Chess Positions Research Articles

Effects of material advantage and space advantage on the Komodo and Stockfish chess engines

Chess engines are computer programs built to play chess. Currently, chess engines are significantly better at chess than the highest ranked human chess players. The utilization of chess engines is the most widely accessible, reliable, and efficient way to study chess. Because of their overwhelming chess capabilities, chess engines are able to aid chess players ranging from amateurs to Grandmasters. A key feature of chess engines is their ability to analyze a chess position and provide a numerical evaluation that describes the degree to which a side is winning. However, different chess engines employ different methods of evaluating a position. Some engines highly value “material advantage” and will greatly favor the side that has captured more pieces. Others put great importance in “space advantage” and will generally try to move their pieces from starting position to positions where they control more squares as early as possible. This study examines how two top-rated chess engines, Stockfish and Komodo, differ in their methodologies for evaluating a chess position. We hypothesized that Komodo’s evaluation would change more than Stockfish’s when material was lost, and that Stockfish’s evaluation would favor the side with more available advancing moves than Komodo. We discovered that Komodo indeed valued material advantage significantly more than Stockfish. However, the two engines did not differ significantly in their evaluations of space advantage. These findings have important implications for chess players, as they allow for accurate imitations of an engine’s play style, which could serve to more effectively increase performance.

Metamorphic testing of chess engines

Chess engines are computer programs that analyse chess positions. The goal of this analysis is to decide which player has an advantage and evaluate how big the advantage is. Using this analysis, chess engines are really powerful players who can consistently beat the best (human) players. Even though these programs are fantastic players, we cannot be sure that the code is fault free because it is very difficult to test them. In particular, we face the oracle problem: if the chess engine plays better than any potential tester, how can a tester claim that a certain evaluation is wrong or that a suggested move is not the best one? The main goal of our work is to provide a metamorphic testing tool to evaluate chess engines. In particular, we are interested in looking for inconsistent behaviours in the best publicly available chess engine, Stockfish, but we would also like to consider other chess engines. We developed a metamorphic testing solution to validate chess engines. First, we defined metamorphic relations that might reveal inconsistent behaviours. The underlying idea was that the evaluation of related positions should be the same. For example, if we consider a position and rotate all the pieces with respect to the central axis, then both positions should have the same evaluation. One of our main priorities was to have a fully automatised tool. Source inputs are obtained from available datasets while follow-up inputs are automatically computed by applying sound transformations to the source inputs with respect to the corresponding metamorphic rule. In order to assess the usefulness of our work, we applied it to analyse a dataset with more than 40,000 positions. Empirical evidence validates the usefulness of our work to analyse the best available chess engine, Stockfish. Our tool revealed non-negligible deviations from the expected behaviour in Stockfish for all the MRs. Additional experiments showed that our tool can be easily used to analyse other chess engines such as Komodo, Houdini and Gull. The experiments demonstrate the usefulness of our approach to identify issues in the latest version of the widely recognised to be the best chess engine: Stockfish (version 15, released in April 2022). Our tool is flexible and can be easily extended with metamorphic relations that can be defined in the future by either us or other users. Since all our metamorphic relations are implemented and the code is freely available, users can use them as a pattern to implement new relations.

RELATIONSHIP BETWEEN CHESS AND MANAGEMENT – AN OVERVIEW

This article intent to find the relationship between chess and management with suitable chess positions linking with business. Chess has a relationship not only with management but with life itself. Chess helps to improve decision making, analysing the situation. Past researchers have worked on these gaps, especially De Jorge-Moreno, J. (2020) [1] study has shown significant relationship. This current study has illustrated different management lessons linked with chess positions.

Developing a Reinforcement Learning based Chess Engine

Traditionally, chess engines use handcrafted evaluation functions based on human strategy. Recently, machine learning has been used as an alternative to direct position scoring. However, this typically involves training a model on human matches. Reinforcement learning has been shown to be a viable machine learning approach that, when combined with self play, can train a neural network for chess position evaluation without the need for human domain knowledge. This paper discusses our implementation of a reinforcement learning based chess engine, trained using self play.

