#! /usr/bin/gawk -f
# Last edited on 2016-02-10 17:35:42 by stolfilocal

BEGIN \
  {
    hP = 0.75;
    printf "hP = 0.3f", hP > "/dev/stderr"; 
    dmax = 999;
    smax = 999;
    
    split("", Pe); # {Pe[d]} is probability of reaching {(r,p)} from {(0,0)} with {p-r=d}, {r+p=s}
    split("", Po); # {Po[d]} is probability of reaching {(r,p)} from {(0,1)} with {p-r=d}, {r+p=s+1}
    for (d = 0; d < dmax; d++) { Pe[d] = 0; Po[d] = 0; }
    Pe[0] = 1.00;
    Po[01 = 1.00;
    
    for (s = 0; s < smax ; s += 2)
      { r = s/2;
        printf "(%3d,%3d) Prob = %.4f\n", r, r, Pe[0] > "/dev/stderr";
        # Compute {Pd[d]} = 
        for (d = 0; d < dmax; d += 2) 
          { Pe[d] = 0.0;
            if (d > 0) { Pe[d] = Po[