Simulate how long it takes until six dice that retain a 1 for 4 turns all show a 1; see https://math.stackexchange.com/questions/3674864.

Question3674864.java

import java.util.Random;

public class Question3674864 {
    final static long ntrials = 10000000;
    final static Random random = new Random();
    
    public static void main (String [] args) {
        long count = 0;
        for (long trial = 0;trial < ntrials;trial++) {
            int [] state = new int [6];
            int nones;
            do {
                count++;
                nones = 0; 
                for (int i = 0;i < 6;i++) {
                    if (state [i] > 0)
                        state [i]--;
                    if (state [i] == 0 && random.nextInt(6) == 0)
                        state [i] = 4;
                    if (state [i] > 0)
                        nones++;
                }
            } while (nones != 6);
        }
        
        System.out.println(count / (double) ntrials);
    }
}