sub avg_roll{
    my($num_dice,
       $sides_of_dice,
       $num_to_lose,
       # We only expect the below to be provided when called
       # recursively
       $rolled_ref,
       $counter_ref)=@_;

    my ($total,$counter); # we declare these with the @_ in the golf
                          # version here we seperate them to show they
                          # arent really parameters.
    $counter_ref||=\$counter; # make a reference to our counter,
                             # unless we were called recursively;
    unless ($num_dice){ # we are done, no more dice

        $total+=$_ # increment the total by the value of the dice
          for (
            sort {$a<=>$b} @$rolled_ref    # sort the results numerica
+lly
                                           # to make avg_roll(4,12,1) 
+work.
          )[$num_to_lose..$#$rolled_ref];  # take a slice
        $$counter_ref++                    # incrememnt the counter
    } else { # we havent finished rolling
        $total+=                     # so increment the total
            avg_roll(                # by the result
               $num_dice-1,          # of the next die
                $sides_of_dice,
                $num_to_lose,
               [                     # pass in a ref,
                 @{$rolled_ref||[]}, # containing the previous rolls
                 $_                  # and the new one
               ],
               $counter_ref          # and a way to access the counter
            )
            for 1..$sides_of_dice    # for each possible roll of the d
+ie
    }
    $rolled_ref ? $total             # if we are not the root of the r
+ecursion
                                     # return the total, whatever it m
+ay be
                : $total/$counter    # return the average.
}
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