PHP: Best random numbers

Question

Hello!

I heard that PHP's rand() function doesn't give good random numbers. So I started to use mt_rand() which is said to give better results. But how good are these results? Are there any methods to improve them again?

My idea:

<?php
function rand_best($min, $max) {
    $generated = array();
    for ($i = 0; $i < 100; $i++) {
        $generated[] = mt_rand($min, $max);
    }
    shuffle($generated);
    $position = mt_rand(0, 99);
    return $generated[$position];
}
?>

This should give you "perfect" random numbers, shouldn't it?

I hope you can help me. Thanks in advance!

Answer 1

There is no such thing as a "perfect" random number. No matter what subjective definition of "perfect" you have. You can only achieve pseudo-random.

I was simply trying to point you in the right direction. You asked a question about perfect random numbers, even if perfect was in quotes. And yes, you can improve randomness. You can even implement heuristic or "natural" algorithms, such ideas like "atmospheric noise" -- but still, you're not perfect, not by any means.

Answer 2

<?php
  function random_number(){
      return 4; // return generated number
                // guaranteed to be random
  }
  ?>

All joking aside, you're getting into a philosophical question of what is "random" or what is "best". Ideally you'd want your random numbers to have few patterns in them over the course of your procedure. Generally system time is used as the seed, but I've also used the previous random number as the seed, the previous random numberth ago as the seed. The problem is, with a powerful enough computer and full knowledge of the hardware running, and generator function, you would be able to predict the entire set of numbers generated. Thus if you had a powerful enough computer (some people put God into this category) that knew all possible variables and functions of the universe you would then be able to predict every event that happened or will happen. Most random number generators are fine on their own but if you know someone who can see the patterns, more likely they are like the guy in Beautiful Mind and you should get them checked into a clinic.

By popular demand :D

Answer 3

Pseudorandom number generators (PRNG) are very complex beast.

There are no real "perfect" random number generators -- in fact the best that can be done from mathematical functions are pseudorandom -- they seem random enough for most intents and purposes.

In fact, performing any additional actions from a number returned by a PRNG doesn't really increase its randomness, and in fact, the number can become less random.

So, my best advice is, don't mess around with values returned from a PRNG. Use a PRNG that is good enough for the intended use, and if it isn't, then find a PRNG that can produce better results, if necessary.

And frankly, it appears that the mt_rand function uses the Mersenne twister, which is a pretty good PRNG as it is, so it's probably going to be good enough for most casual use.

Edit

There was a question in the comments why performing operations on a random number can make it less random. For example, some PRNGs can return more consistent, less random numbers in different parts of the bits -- the high-end can be more random than the low-end.

Therefore, in operations where the high-end is discarded, and the low end is returned, the value can become less random than the original value returned from the PRNG.

I can't find a good explanation at the moment, but I based that from the Java documentation for the Random.nextInt(int) method, which is designed to create a fairly random value in a specified range. That method takes into account the difference in randomness of the parts of the value, so it can return a better random number compared to more naive implementations such as rand() % range.

Answer 4

I'm not sure that what you've done "improves" the randomness. From what I can understand you generate 100 random numbers and then randomly pick one of them.

From what I can remember from my probability course, this probably doesn't increase the randomness, as if there is an underlying bias in the generator function (mt_rand()), then it will still be reflected somehow in the output.

Answer 5

In what way is mt_rand() "bad"?

For example: If it favors a certain number. Lets say mt_rand(1, 10) favours low numbers in the range, ie "1" and "2" occurs on average more than 10% each. Then your "improvement" would still suffer from the same problem.

Selecting a random number out of a faulty sequence will still be faulty.

Answer 6

It is not possible to generate true random numbers, the best you can hope for is pseudo-random which is what rand() provides, your function is no closer to random then rand(). Take a look at this http://en.wikipedia.org/wiki/Random_number_generator

Answer 7

If you don't like PHP's built in rand(), you probably shouldn't use their built-in shuffle() either, since it seems to be built on their rand().

I am halfway sure the "industry standard" shuffle now is the Fisher-Yates shuffle.

Answer 8

It all depends what for you need that random number :) For me ShuffleBag is the best one :)

Answer 9

I'm guessing you're worried about the distribution of mt_rand(). I have tested it and it is very level and both bounds are inclusive.

I added my test to the comments of the documentation for mt_rand() on the php manual, but it was removed by a silly moderator due to politics that are too long winded to go into here.