// MonteCarlo.java
// Written (mostly) in class on Tue 6-Oct-09

// Demonstrates coin flips, dice rolling, and Monte Carlo methods
// (solving De Mere's problem).

import java.util.*;

public class MonteCarlo {
  
  private static final Random random = new Random();
  
  public static boolean doTrialDeMere1() {
    for (int roll=0; roll<4; roll++) {
      if (rollDie(6) == 1)
        return true;
    }
    return false;
  }

  public static boolean doTrialDeMere2() {
    for (int turn=0; turn<24; turn++) {
      int die1 = rollDie(6);
      int die2 = rollDie(6);
      if ((die1 == 1) && (die2 == 1))
        return true;
    }
    return false;
  }

  // odds of a 1 in 4 rolls of a single die
  public static double deMereOdds1(int trials) {
    int ok = 0;
    for (int trial=0; trial<trials; trial++) {
      if (doTrialDeMere1())
        ok++;
    }
    return 1.0 * ok / trials;
  }

  // odds of a double-1 in 24 rolls of two dice
  public static double deMereOdds2(int trials) {
    int ok = 0;
    for (int trial=0; trial<trials; trial++) {
      if (doTrialDeMere2())
        ok++;
    }
    return 1.0 * ok / trials;
  }
  
  public static double oddsOfRollingAOne(int trials) {
    int ok = 0;
    for (int trial=0; trial<trials; trial++) {
      int die = rollDie(6);
      if (die == 1)
        ok++;
    }
    return 1.0 * ok / trials;
  }

  public static int rollDie(int sides) {
    // return a random # in [1,sides] inclusive
    // return 1+(int)(Math.random()*sides);
    return 1+random.nextInt(sides);
  }
  
  public static boolean coinFlip() {
    // return (Math.random() < 0.5);
    return random.nextBoolean();
  }

  public static void main(String[] args) {
    System.out.print("Here are a few sample coin flips... \n   ");
    for (int flip=0; flip<50; flip++) {
      boolean heads = coinFlip();
      System.out.print(heads ? "H" : "T");
    }
    System.out.println();
    
    System.out.print("\nHere are a few sample 6-sided die rolls... \n   ");
    for (int roll=0; roll<50; roll++) {
      int die = rollDie(6);
      System.out.print(die);
    }
    System.out.println();
    
    int trials = 1000*1000; // # of trials for our Monte Carlo simulation
                            // of De Mere's Problem
                            
    System.out.println("\n********* De Mere's Problem ********");
    System.out.print("  Odds of a 1 in 4 rolls of a single die:\n    ");   
    System.out.println(deMereOdds1(trials));
    System.out.print("  Odds of a double-1 in 24 rolls of two dice:\n    ");   
    System.out.println(deMereOdds2(trials));
  }
}