Find cycles of three six-sided dice such that each beats the next one with the same maximal probability; see http://math.stackexchange.com/questions/260072.

Question260072.java

public class Question260072 {
    public static void main (String [] args) {
        int [] [] dice = new int [3] [6];
        int [] counter = new int [3];

        int limit = (int) Math.pow (3,18);
        int max = 0;

        outer:
        for (int selection = 0;selection < limit;selection++) {
            // transform 18-digit ternary number into die sides
            counter [0] = counter [1] = counter [2] = 0;
            int n = selection;
            for (int i = 0;i < 18;i++) {
                int die = n % 3;
                if (counter [die] == 6)
                    continue outer;
                dice [die] [counter [die]++] = i;
                n /= 3;
            }
            
            // determine winning probabilities
            counter [0] = counter [1] = counter [2] = 0;
            for (int i = 0;i < 3;i++)
                for (int j = 0;j < 6;j++)
                    for (int k = 0;k < 6;k++)
                        if (dice [i] [j] > dice [(i + 1) % 3] [k])
                            counter [i]++;

            // are they all the same and maximal?
            if (counter [0] >= max && counter [0] == counter [1] && counter [1] == counter [2]) {
                max = counter [0];
                if (max == 21) {
                    // if this is an optimal set, print it only if the 0 is in the first set to avoid cyclic equivalents
                    boolean zeroHasZero = false;
                    for (int i = 0;i < 6;i++)
                        zeroHasZero |= dice [0] [i] == 0;
                    if (zeroHasZero) {
                        // collapse successive numbers on the same die into one
                        int lastDie = -1;
                        int lim = 18;
                        for (int i = 0;i < lim;) {
                            int die;
                            inner:
                            for (die = 0;die < 3;die++)
                                for (int k = 0;k < 6;k++)
                                    if (dice [die] [k] == i)
                                        break inner;
                            if (die == 4)
                                throw new Error ();
                            if (die == lastDie) {
                                for (int j = 0;j < 3;j++)
                                    for (int k = 0;k < 6;k++)
                                        if (dice [j] [k] >= i)
                                            dice [j] [k]--;
                                lim--;
                            }
                            else {
                                lastDie = die;
                                i++;
                            }
                        }
                        // print the collapsed optimal set
                        for (int i = 0;i < 3;i++) {
                            System.out.print ("   ");
                            for (int j = 0;j < 6;j++)
                                System.out.printf (" %d",dice [i] [j]);
                            System.out.println ();
                        }
                        System.out.println ();
                    }
                }
            }
        }
        
        System.out.println (max);
    }
}