The Legitimacy of Positions in Endgame Databases 1

Abstract

Current endgame databases provide optimal sequences of moves from a given position to conversion or to mate. They do not investigate whether the given position is legitimate. This contribution considers the database as a model of the particular chess configuration under investigation and attempts to classify the positions in legitimate and illegitimate positions. Assuming a position to be legitimate if it can be reached from the starting position by legal moves only, the question is what means do we need to prove the legitimacy of a position.

For this purpose, we first define three new concepts initially illegitimate, derivedly illegitimate and isolatedly illegitimate. Then we propose a constructive procedure which enables us to show that a position can be reached. Related to the new concepts we introduce a broad definition of illegitimacy (based on initially illegitimate only) and a narrow definition (taking into account also derivedly illegitimate). For both cases we have examined the 3- and 4-man databases of which results are given. Further research of 5- and 6-man databases is envisaged.