Estimate the expected number of steps required to span F_2^n using a certain randomised procedure; see http://math.stackexchange.com/questions/1754859.

Question1754859.java

import java.util.Random;

public class Question1754859 {
	final static int ntrials = 100000000;
	final static Random random = new Random ();
	final static double p = 0.5;
	
	final static int [] code = {
		1,2,4,3,6,7,5
	};
	
	public static void main (String [] args) {
		double sum1 = 0;
		double sum2 = 0;
		double sum3 = 0;
		
		double [] sums = new double [6];
		int [] counts = new int [6];
		
		for (int n = 0;n < ntrials;n++) {
			int first = random.nextInt (7);
			do {
				first++;
				first %= 7;
				sum1++;
			} while (random.nextDouble () < p);
			
			int second = first;
			do {
				second++;
				second %= 7;
				sum2++;
			} while (random.nextDouble () < p || second == first);
			
			int index = (second - first + 6) % 7;
			counts [index]++;
			
			int third = second;
			do {
				third++;
				third %= 7;
				sum3++;
				sums [index]++;
			} while (random.nextDouble () < p || third == first || third == second || code [third] == (code [first] ^ code [second]));
		}
		
		sum1 /= ntrials;
		sum2 /= ntrials;
		sum3 /= ntrials;
		
		double p6 = Math.pow (p,6);
		double p7 = Math.pow (p,7);

		double v1 = 1 / (1 - p);
		double v2 = (1 - p7) / ((1 - p) * (1 - p6));
		double v3 = ((((((((p + 2) * p + 1) * p + 4) * p + 5) * p + 4) * p + 1) * p + 2) * p + 1) / ((1 - p6) * (1 + p * p));
		double v = ((((((((2 * p + 4) * p + 4) * p + 8) * p + 9) * p + 8) * p + 5) * p + 4) * p + 3) / ((1 - p6) * (1 + p * p));
				
		System.out.println (sum1 + " / " + v1);
		System.out.println (sum2 + " / " + v2);
		System.out.println (sum3 + " / " + v3);
		System.out.println ();
		System.out.println ((sum1 + sum2 + sum3) + " / " + v + " " + (v1 + v2 + v3));
		System.out.println ();

		for (int i = 0;i < 6;i++)
			System.out.println (i + " : " + sums [i] / counts [i]);
	}
}