Monty Hall Problem solved with Monte Carlo Simulations

monty.java

/*
 *  The Monty Hall Problem is a famous teaching problem
 *  in statistics. It works like this:
 *
 *  Imagine that you are on the show "Let's Make a Deal"
 *  with Monty Hall. Monty shows you three doors and says
 *  that a car exists behind one of them. You may pick
 *  one door and if the car is behind it, you win the car.
 *
 *  You pick a door. Monty then chances the rules. He opens
 *  a different door and shows you that there was a goat
 *  behind it. Good thing you didn't pick that door!
 *  Monty gives you the opportunity to change to the other
 *  unopened door.
 *
 *  Which is better? Stick with your current door or to move
 *  your choice to the other unopened door? Does this even
 *  matter? There are now just two unopened doors. It should
 *  be a 50-50 shot, right?
 *
 *  Turns out it isn't. It take a little bit of thought to
 *  determine why this is, but we can simulate the results
 *  with a million iterations of someone who never changes
 *  their choice and someone who always changes their choice.
 *
 *  You'll have to run the program to see the results.
 */

import java.io.*;
import java.util.*;

public class monty {
    public static void main(String[] args) {
        Random rng = new Random();
        int trials = 1000000;

        System.out.println("Player never changes the door.");
        int wins = 0;
        for (int i = 1; i <= trials; i++) {
            int prize_door = rng.nextInt(3);
            int contestant_door = rng.nextInt(3);

            if (contestant_door == prize_door)
                wins++;
        }

        System.out.println("Total Wins out of "+trials+": "+wins);
        System.out.println("Percent win: "+(double)wins/trials);

        System.out.println("");
        System.out.println("Player always changes the door.");
        wins = 0;
        for (int i = 1; i <= trials; i++) {
            int prize_door = rng.nextInt(3);
            int contestant_door = rng.nextInt(3);

            // Here, we randomly look for doors until
            // we find one that that is wrong, yet still
            // wasn't picked by the contestant.
            int wrong_door = prize_door;
            while (wrong_door == prize_door ||
                   wrong_door == contestant_door) {
                wrong_door = rng.nextInt(3);
            }

            int alternate_door = 3 - (contestant_door + wrong_door);

            // Always switch doors!
            if (alternate_door == prize_door)
                wins++;
        }

        System.out.println("Total Wins out of "+trials+": "+wins);
        System.out.println("Percent win: "+ (double)wins/trials);
    }
}