The Monty Hall Problem

monty-hall.php

<?php
class MontyHall
{
    const CAR  = 'Car';
    const GOAT = 'Goat';

    public $doors;
    public $choice;

    public function __construct()
    {
        // Setup doors with goats
        $this->doors = array_fill(0, 3, static::GOAT);

        // Add a car to one random door
        $key = array_rand($this->doors);

        $this->doors[$key] = static::CAR;
    }

    public function makeChoice()
    {
        $this->choice = array_rand($this->doors);
    }

    public function switchChoice()
    {
        // Find a goat from the 2 unpicked doors
        foreach ($this->doors as $key => $value) {
            // Skip the door we've already picked
            if ($key === $this->choice) {
                continue;
            }

            // Reveal the first goat we find
            if ($value === static::GOAT) {
                $reveal = $key;
                break;
            }
        }

        // Switch our choice to the remaining door
        for ($i = 0; $i < count($this->doors); $i++) {
            if ($i !== $this->choice && $i !== $reveal) {
                $this->choice = $i;
                break;
            }
        }
    }

    public function isCorrect()
    {
        return ($this->doors[$this->choice] === static::CAR);
    }
}

$stick  = 0;
$switch = 0;

// Run through 1,000,000 times
for ($i = 0; $i < 1000000; $i++) {
    $montyHall = new MontyHall;
    $montyHall->makeChoice();

    if ($montyHall->isCorrect()) {
        $stick++;
    }

    $montyHall = new MontyHall;
    $montyHall->makeChoice();
    $montyHall->switchChoice();

    if ($montyHall->isCorrect()) {
        $switch++;
    }
}

echo 'Stick:  ' . round($stick / 1000000 * 100, 2) . '% correct' . PHP_EOL;
echo 'Switch: ' . round($switch / 1000000 * 100, 2) . '% correct' . PHP_EOL;