Game Simulation--MonteHall

问题描述： 1970年互动游戏节目Let's Make a Deal中，参与者面前有三道门，其中一道门后面藏有奖品。参与者首先选择一道门，主持人从另外两道门中选择打开其中一道门（后面没有奖品的门）。参与者获得一次更改选择的机会，重新选择剩下的那道门，问题是参与者是否应该改变选择，从而能够有更大的机会获得奖品。直观上，参与者最初选择的门和剩下的门具有相同的概率可能藏有奖品，所以没必要改变选择。请编写程序MonteHall模拟该游戏，测试直观上是否正确。

/*************************************************************************
 *  Compilation:  javac MonteHall.java
 *  Execution:    java MonteHall N
 *
 *  Plays the Monte Hall game N times with the switching strategy
 *  and reports the fraction of games won.
 *
 *  Sample execution:
 *
 * % java MonteHall 1000
 * Fraction of games won = 0.66
 *
 *  Note:  true winning probability = 2/3.
 *
 *************************************************************************/
public class MonteHall {
    public static void main(String[] args) {
 int N = Integer.parseInt(args[0]); // trials
 int wins = 0;  // times you win by switching

 // repeat experiment N times
 for (int i = 0; i < N; i++) {

     //host hides prize behind 1 of 3 doors uniformly at random
     int prize = 1 + (int)(3 * Math.random());
    // contestant select 1 of 3 doors uniformly at random
     int choice = 1 + (int)(3* Math.random());

     //at random, host reveals an unchosen door not coitaining prize
     int reveal;
     do {
         reveal = 1 + (int)(3*Math.random());
     } while((reveal == choice) || (reveal == prize));

     //hack to compute the remaining door which contestent swithces to

     int other =  1 + 2 + 3 - reveal - choice;

     //switching leads to a win
     if (other == prize) wins++;
 }

     //avoid integer division
     System.out.println("Fraction of games won = " + 1.0 * wins / N);
    }
   }