James_H:

Obviously your "modest laptop" is a bit zippier than my Atom-based desktop, as it took 3:10 to complete. But when I looked at your code, I was wondering why you did a monte-carlo simulation. Since there are only 20 coins, there are a little over a million combinations, so why not compute it exactly?

So I whipped this up:

$ cat 892293.pl
use strict;
use warnings;

my $numTosses = 20;  # Coin tosses per experiment (20 in this example)
my $runs = (1<<$numTosses)-1;

my @tailCnt;
for (my $collection=0; $collection<1<<$numTosses; ++$collection) {
    my $tails=0;
    $tails += ($collection & 1<<$_) ? 1 : 0 for 0 .. $numTosses;
    $tailCnt[$tails]++;
}

print <<EOHDR;
Tails     Count     %
-----   --------  ------
EOHDR
for (my $i = 0; $i < $numTosses+1; $i++) {
    printf "% 4u    % 8u   %5.2f\n",
           $i,  $tailCnt[$i],  100*$tailCnt[$i]/$runs;
}

$ time perl 892293.pl
0x00100000, 1048576
Tails     Count     %
-----   --------  ------
   0           1    0.00
   1          20    0.00
   2         190    0.02
   3        1140    0.11
   4        4845    0.46
   5       15504    1.48
   6       38760    3.70
   7       77520    7.39
   8      125970   12.01
   9      167960   16.02
  10      184756   17.62
  11      167960   16.02
  12      125970   12.01
  13       77520    7.39
  14       38760    3.70
  15       15504    1.48
  16        4845    0.46
  17        1140    0.11
  18         190    0.02
  19          20    0.00
  20           1    0.00

real    0m20.372s
user    0m20.273s
sys     0m0.016s
[download]

It runs quite a bit faster on my machine, and it tried each combination once. Of course, I'm limited by the number of bits available, so large experiments aren't going to work well. You can use Bit::Vector, but I suspect that would be a good deal slower. (I wouldn't know, I didn't try it.)

...roboticus

When your only tool is a hammer, all problems look like your thumb.