Two Envelopes

envelopes.php

<?php

function play($switch, $games, $small) {
    $wins     = 0;
    $winnings = 0;

    for ($x = 0; $x < $games; $x++) {
        //which envelop is double the amount
        $double = rand(0, 1);

        //which envelop is initally chosen
        $choice = rand(0, 1);

        //which envelop wasn't chosen (the other one)
        if ($choice == 0) {
            $other = 1;
        } else {
            $other = 0;
        }

        // switch if that's our strategy
        if ($switch) {
            $choice = $other;
        }

        // we'll always get at least the small amount
        $winnings += $small;

        // if we chose the double envelop we get twice the small amount
        if ($double == $choice) {
            $wins++;
            $winnings += $small;
        }
    }

    echo "$$winnings $wins/$games ",$wins/$games,' ';
    echo $switch ? 'always' : 'never';
    echo ' switched', PHP_EOL;
}

$games = 1000000;
$small  = 1;
play(false, $games, $small);
play(true,  $games, $small);

// $ php envelopes.php 
// $1500308 500308/1000000 0.500308 never switched
// $1500301 500301/1000000 0.500301 always switched