Statistics.java

package com.stackexchange.rpg;

import java.util.Random;

public class Statistics {
	public static void main(String[] args) {
		long total = 0, samples = 0;
		while (true) {
			samples++;
			total += sample();

			if (shouldPrint(samples)) {
				System.out.println("N=" + samples + ", average: " + String.format("%.3f", total / (double)samples));
			}
		}
	}

	private static final Random random = new Random();

	private static int get4d6DropLowest() {
		int lowest = 6, sum = 0;
		for (int i = 0; i < 4; i++) {
			int die = 1 + random.nextInt(6);
			sum += die;
			lowest = Math.min(lowest, die);
		}
		return sum - lowest;
	}

	// https://www.d20pfsrd.com/basics-ability-scores/ability-scores/
	private static final int[] pointsPerScore = { -4, -4, -4, -4, -4, -4, -4, -4, -2, -1, 0, 1, 2, 3, 5, 7, 10, 13,
			17 };

	private static long sample() {
		// Initialize matrix
		int[][] matrix = new int[6][6];
		for (int i = 0; i < 6; i++) {
			for (int j = 0; j < 6; j++) {
				matrix[i][j] = get4d6DropLowest();
			}
		}

		// Compute maximum # of points
		int highest = 0, points = 0;
		for (int i = 0; i < 6; i++) {
			// i-th column
			points = 0;
			for (int j = 0; j < 6; j++) {
				points += pointsPerScore[matrix[i][j]];
			}
			highest = Math.max(highest, points);

			// i-th row
			points = 0;
			for (int j = 0; j < 6; j++) {
				points += pointsPerScore[matrix[j][i]];
			}
			highest = Math.max(highest, points);
		}

		// Diagonal
		points = 0;
		for (int i = 0; i < 6; i++) {
			points += pointsPerScore[matrix[i][i]];
		}
		highest = Math.max(highest, points);

		// Antidiagonal
		points = 0;
		for (int i = 0; i < 6; i++) {
			points += pointsPerScore[matrix[i][5 - i]];
		}
		highest = Math.max(highest, points);

		return highest;
	}

	private static boolean shouldPrint(long n) {
		while (true) {
			if (n == 1 || n == 3)
				return true;
			if (n % 10 != 0)
				return false;
			n /= 10;
		}
	}
}