PHP - Is rand(1,1000) = 1000 as probable as rand(1,1000) = rand(1,1000) ?

Question

Is this how PHP implemented random number generating?

Say I want to calculate a yes or a no. Everytime I have a certain probability percentage (say: 0,05% for this example).

I do:

$possibilities = 100 / $probabilityPercentage; //$possibilities = 2000
$yes = rand(1,$possibilities);

$yesCheck = $possiblities;            //OPTION 1
$yesCheck = rand(1,$possibilities);   //OPTION 2


($yesCheck == $yes) ? return true : return false;

Does it give the same results with either option?

Answer 1

The way most random generators work, the output is not truly random but rather based on an algorithm that should make the returned values appear random and distributed. Based on that I think the real probability that you actually get the same number twice in a row is even less than in the real world if you had two totally unrelated "random generators".

Edit: Having said that I have no inside info whatsoever about how the default random generator in php works.

Answer 2

Option 1 is guaranteed to be correct.

I don't think I learned enough probability and statistics back in the day to say whether Option 2 is correct.

I did, however, learn that one should NEVER trust someone else's random number generator without running test programs on it, to get an idea of how random it REALLY is.

In your case, I'd run a few million test cases through both options, and see whether Option 2 came up with similar statistics to Option 1.

Answer 3

In theory, yes, the two expressions have exactly the same probablity of being true. That's assuming PHP's random number generator is in fact random - if it isn't, one will be more likely than the other.

The best approach would be to run an experiment (thousands of iterations) and see what happens.

Answer 4

IF the random number generator is truly random then both approaches produce the same result. However, computer random number generators aren't perfect. I doubt the flaws are enough to matter but the only way to know for sure is to try it--run a test for as long as possible and see if there is a deviation from what it should be. You'll need millions of random numbers at a minimum.

Answer 5

Let the data speak for itself.

Code

vinko@parrot:~$ more rand.php
<?php

$randrandsum = 0;
$randconstsum = 0;
$count = 20;
for ($j = 0; $j < $count; $j++) {
        $randrand = 0;
        $randconst = 0;
        for ($i = 0; $i < 10000000; $i++ ){
                $a = rand(1,1000);
                $b = rand(1,1000);
                if ($a == $b) $randrand++;
        }
        for ($i = 0; $i < 10000000; $i++ ){
                $a = rand(1,1000);
                $c = 1000;
                if ($c == $a) $randconst++;
        }
        $randrandsum += $randrand;
        $randconstsum += $randconst;
        print ($j+1)." RAND-RAND: $randrand RAND-CONST: $randconst\n";
}
print "AVG RAND-RAND: ".($randrandsum/$count);
print " AVG RAND-CONST: ".($randconstsum/$count)."\n";
?>

Test run

vinko@parrot:~$ php rand.php
1 RAND-RAND: 10043 RAND-CONST: 10018
2 RAND-RAND: 9940 RAND-CONST: 10132
3 RAND-RAND: 9879 RAND-CONST: 10042
4 RAND-RAND: 9878 RAND-CONST: 9965
5 RAND-RAND: 10226 RAND-CONST: 9867
6 RAND-RAND: 9866 RAND-CONST: 9992
7 RAND-RAND: 10069 RAND-CONST: 9953
8 RAND-RAND: 9967 RAND-CONST: 9862
9 RAND-RAND: 10009 RAND-CONST: 10060
10 RAND-RAND: 9809 RAND-CONST: 9985
11 RAND-RAND: 9939 RAND-CONST: 10057
12 RAND-RAND: 9945 RAND-CONST: 10013
13 RAND-RAND: 10090 RAND-CONST: 9936
14 RAND-RAND: 10000 RAND-CONST: 9867
15 RAND-RAND: 10055 RAND-CONST: 10088
16 RAND-RAND: 10129 RAND-CONST: 9875
17 RAND-RAND: 9846 RAND-CONST: 10056
18 RAND-RAND: 9961 RAND-CONST: 9930
19 RAND-RAND: 10063 RAND-CONST: 10001
20 RAND-RAND: 10047 RAND-CONST: 10037
AVG RAND-RAND: 9988.05 AVG RAND-CONST: 9986.8

Given the above results I'd say that for all practical purposes, both options are equivalent, giving the expected 1/1000 result on both cases.

Answer 6

Yes, rand(1,1000) = 1000 is just as probable as rand(1,1000) = rand(1,1000).

Imagine rolling two dices. After you rolled the first one, what is the probability the second one will equal the first when rolled? 1/6.

Now write down a number between 1 and 6 and roll a dice. What is the probability the dice will equal what you have just written? 1/6.

Answer 7

This does not directly address your question, but you may want to look at mt_rand() instead. The PHP documentation states:

Many random number generators of older libcs have dubious or unknown characteristics and are slow. By default, PHP uses the libc random number generator with the rand() function. The mt_rand() function is a drop-in replacement for this. It uses a random number generator with known characteristics using the » Mersenne Twister, which will produce random numbers four times faster than what the average libc rand() provides.

From http://www.php.net/manual/en/function.mt-rand.php.