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Fischer Random Chess. Play Bobby Fischer's randomized Chess variant on Game Courier. (Recognized!)[All Comments] [Add Comment or Rating]

🕸📝Fergus Duniho wrote on Mon, Feb 28, 2011 02:21 AM UTC:

Oh, wait. I understand the criticism now. By beginning with the King, it gives equal probability to six different sets of combinations, but these sets of combinations differ in size. When the King is toward the edge, the sets are smaller than when the King is toward the middle. So, any particular combination with the King in the middle is less likely to be chosen than any particular combination with the King towards the edge.

According to statistics I just took, the Queen appears on each space exactly 120 times, the Knight and Bishops appear on each space exactly 240 times, and only the King and Rooks vary in the frequency that they appear on each space. So, to assure equal probability of each combination, the Queen, Bishops, and Knights should go on first. The order these are placed relative to each other doesn't matter. Then the three remaining spaces should be filled in with Rook, King, Rook. So I have changed the code to the following:

  drop B any a1 c1 e1 g1;
  drop B any b1 d1 f1 h1;
  drop Q any a1 b1 c1 d1 e1 f1 g1 h1;
  drop N any a1 b1 c1 d1 e1 f1 g1 h1;
  drop N any a1 b1 c1 d1 e1 f1 g1 h1;
  drop R first a1 b1 c1 d1 e1 f1;
  drop K first b1 c1 d1 e1 f1 g1;
  drop R last c1 d1 e1 f1 g1 h1;