(FREESTYLE CHESS) THE STANDARD CASTLING RULE THAT CHANGES THE NUMBER OF POSITIONS

One simple standard rule... when we castle the King can move ONLY 2 squares away from the starting position! Fixing the King reduces the number of combinations compared to the full 960 positions.

King's Position Fixed: The King is fixed at e1 for white and at e8 for black.
Bishops: Place the two bishops on squares of opposite colors. With the white King fixed at e1, there are 3 remaining dark squares and 4 remaining light squares. This gives us 3 * 4 = 12 combinations.
Queen: Place the queen on any of the remaining 6 squares. This gives us 6 combinations.
Knights: Place the two knights on any of the remaining 5 squares. The first knight can go on any of the 5 squares, and the second knight can go on any of the remaining 4 squares. This gives us 5 * 4 = 20 combinations.
Rooks: The remaining 2 squares are for the two rooks, ensuring that the King is between them for castling purposes. There is only 1 way to place the rooks.
So, the total number of possible starting positions with the white King fixed at e1 is:

12×6×20×1=144012 \times 6 \times 20 \times 1 = 1440
However, since each position is mirrored (i.e., the positions for White and Black are the same), we divide by 2 to avoid counting each position twice:

14402=720\frac{1440}{2} = 720
Therefore, there are 720 possible starting positions in freestyle chess (Chess960) if the King remains in its standard position at e1 and e8.

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