Monty Hall Program

monty.php

<?php

// This program simulates a number of games involving
// The Monty Hall Problem, and compares two approaches:
// sticking with the player's original choice, or 
// switching to the other option. The program measures
// how successful each approach is and prints the
// result to the screen. I used PHP since it is easy to
// read and understand, but this program could easily
// be ported to any number of other languages.

// Set the number of trials to be performed for
// each option (stick or switch). More trials 
// will lead to better accuracy, but increased
// computing time. 1 million seems to work well:

$trials      = 1000000;

//--------- EDIT BELOW AT YOUR OWN RISK:--------------//
$choices     = array('stick', 'switch');
$wins_stick  = 0;
$wins_switch = 0;
$options = array('A', 'B', 'C');

foreach ($choices as $choice) {

	for ($i=0; $i<$trials; $i++) {

		// Random door has big prize:
		$correct         = $options[rand(0,2)];

		// Contestant picks random door:
		$contestant_pick = $options[rand(0,2)];

		// Figure out Monty's choice of doors to reveal:
		$montys_picks = array();
		foreach ($options as $option) {
			if ($option != $correct && $option != $contestant_pick) {
				array_push($montys_picks, $option);
			}
		}

		// Monty picks a door that doesn't have the prize
		// AND that the contestant hasn't chosen:
		$montys_pick = (count($montys_picks) > 1) ? $montys_picks[rand(0,1)] : $montys_picks[0];

		// Increment if contestant sticks with door and is correct
		if ($choice == 'stick' && $contestant_pick == $correct) {
			$wins_stick++;
		}

		// Increment if contestant switches with door and is correct
		if ($choice == 'switch' && $contestant_pick != $correct) {
			$wins_switch++;
		}

	}

}

// Print results:
print "Contestant stuck by and won the car " . (round(($wins_stick*100/$trials),1)) . "% of the time (based on " . number_format($trials) . " trials).<br />";
print "Contestant switched and won the car " . (round(($wins_switch*100/$trials),1)) . "% of the time (based on " . number_format($trials) . " trials).<br />";

?>