Mea culpa (again). The results from my original function are tent shaped, except the two extreme values are half as big as they would be expected to be.

It's more likely the result of rounding slop on my part than it is an artifact of using random numbers. No such effects are seen when the function is this straightforward 2-dice method:

sub roll_dice {
  my ($low_end, $range) = @_;
  int(rand(int $range/2)) + int(rand(1 + $range - int $range/2)) + $lo
+w_end;
}
[download]

And here's dice-rolling code generalized to let you choose a range and number of dice, and it will figure how many sides each die needs. (No fractional dice, here.)

sub roll_dice {
  my ($low_end, $range, $dice) = @_;
  my $sidesneeded = $range + $dice - 1;
  my $r = 0;
  for (0..$dice-1) {
    my $sides = int($sidesneeded / ($dice-$_));
    $sidesneeded -= $sides;
    $r += int(rand $sides);
  }
  $low_end + $r;
}
[download]