Question

Monty Hall Problem - Suppose you are going to be on a game show, and you will be given the choice of three doors:

• Behind one door is a car;

• behind the other two doors are 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? You could use probability theory to figure out the best strategy, switch or no switch. But instead you decide to write a Java program to simulate millions of plays of the game (such simulation is called Monte Carlo simulation) to help you decide the best strategy.

A single game will involve repeating:

• “hiding” the prize behind one of three doors (starting new game / resetting game),

• Having three players (representing different strategies) making an initial guess SEPARATELY,

• Having three players (representing different strategies) making a second door selection knowing which door is open (has no prize behind it). Opening that door is based on each player’s initial guess (in other words: each player can end up with a different door opened for them, but the prize is in the same place for all).

• Write a Game class with:

  • Attribute/field prizeLocation that will hold a door number (integer from the set {1,2,3}) behind which the prize is hidden,

  • Non-parametrized constructor that will assign random number to prizeLocation,

  • Methods:

    • getPrizeLocation, that returns the value of prizeLocation attribute/field

    • reset, that will restart the game ? assign a new random integer to prizeLocation attribute,

    • getOpenDoor, which, given an integer argument initialGuess (Player’s FIRST guess), will “open one door” (NOT the door with the prize behind it and NOT the initialGuess door – the other one) and return its number (integer)

Using Java

Answer 1

Following is the output and the code for the solution as asked in the problem. The code is appropriately commented for better understanding and a GameDemo class has also been added to give an idea of how the game works.

Also, screenshots of the code have been attached for help on code indentation.

Output:

E:\Study\Java>java GameDemo
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|                                                                      |
|   Welcome to the Game Show. Here you have a chance to win a car.     |
|                                                                      |
| In case you hit the jackpot, you get a chance to take home a goat!!! |
|                                                                      |
|                              Enter choice:                           |
|                              1 to play                               |
|                                 OR                                   |
|                              0 to exit                               |
1
|                                                                      |
|                              Make a guess!                           |
|                                                                      |
|                      The car is behind which door!                   |
|                                                                      |
|                              Enter choice:                           |
|                              1 for Door1.                            |
|                              2 for Door2.                            |
|                              3 for Door3.                            |
2
|                                                                      |
|                      The car is not behind door 3 !                  |
|                                                                      |
|         Enter new choice if you wish to change your choice:          |
|                                 OR                                   |
|                           Enter old choice:                          |
2
|                                                                      |
|                  Jackpot!!! You have won the goat.                   |
|                                                                      |
|                              Enter choice:                           |
|                              1 to play                               |
|                                 OR                                   |
|                              0 to exit                               |
0
|                                                                      |
|             Exiting game. Thank you for participating.               |
|                                                                      |
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Code:

public class Game {

    private int prizeLocation;

    /* The game constructor which puts the

     * prize at a new location in the field

     * prizeLocation.

     *

     * The constructor only calls the reset

     * method.

     */

    public Game() {

        this.reset();

    }

    // Setter method for prizeLocation field.

    private void setPrizeLocation(int num) {

        this.prizeLocation = num;

    }

    /* Random number generator method.

     *

     * Math.random() method generates a double

     * (floating point value) between

     * 0.0 (included) and 1.0 (excluded).

     *

     * Multiplying the generated number by 3

     * gives a double value between 0.0 and

     * approx. 2.9.

     *

     * Casting the resulting value to int gives

     * one value out of 0, 1, and 2.

     *

     * Adding 1 to the int value gives us the

     * desired range: 1, 2, or 3.

     */

    private int getRandomNum() {

        int randomNum = (int)(Math.random() * 3) + 1;

        return randomNum;

    }

    // Getter method for prizeLocation field.

    public int getPrizeLocation() {

        return this.prizeLocation;

    }

    /* The reset method which generates a random

     * number and sets it to the prizeLocation

     * field.

     */

    public void reset() {

        int randomNum = getRandomNum();

        this.setPrizeLocation(randomNum);

    }

    /* This method takes an argument, which is the

     * initial guess of the player.

     *

     * This method checks the actual prize location

     * and the player's guess and returns another

     * door value, which does not have the car behind

     * it.

     */

    public int getOpenDoor(int initialGuess) {

        int otherDoor = getRandomNum();

        while(otherDoor == initialGuess || otherDoor == this.prizeLocation) {

            otherDoor = getRandomNum();

        }

        return otherDoor;

    }

}

===================================================================================

import java.util.Scanner;

/* Demo class to run the game for a single player.

* This class is an intefrace for playing the game

* for a single player.

*

* This class is only written to give you an idea

* of how the game works.

*/

public class GameDemo {

    private static Scanner scanner = new Scanner(System.in);

    private static int mainMenuOption = 1;

    public static void main(String[] args) {

        System.out.println("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~");

        System.out.println("|                                                                      |");

        System.out.println("|   Welcome to the Game Show. Here you have a chance to win a car.     |");

        System.out.println("|                                                                      |");

        System.out.println("| In case you hit the jackpot, you get a chance to take home a goat!!! |");

        startGame();

    }

    public static void startGame() {

        Game game;

        while(mainMenuOption != 0) {

            showMainMenu();

            mainMenuOption = scanner.nextInt();

            if(mainMenuOption == 0) {

                break;

            } else if(mainMenuOption == 1) {

                game = new Game();

                playGame(game);

            } else {

                System.out.println("|                                                                      |");

                System.out.println("|                 Invalid option. Please retry.                        |");

            }

        }

        exitGame();

    }

    public static void showMainMenu() {

        

        System.out.println("|                                                                      |");

        System.out.println("|                              Enter choice:                           |");

        System.out.println("|                              1 to play                               |");

        System.out.println("|                                 OR                                   |");

        System.out.println("|                              0 to exit                               |");

    }

    public static void playGame(Game game) {

        System.out.println("|                                                                      |");

        System.out.println("|                              Make a guess!                           |");

        System.out.println("|                                                                      |");

        System.out.println("|                      The car is behind which door!                   |");

        System.out.println("|                                                                      |");

        System.out.println("|                              Enter choice:                           |");

        System.out.println("|                              1 for Door1.                            |");

        System.out.println("|                              2 for Door2.                            |");

        System.out.println("|                              3 for Door3.                            |");

        int guess = scanner.nextInt();

        int openDoor = game.getOpenDoor(guess);

        System.out.println("|                                                                      |");

        System.out.println("|                      The car is not behind door " + openDoor + " !                  |");

        System.out.println("|                                                                      |");

        System.out.println("|         Enter new choice if you wish to change your choice:          |");

        System.out.println("|                                 OR                                   |");

        System.out.println("|                           Enter old choice:                          |");

        int secondGuess = scanner.nextInt();

        if(secondGuess == game.getPrizeLocation()) {

            System.out.println("|                                                                      |");

            System.out.println("|                Congratulations. You have won the car.                |");

        } else {

            System.out.println("|                                                                      |");

            System.out.println("|                  Jackpot!!! You have won the goat.                   |");

        }

    }

    public static void exitGame() {

        scanner.close();

        System.out.println("|                                                                      |");

        System.out.println("|             Exiting game. Thank you for participating.               |");

        System.out.println("|                                                                      |");

        System.out.println("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~");

    }

}

Screenshots:

Game.java file:

GameDemo.java file: