CODEWITHSUNDEEP
phpif-statementrandom
Joe
Joe

Reputation: 143

Why does rand seem more random than mt_rand when only doing (1, 2)?

I have some elements that I'm trying to randomize at 50% chance of output. Wrote a quick if statement like this.

$rand = mt_rand(1, 2);

if ( $rand == 1 ) {
echo "hello";
} else {
echo "goodbye";
}

In notice that when using mt_rand, "goodbye" is output many times in a row, whereas, if I just use "rand," it's a more equal distribution.

Is there something about mt_rand that makes it worse at handling a simple 1-2 randomization like this? Or is my dataset so small that these results are just anecdotal?

Upvotes: 0

Views: 88

Answers (1)

trincot
trincot

Reputation: 350272

To get the same value "many times in a row" is a possible outcome of a randomly generated series. It would not be completely random if such a pattern were not allowed to occur. If you would continue taking samples, you would also find that the opposite value will sometimes occur several times in a row, provided you keep going long enough.

One way to test that the generated values are indeed quite random and uniformly distributed, is to count how many times the same value is generated as the one generated before, and how many times the opposite value is generated.

Note that the strings "hello" and "goodbye" don't add much useful information; we can just look at the values 1 and 2.

Here is how you could do such a test:

// $countAfter[$i][$j] will contain the number of occurrences of 
//    a pair $i, $j in the randomly generated sequence.
// So there is an entry for [1][1], [1][2], [2][1] and [2][2]:
$countAfter = [1 => [1 => 0, 2 => 0], 
               2 => [1 => 0, 2 => 0]];
$prev = 1; // We assume for simplicity that the "previously" generated value was 1              
for ($i = 0; $i < 10000; $i++) { // Produce a large enough sample
    $n = mt_rand(1, 2);
    $countAfter[$prev][$n]++; // Increase the counter that corresponds to the generated pair
    $prev = $n;
}
print_r($countAfter);

You can see in this demo that the 4 numbers that are output do not differ that much. Output is something like:

Array (
    [1] => Array (
        [1] => 2464
        [2] => 2558
    )
    [2] => Array (
        [1] => 2558
        [2] => 2420
    )
)

This means that 1 and 2 are generated about an equal number of times and that a repetition of a value happens just as often as a toggle in the series.

Obviously these numbers are rarely exactly the same, since that would mean the last couple of generated values would not be random at all, as they would need to bring those counts to the desired value.

The important thing is that your sample needs to be large enough to see the pattern of a uniform distribution confirmed.

Upvotes: 2

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