September 18th, 2008

Monty Hall problem, by brute force.

Ever heard of the Monty Hall Problem? If not, go here for some supplemental reading

Here's a little script that plays the game a hundred times using the "switch" strategy, and reveals the number of times the player wins or loses - showing that you are more likely to win if you "switch". For more accurate averages, change the loop condition to a number higher than 100. Running this game with 10000 iterations, the average converges on 2:1 odds.

<?php
$totalwin = 0;
$totallose = 0;
for($i=0;$i<100000;$i++){
	$doors = array(false,false,false);
	$doors[rand(0,2)] = true;
	
	$trace .= "<br/>";
	for($x=0;$x<3;$x++){
		$trace .= ($doors[$x]==true?"X":"O");
	}
	
	
	$choice = rand(0,2);
	$trace .= " . . 1st choice is ".$choice;
	
	$unchosen = array();
	for($exp=0;$exp<3;$exp++){
		// there's either one to show (user chose false) or two (user chose true)
		if($exp!=$choice && !$doors[$exp]){
			$unchosen[] = $exp;
		}
	}
	$toshow = rand(0,count($unchosen)-1);
	$trace .= ", Monty shows door ".$unchosen[$toshow];
	$exposed = $unchosen[$toshow];

// choose the other door
	for($d=0;$d<3;$d++){
		if($d!=$choice && $d!=$exposed){
			$final = $d;
			break;
		}
	}
	$trace .= ", switch to door ".$final;
	if($doors[$final]){
		$trace .= " - WIN!";
		$totalwin++;
	}else{
		$trace .= " - lose.";
		$totallose++;
	}
}
// echo  $trace;
echo "<br/>total won:" . $totalwin;
echo "<br/>total lost:" . $totallose;
echo "<br/>odds of winning: ". number_format($totalwin/$totallose,2).":1";
?>

Enjoy!

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Monty Hall problem, by brute force.

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