Space-efficient indexing of endgame tables for chess

Chess endgame tables should provide efficiently the value and depth of any required position during play. The indexing of an endgame’s positions is crucial to meeting this objective. This paper updates Heinz’ previous review of approaches to indexing and describes the latest approach by the first and third authors. Heinz’ and Nalimov’s endgame tables (EGTs) encompass the en passant rule and have the most compact index schemes to date. Nalimov’s EGTs, to the Distance-to-Mate (DTM) metric, require only 30.6 × 109 elements in total for all the 3-to-5-man endgames and are individually more compact than previous tables. His new index scheme has proved itself while generating the tables and in the 1999 World Computer Chess Championship where many of the top programs used the new suite of EGTs

Strategies for Constrained Optimisation

The latest 6-man chess endgame results confirm that there are many deep forced mates beyond the 50-move rule. Players with potential wins near this limit naturally want to avoid a claim for a draw: optimal play to current metrics does not guarantee feasible wins or maximise the chances of winning against fallible opposition. A new metric and further strategies are defined which support players’ aspirations and improve their prospects of securing wins in the context of a k-move rule

Space-efficient Indexing of Chess Endgame Tables

Chess endgame tables should provide efficiently the value and depth of any required position during play. The indexing of an endgame’s positions is crucial to meeting this objective. This paper updates Heinz’ previous review of approaches to indexing and describes the latest approach by the first and third authors. Heinz’ and Nalimov’s endgame tables (EGTs) encompass the en passant rule and have the most compact index schemes to date. Nalimov’s EGTs, to the Distance-to-Mate (DTM) metric, require only 30.6 × 10^9 elements in total for all the 3-to-5-man endgames and are individually more compact than previous tables. His new index scheme has proved itself while generating the tables and in the 1999 World Computer Chess Championship where many of the top programs used the new suite of EGTs

Material Symmetry to Partition Endgame Tables

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 rel- atively 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

The Nature of Retrograde Analysis for Chinese Chess

Retrograde analysis has been successfully applied to solve Awari and construct 6-piece Western chess endgame databases. However, its application to Chinese chess is limited because of the special rules about indefinite move sequences. Problems caused by the most influential rule, checking indefinitely were successfully solved in practical cases, with $50$ selected endgame databases constructed in accord with this rule, where the 60-move-rule was ignored. Other special rules have much less impact on contaminating the databases, as verified by the rule-tolerant algorithms. For constructing complete endgame databases, we need rigorous algorithms. There are two rule sets in Chinese chess: Asian rule set and Chinese rule set. In this paper, an algorithm is successfully developed to construct endgame databases in accord with the Asian rule set. The graph-theoretical properties are also explored as well

Use-driven concept formation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 161-165).When faced with a complex task, humans often identify domain-specific concepts that make the task more tractable. In this thesis, I investigate the formation of domain-specific concepts of this sort. I propose a set of principles for formulating domain-specific concepts, including a new inductive bias that I call the equivalence class principle. I then use the domain of two-player, perfect-information games to test and refine those principles. I show how the principles can be applied in a semiautomated fashion to identify strategically-important visual concepts, discover highlevel structure in a game's state space, create human-interpretable descriptions of tactics, and uncover both offensive and defensive strategies within five deterministic, perfect-information games that have up to forty-two million states apiece. I introduce a visualization technique for networks that discovers a new strategy for exploiting an opponent's mistakes in lose tic-tac-toe; discovers the optimal defensive strategies in five and six men's morris; discovers the optimal offensive strategies in pong hau k'i, tic-tac-toe, and lose tic-tac-toe; simplifies state spaces by up to two orders of magnitude; and creates a hierarchical depiction of a game's state space that allows the user to explore the space at multiple levels of granularity. I also introduce the equivalence class principle, an inductive bias that identifies concepts by building connections between two representations in the same domain. I demonstrate how this principle can be used to rediscover visual concepts that would help a person learn to play a game, propose a procedure for using such concepts to create succinct, human-interpretable descriptions of offensive and defensive tactics, and show that these tactics can compress important information in the five men's morris state space by two orders of magnitude.by Jennifer M. Roberts.Ph.D

PSO-based coevolutionary Game Learning

Games have been investigated as computationally complex problems since the inception of artificial intelligence in the 1950’s. Originally, search-based techniques were applied to create a competent (and sometimes even expert) game player. The search-based techniques, such as game trees, made use of human-defined knowledge to evaluate the current game state and recommend the best move to make next. Recent research has shown that neural networks can be evolved as game state evaluators, thereby removing the human intelligence factor completely. This study builds on the initial research that made use of evolutionary programming to evolve neural networks in the game learning domain. Particle Swarm Optimisation (PSO) is applied inside a coevolutionary training environment to evolve the weights of the neural network. The training technique is applied to both the zero sum and non-zero sum game domains, with specific application to Tic-Tac-Toe, Checkers and the Iterated Prisoners Dilemma (IPD). The influence of the various PSO parameters on playing performance are experimentally examined, and the overall performance of three different neighbourhood information sharing structures compared. A new coevolutionary scoring scheme and particle dispersement operator are defined, inspired by Formula One Grand Prix racing. Finally, the PSO is applied in three novel ways to evolve strategies for the IPD – the first application of its kind in the PSO field. The PSO-based coevolutionary learning technique described and examined in this study shows promise in evolving intelligent evaluators for the aforementioned games, and further study will be conducted to analyse its scalability to larger search spaces and games of varying complexity.Dissertation (MSc)--University of Pretoria, 2005.Computer Scienceunrestricte