Question

1. Game simulation, Java programming. In the game show Let’s Make a Deal, a contestant is presented with three doors. Behind one of them is a valuable prize. After the contestant chooses a door, the host opens one of the other two doors (never revealing the prize, of course). The contestant is then given the opportunity to switch to the other unopened door. Should the contestant do so? Intuitively, it might seem that the contestant’s initial choice door and the other unopened door are equally likely to contain the prize, so there would be no incentive to switch.

Write a program MonteHall to test this intuition by simulation. Your program should take a command-line argument n, play the game n times using each of the two strategies (switch or do not switch), and print the chance of success for each of the two strategies.

Answer 1

If you have any problem with the code feel free to comment.

Program

import java.text.DecimalFormat;
import java.util.Arrays;

class MonteHall {
   // arraay represent gates
   private String[] gate = new String[3];
   private int priceGate;

   private void init() {
       // fill array with loss
       Arrays.fill(gate, "Loss");
       priceGate = (int) (Math.random() * 3);// get the win gate
       gate[priceGate] = "Win";// put the win gate in the array
   }

   // when no switching gate happens
   public boolean noSwitch() {
       init();
       // get user choice
       int userChoice = (int) (Math.random() * 3);
       // since opening the bluff gate doesn't impact user choice
       // thats why haven't used that method here
       if (gate[userChoice].equals("Win"))
           return true;
       else
           return false;
   }

   // when switching gate occurs
   public boolean switchGate() {
       init();
       int userChoice = (int) (Math.random() * 3);
       int openIndex = openGate(userChoice);

       // switcing the gate
       int sw = (int) (Math.random() * 2);
       if (openIndex == 0)
           userChoice = (sw == 0) ? 1 : 2;
       else if (openIndex == 1)
           userChoice = (sw == 0) ? 0 : 2;
       else
           userChoice = (sw == 0) ? 0 : 1;

       if (gate[userChoice].equals("Win"))
           return true;
       else
           return false;

   }

   private int openGate(int userChoice) {
       // opening the bluff gate
       if (priceGate == 0) {
           return (userChoice == 0 || userChoice == 2) ? 1 : 2;
       } else if (priceGate == 1) {
           return (userChoice == 1 || userChoice == 2) ? 0 : 2;
       } else
           return (userChoice == 0 || userChoice == 2) ? 1 : 0;
   }

}

public class Test {// driver class
   public static void main(String[] args) {

       // if you want to use commandline input use the commented line given below
       int n = 1000;// Integer.parseInt(args[0])

       float sum = 0, percentage;

       DecimalFormat df = new DecimalFormat("##.##");// for formating percentage to 2 decimal places

       MonteHall obj1 = new MonteHall();
       MonteHall obj2 = new MonteHall();

       // no switch
       for (int i = 0; i < n; i++) {
           if (obj1.noSwitch())
               sum++;
       }
       percentage = (sum / n) * 100;
       System.out.println("Sucess rate of no switch: " + df.format(percentage) + "%");

       sum = 0;

       // switching
       for (int i = 0; i < n; i++) {
           if (obj2.switchGate())
               sum++;
       }
       percentage = (sum / n) * 100;
       System.out.println("Sucess rate of switching gate: " + df.format(percentage) + "%");

   }
}

Output