/** Dice.java - Let's simulate some dice rolls.  Let the user specify the
 *  number of dice, the desired sum, and how many trials.  The results can
 *  be used to compute empirical probability.  Here are some examples we can
 *  check.  Rolling a sum of 11 with 3 dice should be 0.125.  Rolling a sum
 *  of 19 with 5 dice should be about 0.0945.
 *
 *  The purpose of the program is to illustrate if statments and loops in
 *  Java.  We also do a little error checking of the input.  We give up if
 *  the input is invalid.
 */
public class Dice
{
  public static void main(String [] args)
  {
    if (args.length != 3)
    {
      System.out.println("You need to supply three inputs:  <num dice> " +
                         "<desired sum> <num trials>");
      System.exit(1);
    }

    int numDice = Integer.parseInt(args[0]);
    int desiredSum = Integer.parseInt(args[1]);
    int numTrials = Integer.parseInt(args[2]);

    if (numDice <= 0 || desiredSum <= 0 || numTrials <= 0)
    {
      System.out.println("All inputs must be positive.");
      System.exit(1);
    }

    // Now that we know we have good input, let the experiment begin!
    // Let's count how many times the desired sum occurs.
    
    int count = 0;
    for (int i = 0; i < numTrials; ++i)
    {
      int sum = 0;
      for (int j = 0; j < numDice; ++j)
      {
        int roll = (int)(Math.random() * 6) + 1;
        sum += roll;
      }

      if (sum == desiredSum)
        ++count;
    }

    // Output
    double prob = 1.0 * count / numTrials;
    System.out.println("" + count + " out of " + numTrials +
                       " yielded a sum of " + desiredSum +
                       ".  Probability = " + prob);
  }
}