Space-Efficient Indexing of Chess Endgame Tables1

Lin

IEEE Trans. Comput. Intell. AI Games

et al. 2015

Chinese Dark Chess, a nondeterministic two-player game, has not been studied thoroughly. State-of-the-art programs focus on using search algorithms to explore the probability behavior of flipping unrevealed pieces in the opening and the midgame phases. There has been comparatively little research on opening books and endgame databases, especially endgames with nondeterministic flips. In this paper, we propose an equivalence relation that classifies the complex piece relations between the material combinations of each player, and derive a partition for all such material combinations. The technique can be applied to endgame database compression to reduce the number of endgames that need to be constructed. As a result, the computation time and the size of endgame databases can be reduced substantially. Furthermore, understanding the piece relations facilitates the development of a well-designed evaluation function and enhances the search efficiency. In Chinese Dark Chess, the number of nontrivial material combinations comprised of only revealed pieces is 8 497 176, and the number that contain at least one unrevealed piece is 239 980 775 397. Under the proposed method, the compression rates of the above material combinations reach 28.93% and 42.52%, respectively; if the method is applied to endgames comprised of three to eight pieces, the compression rates reach 5.82% and 5.98%, respectively.

Section: B Endgame Databasesmentioning

confidence: 99%

Equivalence Classes in Chinese Dark Chess Endgames

Lin

IEEE Trans. Comput. Intell. AI Games

et al. 2015

“…Indeed, di erent sets of pieces might lead to tables of di erent size and equivalence classes might have di erent number of elements. For instance, in chinese dark chess the Kkm le corresponds to 29,760 positions, while the kPP le corresponds only to 14,880 positions because the two pawns are indistinguishable. In this section, we assume that we store the result for every position in the corresponding le using a perfect hashing function, or index.…”

Section: Equivalence Classesmentioning

confidence: 99%

“…It has been used in chess to build endgame databases of up to six pieces [19,20,14]. It has also been used in a similar way to build endgame databases for checkers [17] that have helped solving the game [18].…”

Section: Introductionmentioning

confidence: 99%

Material Symmetry to Partition Endgame Tables

Saffidine

Jouandeau

Buron

et al. 2014

Computers and Games

Abstract. Many games display some kind of material symmetry. That is, some sets of game elements can be exchanged for another set of game elements, so that the resulting position will be equivalent to the original one, no matter how the elements were arranged on the board. Material symmetry is routinely used in card game engines when they normalize their internal representation of the cards.Other games such as chinese dark chess also feature some form of material symmetry, but it is much less clear what the normal form of a position should be. We propose a principled approach to detect material symmetry. Our approach is generic and is based on solving multiple relatively small sub-graph isomorphism problems. We show how it can be applied to chinese dark chess, dominoes, and skat.In the latter case, the mappings we obtain are equivalent to the ones resulting from the standard normalization process. In the two former cases, we show that the material symmetry allows for impressive savings in memory requirements when building endgame tables. We also show that those savings are relatively independent of the representation of the tables.

Lecture Notes in Computer Science

“…An EGT gives the theoretical value and Depth to Goal of every legal position for an endgame force, e.g., King & Queen v King & Rook (KQKR). The most compact and prevalent EGTs are those of Nalimov [6], providing Depth to Mate (DTM) where mate is the end-goal of chess: these are used by many chess engines on a simple look-up basis. EGTs for all required 3-, 4-, 5-and 6-man endgames are available up to KPPKPP.…”

Section: Absolute Skill In the Chess Endgamementioning

confidence: 99%

Performance and Prediction: Bayesian Modelling of Fallible Choice in Chess

Haworth

Regan

Fatta

2010

Abstract. Evaluating agents in decision-making applications requires assessing their skill and predicting their behaviour. Both are well developed in Poker-like situations, but less so in more complex game and model domains. This paper addresses both tasks by using Bayesian inference in a benchmark space of reference agents. The concepts are explained and demonstrated using the game of chess but the model applies generically to any domain with quantifiable options and fallible choice. Demonstration applications address questions frequently asked by the chess community regarding the stability of the rating scale, the comparison of players of different eras and/or leagues, and controversial incidents possibly involving fraud. The last include alleged under-performance, fabrication of tournament results, and clandestine use of computer advice during competition. Beyond the model world of games, the aim is to improve fallible human performance in complex, high-value tasks.