Vanishing Bag - Solution

import java.util.*;

class Main {
    public static void main(String[] args) {
        // Uncomment this line if you want to read from a file
        In.open("public/test1.in");
        Out.compareTo("public/test1.out");

        int t = In.readInt();
        for (int i = 0; i < t; i++) {
            testCase();
        }

        // Uncomment this line if you want to read from a file
        In.close();
    }

    public static void testCase() {
        // Input using In.java class
        int w = In.readInt();
        int b = In.readInt();

        double[][] DP = new double[w+1][b+1]; // Chance of me winning if he starts with i white j black
        for (int i = 0; i <= w; i++) {
          for (int j = 0; j <= b; j++) {
            if (i == 0) {
              DP[i][j] = 1;
            } else {
              DP[i][j] = -1;
            }
          }
        }

        double res = solve(w, b, DP);

        boolean print = false;
        if (print) {
          for (int i = 0; i <= w; i++) {
            for (int j = 0; j <= b; j++) {
              System.out.print(String.format("|%5.2f", DP[i][j]));
            }
            System.out.print("|\n");
          }
        }

        Out.println(res);
    }

    public static double solve(int i, int j, double[][] DP) {
      float w = i; float b = j;

      if (i == 0) {
        return 1; // Instant win
      }
      if (i < 0 || j <= 0) {
        return 0; // Instant loose
      }

      if (DP[i][j] != -1) {
        return DP[i][j]; // Already calculated
      }

      double tot = w+b;

      double pOppNw = b/tot; // Prob opponent wins
      double pB = (b-1)/(tot-1); // Given opp. wins prob. that black drawn by "ghost"
      double pW = w/(tot-1); // Given opp. wins prob. that white drawn by "ghost"
      double pBs = (tot > 2) ? w/(tot-2) : 1; // Probability that I win after black ghost draw
      double pWs = (tot > 2) ? (w-1)/(tot-2) : 1; // Probability that I win after white ghost draw

      // Probability of win in next round (DP) when drawn 3 black (1 opp, 1 ghost, 1 me)
      double pBn = p(w,b-3,false)*solve(i,j-4,DP)+p(w,b-3,true)*solve(i-1,j-3,DP);
      // Probability of win in next round (DP) when drawn 2 black 1 white (black: 1 opp, 1 me; white: 1 ghost)
      double pWn = p(w-1,b-2,false)*solve(i-1,j-3,DP)+p(w-1,b-2,true)*solve(i-2,j-2,DP);

      DP[i][j] = pOppNw*(pB*(pBs+(1-pBs)*pBn)+pW*(pWs+(1-pWs)*pWn));

      return DP[i][j];
    }

    public static double p(double w, double b, boolean white) {
      if (w <= 0 || b <= 0) {
        return 1;
      }
      return (white) ? w/(b+w) : b/(b+w);
    }
}