One diagram, 192 possible positions!

Jun 17, 2017, 7:10 PM |

Skip to the final move, and you have a diagram which could potentially represent no less than 192 separate legal chess positions.



This is the absolute maximum number of legal positions which can be represented by a single diagram. Remember, a position is distinct based on side to move, castling rights, and en passant possibilities. In this position, all four rooks may or may not have castling rights, and ten different pawns may or may not be captured through en passant. And of course, it might be either side's turn to move.


Side to move is a factor of two. Castling rights is a factor of 16 (2*2*2*2). En passant is a factor of six (each side to move has five pawns to potentially capture, and there's a sixth possibility that none can be captured). 2*16*6=192.


The game displayed above was intentionally designed so that the other 191 positions could be trivially obtained by reordering or adding just a few moves.


If you really want to go crazy and throw in the 50 move count and threefold repetition count, the number of distinct positions balloons to 9,472.


And if you're masochistic enough to factor in FIDE's stupid rules about 75 moves and fivefold repetition, you've got a diagram with 23,040 potential states. A total nightmare for any computer program attempting to solve chess!