Compute the probability for a two-dimensional random walk with duplication and vanishing to produce at least one duplicate at the origin; see https://math.stackexchange.com/questions/2906613.

Question2906613.java

public class Question2906613 {
	final static int maxn = 1026;
	final static int [] [] ds = {
			{0,1},
			{-1,0},
			{0,-1},
			{1,0}
	};
	public static void main (String [] args) {
		double [] [] a = new double [maxn + 1] [maxn + 1];
		a [0] [0] = 1;
		
		for (int n = 1;n <= maxn;n += n) {
			double s = Double.POSITIVE_INFINITY;
			for (;;) {
				double sum = 0;
				for (int x = 0;x < n;x++)
					for (int y = 0;y < n;y++)
						if (x + y != 0) {
							double die = 1;
							for (int [] d : ds)
								die *= 1 - a [Math.abs (x + d [0])] [Math.abs (y + d [1])] / 4;
							sum += die;
							a [x] [y] = 1 - die;
						}
				if (sum >= s)
					break;
				s = sum;
			}
			System.out.println (n + " " + (1 - Math.pow (1 - a [0] [1] / 4,4)));
		}
	}
}