三门问题 PHP 模拟代码

monty-hall-problem.php

<?php
define('GOAT', 0);
define('CAR', 1);


echo "尝试五次，每次1000遍，换门的中奖率\n";
for($j=0;$j<5;$j++) {
	$exchange = true;
	simulation($exchange);
}
echo "\n再尝试五次，每次1000遍，不换门的中奖率\n";
for($j=0;$j<5;$j++) {
	$exchange = false;
	simulation($exchange);
}

//运行模拟，每次模拟运行1000次
function simulation($exchange)
{
	$pool = [];
	for($i=0; $i<1000; $i++) {
		$pool[$i] = start($exchange);
	}
	//过滤掉山羊
	$cars = array_filter($pool);
	
	$total = count($pool);
	$car_total = count($cars);
	
	echo sprintf("%.2f%%\n", ($car_total / $total) * 100);
}

//节目开始
function start($exchange)
{
	
	//有三扇门
	$doors = generate_doors();

	//随机选中一扇
	$choose_pos = choose_door();

	//主持人打开有山羊的一扇
	$open_pos = open_door($doors, $choose_pos);

	//换吗？
	if($exchange) { 
		//换：找到最后一扇门
		$diff = array_diff([0, 1, 2], [$choose_pos, $open_pos]);
		$last_door_pos = array_shift($diff);
	} else {
		//不换
		$last_door_pos = $choose_pos;
	}
	
	if($doors[$last_door_pos]==GOAT) {
		//没中奖
		return false;
	} else {
		//中奖了
		return true;
	}
}

function generate_doors()
{
	//0 是山羊
	//1 是汽车
	$pos = mt_rand(0, 2);
	//在所有门里放满羊
	$doors = [GOAT, GOAT, GOAT];
	//然后把其中一扇门里的羊改成汽车
	$doors[$pos] = CAR;
	return $doors;
}


function choose_door()
{
    return mt_rand(0, 2);
}

function open_door($doors, $choose_pos)
{
	$doors[$choose_pos] = -1;
	//找到剩下的山羊
	return array_search(GOAT, $doors);
}