Simulate the expected average of dice rolls if the first roll is 1 and the trial ends when a roll repeats; see https://math.stackexchange.com/questions/3606037.

Question3606037.java

import java.util.Random;

public class Question3606037 {
    final static long ntrials = 100000000;
    final static Random random = new Random();
    
    public static void main(String [] args) {
        double total = 0;
        for (long n = 0;n < ntrials;n++) {
            double sum = 1;
            int count = 1;
            int last = 1;
            for (;;) {
                int roll = random.nextInt(6) + 1;
                if (roll == last)
                    break;
                sum += roll;
                count++;
                last = roll;
            }
            total += sum / count;
        }
        System.out.println(total / ntrials);
    }
}