Calculate the exaxt probability distribution for the number of pairs of consecutive cards with matching suits; see https://math.stackexchange.com/questions/3602087.

Question3602087a.java

package temp;

import java.math.BigInteger;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;

public class Question3602087a {
    final static int NSUITS = 4;
    final static int NRANKS = 13;
    final static int NCARDS = NRANKS * NSUITS;

    static class DeckState {
        int [] ranksLeft;
        int previousSuit;
        
        public DeckState() {
            ranksLeft = new int [NSUITS];;
            Arrays.fill(ranksLeft, NRANKS);
            previousSuit = -1;
        }
        
        public DeckState (DeckState state) {
            ranksLeft = state.ranksLeft.clone();
        }

        public int hashCode() {
            return Arrays.hashCode(ranksLeft) * NSUITS + previousSuit;
        }

        public boolean equals(Object o) {
            DeckState s = (DeckState) o;
            return s.previousSuit == previousSuit && Arrays.equals(ranksLeft, s.ranksLeft);
        }
    }

    static class Statistics {
        static BigInteger [] zeroCounts = new BigInteger [NCARDS];
        static {
            Arrays.fill(zeroCounts, BigInteger.ZERO);
        }
        BigInteger [] counts = zeroCounts.clone();
    }
    
    public static void main(String [] args) {
        Map<DeckState,Statistics> stateMap = new HashMap<>();
        stateMap.put(new DeckState(), new Statistics());
        stateMap.values().iterator().next().counts [0] = BigInteger.ONE;
        for (int i = 0;i < NCARDS;i++) {
            Map<DeckState,Statistics> newStateMap = new HashMap<>();
            for (DeckState state : stateMap.keySet()) {
                Statistics statistics = stateMap.get(state);
                for (int suit = 0;suit < NSUITS;suit++)
                    if (state.ranksLeft [suit] > 0) {
                        BigInteger factor = BigInteger.valueOf(state.ranksLeft [suit]);
                        DeckState newState = new DeckState(state);
                        newState.ranksLeft [suit]--;
                        newState.previousSuit = suit;
                        Statistics newStatistics = newStateMap.get(newState);
                        if (newStatistics == null) {
                            newStatistics = new Statistics();
                            newStateMap.put(newState, newStatistics);
                        }
                        int offset = suit == state.previousSuit ? 1 : 0;
                        for (int j = 0;j + offset < NCARDS;j++)
                            newStatistics.counts [j + offset] = newStatistics.counts [j + offset].add(statistics.counts [j].multiply(factor)); 
                    }
            }
            stateMap = newStateMap;
        }
        
        // there are NSUITS states left, one for each suit of the last card

        Statistics total = new Statistics();
        BigInteger sum = BigInteger.ZERO;
        
        for (Statistics statistics : stateMap.values())
            for (int i = 0;i < NCARDS;i++) {
                total.counts [i] = total.counts [i].add(statistics.counts [i]);
                sum = sum.add(statistics.counts [i]);
            }
        
        for (int i = 0;i < NCARDS;i++)
            System.out.println(i + " : " + total.counts [i].doubleValue() / sum.doubleValue());
    }
}