Uniqueness in chess studies

Van der Heijden’s ENDGAME STUDY DATABASE IV, HhdbIV, is the definitive collection of 76,132 chess studies. In each one, White is to achieve the stipulated goal, win or draw: study solutions should be essentially unique with minor alternatives at most. In this second note on the mining of the database, we use the definitive Nalimov endgame tables to benchmark White’s moves in sub-7-man chess against this standard of uniqueness. Amongst goal-compatible mainline positions and goal-achieving moves, we identify the occurrence of absolutely unique moves and analyse the frequency and lengths of absolutely-unique-move sequences, AUMSs. We identify the occurrence of equi-optimal moves and suboptimal moves and refer to a defined method for classifying their significance

Western Chess: Zugzwang data

This data is derived from Eugene Nalimov's Depth-to-Mate Endgame Tables for Western Chess. While having the move is normally advantageous, there are positions where the side-to-move would have a better theoretical result if it were the other side to move. These are (Type A) 'zugzwang' positions where the 'obligation to act' is unwelcome. This data provides lists of all zugzwangs in sub-7-man chess, and summary data about those sets of zugzwangs including exemplar zugzwangs of maximum depth

Intrinsic Chess Ratings

This paper develops and tests formulas for representing playing strength at chess by the quality of moves played, rather than by the results of games. Intrinsic quality is estimated via evaluations given by computer chess programs run to high depth, ideally so that their playing strength is sufficiently far ahead of the best human players as to be a ‘relatively omniscient’ guide. Several formulas, each having intrinsic skill parameters s for sensitivity and c for consistency, are argued theoretically and tested by regression on large sets of tournament games played by humans of varying strength as measured by the internationally standard Elo rating system. This establishes a correspondence between Elo rating and the parameters. A smooth correspondence is shown between statistical results and the century points on the Elo scale, and ratings are shown to have stayed quite constant over time. That is, there has been little or no ‘rating inflation’. The theory and empirical results are transferable to other rationalchoice settings in which the alternatives have well-defined utilities, but in which complexity and bounded information constrain the perception of the utility values