Chess Position Evaluation Using Radial Basis Function Neural Networks

The game of chess is the most widely examined game in the field of artificial intelligence and machine learning. In this work, we propose a new method for obtaining the evaluation of a chess position without using tree search and examining each candidate move separately, like a chess engine does. Instead of exploring the search tree in order to look several moves ahead, we propose to use the much faster and less computationally demanding estimations of a properly trained neural network. Such an approach offers the benefit of having an estimation for the position evaluation in a matter of milliseconds, while the time needed by a chess engine may be several orders of magnitude longer. The proposed approach introduces models based on the radial basis function (RBF) neural network architecture trained with the fuzzy means algorithm, in conjunction with a novel set of input features; different methods of network training are also examined and compared, involving the multilayer perceptron (MLP) and convolutional neural network (CNN) architectures and a different set of input features. All methods were based upon a new dataset, which was developed in the context of this work, derived by a collection of over 1500 top-level chess games. A Java application was developed for processing the games and extracting certain features from the arising positions in order to construct the dataset, which contained data from over 80,000 positions. Various networks were trained and tested as we considered different variations of each method regarding input variable configurations and dataset filtering. Ultimately, the results indicated that the proposed approach was the best in performance. The models produced with the proposed approach are suitable for integration in model-based decision-making frameworks, e.g., model predictive control (MPC) schemes, which could form the basis for a fully-fledged chess-playing software.

Pavlinsky Geliy Veniaminovich (1935–2023)

Pavlinsky Geliy Veniaminovich (1935–2023)

Expertise-dependent perceptual performance in chess tasks with varying complexity.

Perceptual performance, anticipating opponents' strategies, and judging chess positions especially in subliminal processing is related to expertise level and dependent on chunking processes. It becomes obvious that chess expertise is a multidimensional phenomenon related predominantly to experience. Under consideration of chess expertise categorization, we conducted two priming experiments expanding existing designs by gradually increasing the target and task complexity. The main aim was the evaluation of potential visuocognitive limitations. The results reveal experts' perceptual superiority manifested by their faster reaction times in settings with increased stimulus and task complexity. Further, experts' priming effects seem to be affected by the target content and/ or priming duration. For short prime duration, experts show priming effects only for less complex prime-target content. Interestingly, for longer prime duration and more complex prime-target content, all participants reveal priming effects. In summary, we argue that experts' visuocognitive processing (i.e., detecting or anticipating potential threats to the king) is rooted in a more efficient visuocognition due to stored chunks of checking and mating constellations. We suggest that visuocognitive limitations are related also to the prime-target complexity as well as to the task. Further investigations must be conducted in order to elucidate the factors with an increased impact on chess players' performance.

Understanding and Synergy: A Single Concept at Different Levels of Analysis?

Biological systems differ from the inanimate world in their behaviors ranging from simple movements to coordinated purposeful actions by large groups of muscles, to perception of the world based on signals of different modalities, to cognitive acts, and to the role of self-imposed constraints such as laws of ethics. Respectively, depending on the behavior of interest, studies of biological objects based on laws of nature (physics) have to deal with different salient sets of variables and parameters. Understanding is a high-level concept, and its analysis has been linked to other high-level concepts such as “mental model” and “meaning”. Attempts to analyze understanding based on laws of nature are an example of the top-down approach. Studies of the neural control of movements represent an opposite, bottom-up approach, which starts at the interface with classical physics of the inanimate world and operates with traditional concepts such as forces, coordinates, etc. There are common features shared by the two approaches. In particular, both assume organizations of large groups of elements into task-specific groups, which can be described with only a handful of salient variables. Both assume optimality criteria that allow the emergence of families of solutions to typical tasks. Both assume predictive processes reflected in anticipatory adjustments to actions (motor and non-motor). Both recognize the importance of generating dynamically stable solutions. The recent progress in studies of the neural control of movements has led to a theory of hierarchical control with spatial referent coordinates for the effectors. This theory, in combination with the uncontrolled manifold hypothesis, allows quantifying the stability of actions with respect to salient variables. This approach has been used in the analysis of motor learning, changes in movements with typical and atypical development and with aging, and impaired actions by patients with various neurological disorders. It has been developed to address issues of kinesthetic perception. There seems to be hope that the two counter-directional approaches will meet and result in a single theoretical scheme encompassing biological phenomena from figuring out the best next move in a chess position to activating motor units appropriate for implementing that move on the chessboard.

