Methods For Creating The Starting Position
There are many procedures for creating the starting position for a game of Chess960. The methods that are presented below fall into two general categories:
- There is a separate randomization event for each placement of a piece, or at least most of them. The die and coins methods fall into this category. The main problems are the placements of the king and rooks. Analysis of the 960 starting positions shows that the knights, bishops and queen are spread evenly across the eight files; however, the king should stand on the files b through g with the respective probabilities 9/80, 14/80, 17/80, 17/80, 14/80, 9/80, and the rook's probabilities for the files a through h are, respectively, 30/80, 21/80, 16/80, 13/80, 13/80, 16/80, 21/80, 30/80. It is very doubtful that any simple method can achieve these numbers unless the king and rooks are placed last (when there is only one choice) and proper balance is maintained for the previous placements of the knights, bishops and queen.
- There is a single randomization event for the placement of all eight pieces. The cards and drawing methods are in this category. The difficulty here is how to cope when the bishops start out on squares of the same color. There are 5040 distinct arrangements of the pieces. Of the positions, 2880 of them have the bishops on squares of different colors, and 2160 of these have bishops on squares of the same color. Thus it is impossible to get a proper balance by linking each of the latter arrangements to its own single arrangement with the bishops on different colored squares. Some further randomization is needed. David Wheeler's suggestion of having a randomly selected bishop move to a randomly selected square of the opposite color is a very handy way to do this. It involves an eight-way choice, and gives equal probabilities to all 2880 positions.
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