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Clear out junk files and repair common Windows errorsFree Scan →Scan for outdated or missing drivers - takes under a minuteDriver Scan →To run a Monte Carlo simulation in PHP, define a probability model, generate repeated random samples, count or aggregate the outcomes, and calculate an estimate from that aggregate. On PHP 8.2 and later, RandomRandomizer lets you keep the random engine local to the simulation and choose a deterministic seed for repeatable runs.
How a Monte Carlo simulation works
- Define the question and model. Specify the quantity or event you want to estimate and the assumptions that determine each sample.
- Generate samples. Draw values from the model for each trial using a suitable pseudorandom engine.
- Evaluate each trial. Apply a rule to each sample and record the result, often as a count or sum.
- Calculate the estimate. Convert the aggregate into the quantity you want to estimate.
- Record the run. Save the engine, seed, PHP version, trial count, input data, and model assumptions when you need to reproduce or interpret it.
The random generator supplies samples; it does not decide whether the model is appropriate or make a single estimate exact.
Estimate π with PHP 8.2 or later
This example draws points uniformly from the unit square. A point falls inside the quarter-circle when x² + y² ≤ 1. The quarter-circle occupies one quarter of a unit circle, so four times the fraction of points inside it estimates π.
<?php
use RandomEnginePcgOneseq128XslRr64;
use RandomRandomizer;
$trials = 1_000_000;
$seed = 20261007;
$random = new Randomizer(new PcgOneseq128XslRr64($seed));
$inside = 0;
for ($i = 0; $i < $trials; $i++) {
$x = $random->nextFloat();
$y = $random->nextFloat();
if ($x * $x + $y * $y <= 1.0) {
$inside++;
}
}
$estimate = 4.0 * $inside / $trials;
printf("Inside: %d of %dnEstimate of pi: %.10fn", $inside, $trials, $estimate);
RandomRandomizer is available from PHP 8.2. Its nextFloat() method returns a value in the half-open interval [0.0, 1.0), matching the coordinates needed here. The PHP manual documents the [Randomizer API] and the available engine classes.
What to change for your own problem
- Replace the point-generation code with samples from your model.
- Replace the circle predicate with the condition that defines a success, or accumulate a value if estimating an average or total.
- Use an estimator that matches the target quantity. For this example, it is four times the success fraction.
- Try a different trial count and observe how the estimate changes. A larger run is not a guarantee that the model is correct or that an individual result is exact.
Choose an API and engine deliberately
| Choice | Useful when | Reproducibility and cautions |
|---|---|---|
RandomRandomizer with a deterministic engine |
Writing new code on PHP 8.2 or later and wanting an explicit, local random stream. | Choose and record the engine and seed. Engines differ in security and seed properties; the API documents engines including Mt19937, PcgOneseq128XslRr64, Xoshiro256StarStar, and Secure. See the Randomizer manual and mt_srand manual. |
mt_rand() and mt_srand() |
Maintaining older code or supporting PHP versions without the Randomizer API. | The legacy Mersenne Twister generator is automatically seeded. Explicit seeding can make a run repeatable, but it uses shared global generator state. PHP’s manual recommends Randomizer methods for newly written code and warns that mt_rand() is not cryptographically secure. See mt_rand and mt_srand. |
random_int() |
Choosing an unpredictable integer for security-sensitive uses. | It returns a uniformly selected integer over an inclusive range using operating-system cryptographic randomness. That security property does not make it the default for a simulation that needs a repeatable stream. See the random_int manual. |
Make a run reproducible
Use a local Randomizer for new code
Construct the engine and Randomizer inside the simulation or pass the Randomizer into it. This makes the source of draws explicit and avoids unrelated random calls changing the simulation’s sequence. The example uses an explicit PcgOneseq128XslRr64 engine and seed; to repeat the same run, keep those choices and the simulation inputs and code compatible.
Keep a useful run record
- Engine class and seed.
- PHP version and runtime environment.
- Trial count and any input data.
- Model assumptions, sampling method, and the rule used to evaluate each trial.
A seed alone is not a complete scientific record. Reproducing a random stream also does not establish that the model represents the real process you intend to study.
Rank #2
Know the Mt19937 seed limit
The PHP manual says Mt19937 accepts a single 32-bit seed, giving 232 possible seed-derived sequences. It reports a 50% duplicate-seed probability before 80,000 randomly generated seeds and about a 10% probability at roughly 30,000. These are collision probabilities among randomly generated seeds, not measures of the statistical quality of an individual simulation. If many independent reproducible runs need a larger seed space, the manual identifies Xoshiro256StarStar and PcgOneseq128XslRr64 as engines with larger seed support. See mt_srand.
Compatibility notes for older PHP versions
RandomRandomizerrequires PHP 8.2 or later.random_int()is available from PHP 7.0.rand()became an alias ofmt_rand()in PHP 7.1. PHP 7.2 corrected a modulo-bias issue inmt_rand(), so historical seeded sequences can differ across these version boundaries.- The legacy Mersenne Twister is seeded automatically; you do not need to call
mt_srand()simply to get random output. In PHP 8.3, its seed became nullable and the old behavior-mode parameter was deprecated.
For a new simulation on PHP 8.2 or later, prefer the Randomizer API. For legacy applications, check the deployed PHP version and test any seeded sequence on that runtime. The PHP manual’s mt_rand page, mt_srand page, and the PHP RNG RFC describe the API history.
Quick Recap
Best Value
Rank #4
Common mistakes to avoid
- Choosing a generator because it sounds more accurate.
random_int()is designed for cryptographic unpredictability; select a simulation engine for the repeatable workflow you need, not for a security property the simulation does not require. - Using a simulation generator for secrets. The legacy Mersenne Twister is explicitly not cryptographically secure. Use a cryptographic API for tokens, passwords, and other security-sensitive values.
- Seeding without recording the engine. A seed has meaning in relation to the engine and implementation that consumes it.
- Assuming a reproducible result is a valid result. Repeatability helps investigate a run; it does not validate the sampling model, assumptions, or estimator.
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