singlensa.blogg.se - Tablebase endgame online

(This work was in fact first done and published by Thomas Strohlein, Munich, in 1970, but only a single analytical line is contained in his doctoral thesis.)' 'Niblett and Kopec described, and later demonstrated, the optimal 0103 data base. Untersuchungen über kombinatorische Spiele Ph.D. Proceedings of the National Academy of Sciences of the United States of America 53 (2): 244–246. 'On the application of dynamic programming to the determination of optimal play in chess and checkers'. Department of Computer Science, University of Limburg. Searching for Solutions in Games and Artificial Intelligence. ^ examples of long endings for Gothic chess.

^Website of KingsRow about the creation of the eight-piece endgame tablebase.

John Nunn has written three books based on detailed analysis of endgame tablebases:

Ke6! Stiller reported the DTC as 243 moves, and the DTM was later found to be 262 moves. Even more amazing is the position at right, where White wins starting with 1. The longest win in KRBKNN has a DTC of 223 and a DTM of 238 moves (not shown). Stiller's DTC tablebase revealed several lengthy wins in these endgames. KRNKNN and KRBKNN are won for the strongest side in 78% and 95% of the cases, respectively.

KRNKNN and KRBKNN - Friedrich Amelung had analyzed these two endgames in the 1900s.

In both this endgame and KQQKQQ, the first player to check usually wins. The maximum DTC is 92, and the maximum DTM is 117.

KQRKQR - Despite the equality of material, the player to move wins in 67.74% of positions.

KNNNNKQ - The knights win in 62.5 percent of positions, with maximum DTM = 85 moves.

Analysis of the tablebases has clarified that even if the pawn has crossed the Troitzky line, White can sometimes win by forcing zugzwang.

KNNKP - Alexey Troitsky established this as a win for the knights if the pawn was blocked behind the Troitzky line.

KBBKN - Bernhard Horwitz and Josef Kling (1851) proposed that Black can draw by entering a defensive fortress, but tablebases demonstrated a general win, with maximum DTC = 66 or 67 and maximum DTM = 78.

The following interesting results have emerged: In contexts where the fifty-move rule may be ignored, tablebases have answered longstanding questions about whether certain combinations of material are wins or draws.