Running for 10,000,000 twice I got 3.1405 the first run, and 3.1424 the second. (for an average of 3.1415) It's quite likely your rand() isn't perfect. (neither is mine 10,000,000 runs should give me a digit or two more accuracy).

Anyway, here is my favorite approximation for pi, mainly because it only uses the number 2. Even though two is normally a computer friendly number, this algorithm isn't, because it also uses sqrt's. With my perl, 14 iterations is gives the maximum accuracy: 3.14159265480759

#!/usr/bin/perl -w
use strict;

print "Enter how many iterations:\n";
chomp(my $i = <>);

my $x = $i - 1;
my $y = sqrt(2);
do { $y = sqrt(2 + $y) while (--$x);
     $y = sqrt(2 - $y);
   } if $x;

my $z = $y * (2 ** $i);

print "Pi is close to: $z\n";
[download]

So, while not the best, but I have some strange affinity to it. :)

Ciao,
Gryn

p.s. Sorry for the cryptic code for a quick decrypt its: (2**n)*sqrt(2-sqrt(2+sqrt(2+sqrt(2+sqrt(2))))) with the number of 2's inside the sqrt equaling n.

#!/usr/bin/perl
# This is a quick program to calculate pi using the Monte Carlo method
+.
# I recomend inputting  a value for $cycles greater that 1000. 
# I am working on a detailed explanation of how and why this works. 
# I will add it as soon as I'm done.
use strict;
open(PI, ">>pi.dat") || die "pi.dat";
my ($i, $j, $yespi, $pi) = 1;
my $cycles = 1;
srand;
while ($j <= 100000) {
    $cycles = $j;
    while ($i <= $cycles) {
    my ($x, $y, $cdnt) = 1;
    $x = rand;
    $y = rand;
    $cdnt = $x**2 + $y**2;
    if ($cdnt <= 1) {
        ++$yespi;
    }    
    $i=$i + 10;
    $pi = ($yespi / ($cycles / 10)) * 4; # since I add 10 every time.
    print PI "$cycles $pi\n";
    }
$j = $j + 10;
}
close(PI) || die "pi.dat";
[download]

Here is the modified script I was talking about. If you look at pi.dat it starts getting inacurate at one point. I will try using one of the ways to genereate seeds that are slightly more random than plain srand. Note: you need to make a file pi.dat for the script to run.

Oops forgot to log in, above post was mine

Supposedly there is a modern pi generating algorithm which takes constant time to generate any given digit of pi requested.

Ciao,
Gryn

The former is available from Google, laziness is no excuse. The latter only works for base 16.