(Number of Unique Legal Positions in chess endgames)

These pages describe NULP (Number of Unique Legal Positions) as the measure of state-space complexity of chess endgames. The choices of uniqueness and legality definitions are discussed. NULP values of various endgames are then shared.

These pages are updated when I get new ideas or results. Please send questions, comments, ideas or other contribution to <>. Especially welcome are confirmations or corrections of any results.


April 14, 2014
Counted 8-piece positions with/without en passant and castling rights.
April 11, 2014
Counted positions with/without en passant and castling rights, for up to 7 pieces.
January 6, 2014
The number of Chess960 positions with 8 pieces is 39,587,704,309,395,475. This is 1.037 times larger than in Chess.
December 27, 2013
The number of Chess positions with 8 pieces is 38,176,306,877,748,245 (38 quadrillion), about 90 times larger than with 7 pieces.
February 28, 2013
Counted positions with castling rights and up to 7 pieces in Chess and Chess960.
February 24, 2013
Web-site created, with NULP values for chess endgames with up to 7 pieces.


© 2013–2014 Kirill Kryukov
Available under the CC BY 3.0 License