Calculate probabilities for a variant of blackjack; see http://math.stackexchange.com/questions/282743.

Question282743.java

import java.util.Locale;

public class Question282743 {
    final static int max = 28;

    static boolean [] [] cached = new boolean [max] [max];
    static double [] [] p = new double [max] [max];

    static double p (int a,int b) {
        if (!cached [a] [b]) {
            p [a] [b] = calculateP (a,b);
            cached [a] [b] = true;
        }
        return p [a] [b];
    }

    static double calculateP (int a,int b) {
        return
            a < b || a > b + 5 ? 0 :
            b == 1 ? 1/6. :
            p (a,b - 1) + p (b - 1,b - 1) / 6;
    }

    public static void main (String [] args) {
        for (int b = 16;b <= 21;b++) {
            double sum = 0;
            for (int a = b;a <= 21;a++)
                for (int c = 22;c <= a + 6;c++)
                    sum += p (a,b) * p (c,a + 1);
            System.out.printf (Locale.ENGLISH,"%d&%.5f\\\\\n",b,sum);
        }

        double pPlayer21 = p (21,19);
        double pDealer21 = p(19,19) * p(21,20) + p(20,19) * p(21,21);
        System.out.println (pPlayer21);
        System.out.println (pDealer21);
        System.out.println (pPlayer21 + pDealer21);
    }
}