In the 17th century, the discipline of probability theory got its start when a gambler asked a mathematician friend to explain some observations about dice games. Why did he, on average, lose a bet that at least one six would appear when rolling a die four times? And why did he seem to win a similar bet, getting at least one double six when rolling a pair of dice 24 times?

Nowadays, it seems astounding that any person would roll a pair of dice 24 times in a row, and then repeat that many times over. Lets do that experiment on a computer instead. Simulate each game a million times and print out the wins and losses.

Use the files in the zip file for Assignment 1 as a starting point.

There is a Die class which simulates the throw of a die.

There is a Die Odds Tester class which you should use as a test program to show your

program working.

The GameSimulator class is where you write your code. Please fill in all the code where

it is indicated.

DieOddsTester:

/** This program simulates the wins and losses for two different games of dice. */ public class DiceOddsTester { public static void main(String[] args) {

GameSimulator simulator = new GameSimulator(6, 1000000);

simulator.runSingleDieSimulation(); System.out.println("Game #1 wins: " + simulator.getWinPercent()); System.out.println("Expected: .51");

simulator.runDoubleDieSimulation(); System.out.println("Game #2 wins: " + simulator.getWinPercent()); System.out.println("Expected: .49"); } }

Die:

import java.util.Random; /** This class models a die that, when cast, lands on a random face. */ public class Die { private Random generator; private int sides;

/** Constructs a die with a given number of sides. @param s the number of sides, e.g., 6 for a normal die. */ public Die(int s) { sides = s; generator = new Random(); }

/** Simulates a throw of the die. @return the face of the die. */ public int cast() { return 1 + generator.nextInt(sides); } }

GameSimular:

/** This program sumulates the wins and losses for two different games of dice. */ public class GameSimulator { private int tries; private Die d1, d2; private int wins; private int losses;

/** Construct a simulator object for die games. @param numSides the number of sides on the die. @param numTries the number of times to run the simulation. */ public GameSimulator(int numSides, int numTries) { . . . }

/** Runs a single die simulation. One die is cast 4 times. If a six appears in those 4 casts, then wins is incremented, otherwise losses is incremented. Simulation is run according to the number of tries set. */ public void runSingleDieSimulation() { . . . }

/** Runs a double die simulation. A pair of dice are cast 24 times. If a double-six appears in those 24 casts, then wins is incremented, otherwise losses is incremented. The simulation is run according to the number of tries set. */ public void runDoubleDieSimulation() { . . . }

/** Returns the % of wins. @return the % of wins. */ public double getWinPercent() { return (double)(wins) / (wins + losses); }

/** Returns the number of wins. @return the number of wins. */ public int getWins() { return wins; }

/** Returns the number of losses. @return the number of losses. */ public int getLosses() { return losses; } }