    my $sum;
    foreach my $die ( ( sort @digits )[$dice_drop..$dice_num-1] )
    {
        $sum += $die;
    }
    
    $total += $sum;
    $count++;

#   use this for intermediate results    
#    print "(@digits) sum=$sum, t=$total, c=$count\n";
}

our $avg = $total/$count;
print "${dice_num}d${dice_side}-${dice_drop}: $total/$count=$avg\n";

__END__
[download]

This gives the following:

>dnd.pl 4 6
4d6-1: 15869/1296=12.2445987654321
[download]

Note for craps players:

>dnd.pl 2 6 0
2d6-0: 252/36=7
[download]