Verifying and Codifying Strategies in the KNNKP(h) Endgame 1

The extreme complexity of chess endgames with five or more men occasionally tempts human experts into making necessarily incomplete and sometimes erroneous statements. To some extent, increased computational speed and expanded memory, when combined with a full-width backward-chaining procedure nowadays may result in databases which embrace complete knowledge over a certain endgame domain. The major remaining problem after having obtained such knowledge is not (trivially) indicating the best move, but explaining why this move should be best. In other words: the true task is the formulation of rules and strategies implying how the endgame should be played.

The present article broaches the subject by verifying, via a database, two statements of Troitzky’s (1934) about the domain KNNKP(h). The statements are found to be unassailable in all details. The present work extends Troitzky’s by a few maximin results. Depth charts (Roycroft, 1986) are discussed as a potential limited aid towards formulating a strategy. The new notion of tablebases is introduced, whereas a slight generalization in tablebase construction permits a relatively comfortable way of verifying strategies.