Monty Hall problem (Three-Door problem)

http://en.wikipedia.org/wiki/Monty_Hall_problem

The most well known statement of the problem is:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? (Whitaker, 1990, as quoted by vos Savant 1990a)

Vos Savant's response was:

Yes; you should switch. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance. Here’s a good way to visualize what happened. Suppose there are a million doors, and you pick door #1. Then the host, who knows what’s behind the doors and will always avoid the one with the prize, opens them all except door #777,777. You’d switch to that door pretty fast, wouldn’t you?

So the ratio between WIN vs LOSE should be 66.6 : 33.3

I spend some time to write a simulator to check. (code is a bit ugly but it works)

Game class:

/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */
package montyhallproblem;

/**
 *
 * @author celeron533
 */
public class Game {

    public Door[] doors;

    public Game() {
        this.doors = new Door[]{new Door(), new Door(), new Door()};//create doors
        doors[(int) (Math.random() * 3)].item = Item.car;//allocate the prize
    }
    public int playerInitial;

    public void playerInitialSelection(int s) {
        playerInitial = s;
    }

    public int hostOpenGoatDoor() {
        if (doors[playerInitial].item == Item.car) {
            //open one door of the rest
            int open;
            do {
                open = (int) (Math.random() * 3);
            } while (open == playerInitial);
            doors[open].opened = true;
            return open;
        } else {//when player select a goat door, host open the left goat door
            for (int i = 0; i < 3; i++) {
                if (i == playerInitial) {//skip player selection
                    continue;
                } else {
                    if (doors[i].item == Item.car) {//skip car door
                        continue;
                    } else {//open
                        doors[i].opened = true;
                        return i;
                    }
                }
            }
        }
        return -1;
    }

    public class Door {

        public boolean opened = false;
        public Item item = Item.goat;
    }

    public enum Item {
        car, goat
    }

    @Override
    public String toString() {
        String result = "select_" + playerInitial + " ";
        for (int i = 0; i < 3; i++) {
            result += doors[i].item + "_" + doors[i].opened + " ";
        }
        return result;
    }
}

Main class:

/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */
package montyhallproblem;

/**
 *
 * @author celeron533
 */
public class MontyHallProblem {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        // TODO code application logic here
        Game game;
        int playerSelect, hostOpen;
        int keepSelectionWins = 0;
        int switchSelectionWins = 0;
        for (int i = 0; i < 10000000; i++) {
            game = new Game();
            playerSelect = (int) (Math.random() * 3);
            game.playerInitialSelection(playerSelect);
            hostOpen = game.hostOpenGoatDoor();
            //Statistical results
            if (game.doors[playerSelect].item == Game.Item.car) {
                keepSelectionWins++;
            } else {
                switchSelectionWins++;
            }
            //System.out.println(game.toString());
        }
        System.out.println("keepSelectionWins: " + keepSelectionWins);
        System.out.println("switchSelectionWins:" + switchSelectionWins);
    }
}

 

And the perfect result:

run:
keepSelectionWins: 3333349
switchSelectionWins:6666651
BUILD SUCCESSFUL (total time: 3 seconds)