Use probability to approach Pi

Once I found this interview question: calculate Pi. Where, all of us have learned calculating Pi in our primary math class by using regular polygon to approach a circle.

Today I am gonna show you a probability way.

Method

Check the following graph. I hope it is self-explanatory.

Code

Java Code Gist

class Pi {
    public static void main(String[] args) {
        if (args.length < 1)
            System.exit(0);

        long iter = Long.parseLong(args[0]);
        double pi = calculate(iter);
        System.out.println(String.format("after %d iterations, pi is %f", iter, pi));
    }

    public static double calculate(long simNum) {
        long i = 0L;
        long count = 0L;
        while (i++ < simNum) {
            double x = Math.random();
            double y = Math.random();
            double result = x * x + y * y;
            if (result < 1.0D) {
                count++;
            }
        }
        return 4.0D * count / simNum;
    }
}

Experiment

lucas@lucas-ubuntu:~/dev/workspace/pi$ java Pi 1000
after 1000 iterations, pi is 3.032000
lucas@lucas-ubuntu:~/dev/workspace/pi$ java Pi 10000
after 10000 iterations, pi is 3.137200
lucas@lucas-ubuntu:~/dev/workspace/pi$ java Pi 100000
after 100000 iterations, pi is 3.140240
lucas@lucas-ubuntu:~/dev/workspace/pi$ java Pi 1000000
after 1000000 iterations, pi is 3.144108
lucas@lucas-ubuntu:~/dev/workspace/pi$ java Pi 10000000
after 10000000 iterations, pi is 3.141199
lucas@lucas-ubuntu:~/dev/workspace/pi$ java Pi 100000000
after 100000000 iterations, pi is 3.141486
lucas@lucas-ubuntu:~/dev/workspace/pi$

Conclusion

When iteration is set to 100,000,000, it takes about half a minute on my i7 Core Mac Pro with precision only to 3 digits.

This algorithm is unacceptable.
The precision cannot be guaranteed as it is using a probabilistic way.