Can't agree more with BrowserUk.

Whatever you do always verify the statistical distribution of your method for producing random numbers. In order to do that you need to produce a large bunch of these random numbers and plot a histogram of their values or, much more accurate, run a test for verifying the distribution. Here is a test for a discrete distribution, e.g. dice numbers: https://stackoverflow.com/questions/21204733/a-better-chi-square-test-for-perl

Perl's rand() will, in theory, produce random numbers drawn from a uniform distribution: all values from 0 to 1 have equal probability to appear. The histogram of such a distribution is more-or-less a flat line (the equal probabilities). Provided that you draw *a lot* of random numbers you will be approximating that.

Now if you *add* two rand() values in order, for example, to get a 64-bit random value you will find that the histogram of the numbers you get is not a flat line anymore but resembling more of a bell-curve, the trademark of a Gaussian (aka Normal) distribution. I would love to play poker against a machine which uses this method ...

Here is some code to demonstrate this: 
#!/usr/bin/env perl

use strict;
use warnings;

use Statistics::Histogram;

my $num_bins = 50;
my $use_linear_axes = 1;

srand(1234);

### Produce a lot of random numbers:
# 1) expecting a flat line (uniform distribution):
my @x = map { rand() } 1..1000000;

# 2) sum of two rand() to get larger random number
# - I am getting larger numbers and I am expecting a flat line.
# - you wanna bet?
my @y = map { rand()+rand() } 1..1000000;

# Now draw the histograms of obtained random numbers:
# 1) perl's rand is quite uniform, I see a flat line:
print Statistics::Histogram::get_histogram(\@x, $num_bins, $use_linear
+_axes);

# 2) !!ouch - that hurt !!
print Statistics::Histogram::get_histogram(\@y, $num_bins, $use_linear
+_axes);

[download]

Bottomline: I always wanted to ask Einsten to clarify whether "dice" in his famous "God does not play dice" is plurar or singular. I guess I will never know although maybe 60 years ago dice did have the singular of die. If God plays with a single dice his or her distributions will be Uniform (the flat lines). However, if God plays with two dice (and sums up the two rands) his/her distributions will be Gaussian (the bell shape) and that makes a lot of difference for the Universe.

bliako

In reply to Re: how to get a 64bit random number with rand() ? by bliako
in thread how to get a 64bit random number with rand() ? by iglake

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