Simulate the expected number of suit matches in pairs of consecutive cards in a standard 52-card deck; see https://math.stackexchange.com/questions/3602087.

Question3602087

import java.util.Random;

public class Question3602087 {
    final static long ntrials = 10000000;

    final static Random random = new Random();
    
    final static int NSUITS = 4;
    final static int NRANKS = 13;
    final static int NCARDS = NRANKS * NSUITS;
    
    public static void main(String [] args) {
        int [] deck = new int [NCARDS];
        for (int i = 0;i < NCARDS;i++)
            deck [i] = i % NSUITS;
        
        long s = 0;
        long s2 = 0;
        
        for (long n = 0;n < ntrials;n++) {
            int last = 0;
            long count = 0;
            for (int i = 0,next = NCARDS;i < NCARDS;i++) {
                int pos = random.nextInt(next--);
                int card = deck [pos];
                deck [pos] = deck [next];
                deck [next] = card;
                if (i != 0 && card == last)
                    count++;
                last = card;
            }
            
            s += count;
            s2 += count * count;
        }
        
        double e = s / (double) ntrials;
        double e2 = s2 / (double) ntrials;
        System.out.println("mean: " + e);
        System.out.println("variance: " + (e2 - e * e));
    }
}