Equiprobable and attacked-square chess entropies by phases, levels of play and game outcomes

In any legal chess position, we define an attacked-square entropy [Formula: see text] for either Black or White pieces in terms of the square occupation probability [Formula: see text], where [Formula: see text] is the number of all possible movements to square [Formula: see text] (free or occupied by an opponent’s piece) and [Formula: see text] is the total mobility defined as the sum of all possible movements. Thus, each attacked square contributes to the entropy according to its received “firepower” concentration. A simpler nonsquare-dependant equiprobable entropy [Formula: see text] in terms of equal probabilities [Formula: see text] always yields [Formula: see text]. On average, the difference [Formula: see text] is very large in the Opening phase and [Formula: see text] decreases faster for lower ranked players after move 25. A major cause of the reduction of [Formula: see text] during a game is material loss, which is an irreversible process. By game outcome, gaps in average [Formula: see text] among winners, draws and losers are larger for Amateur players than for Elite players, both in the Middlegame and Endgame. Statistically, Elite players exhibit narrower dispersions in [Formula: see text]. Also, the entropy rates of the Elite level fluctuate much less than the entropies of other levels. Density of attacks in the four-square central zone is very high in the Opening, specially for Elite players.

Musical expertise, musical style, and visual attention

Research has repeatedly demonstrated that people with experience within a particular domain have exceptional cognitive abilities for domain-specific information. Chess masters, for instance, are far better at memorizing visually presented chess positions than amateurs, and professional American football experts are highly sensitive to semantic changes in domain-related scenes. However, for non-domain-related material, experts’ performance becomes similar to novice performance. But how does this apply to music? We compared experienced musicians’ and novices’ attentional function and visual working memory using the change blindness flicker paradigm. The task was to detect minor changes between two otherwise identical music scores of differing styles: traditional (C-major, regular rhythms), contemporary (atonal, irregular rhythms), and random (nonsense music). We expected that (1) experienced musicians would detect changes faster, (2) the between-group difference would be larger for traditional than contemporary music, and (3) the groups’ performance would be more similar for random music. The experienced musicians detected changes significantly faster in both the contemporary and traditional music material, whereas the difference was nonsignificant for the random condition. The difference between groups was largest for contemporary music, despite its higher level of complexity. We discuss these results in relation to existing literature on expertise in visual information processing.

The influence of context on information processing.

The main research question of this study is how the processing of information relates to different contextual characteristics. More specifically, how the context is associated with efficiency of information processing (success and speed), size of chunks, speed of chunk processing and the recall of a chunk. The research domain was the game of chess. The efficiency of information processing and the chunk characteristics were defined with the reconstruction of sequences of chess moves. Context variables were defined using a slightly adapted chess program. Variables on information dispersion, deviation, complexity and positivity were extracted in each chess position. Overall, the results showed that higher dispersion and complexity and lower positivity of information in a context lead to less efficient information processing. The results support the assumptions of the cognitive load theory about the negative effects of external factors burden on information processing and working memory. Our results also support the ACT-R theory, which suggests that more frequent information has a higher activation level and can therefore be retrieved more easily and quickly. The results are also congruent with the positivity effect, which proposes that it is easier to remember positive information than negative information. The findings of our study can be beneficial for the development of intelligent tutoring systems and the design of human-computer interaction systems.

Augmented Reality Chess Analyzer (ARChessAnalyzer): In-Device Inference of Physical Chess Game Positions through Board Segmentation and Piece Recognition using Convolutional Neural Networks

Chess game position analysis is important in improving one’s game. One method requires entry of logged moves into a chess engine which is cumbersome and error prone. A quick and effective method for analysis is hence strongly desired. Our hypothesis was that a faster chess game entry method can be built using a combination of vision and machine learning techniques to be analyzed directly in a chess engine. To test the hypothesis, we developed the Augmented Reality Chess Analyzer (ARChessAnalyzer), a complete pipeline from a live image capture of a physical chess game, to board and piece recognition, to move analysis and finally to augmented reality overlay of the position and best move on the physical board. The chess position predictor is like a scene predictor - it is an ensemble of traditional image and vision techniques and image classifier for chess board recognition and Convolutional Neural Network (CNN) for chess piece recognition. ARChessAnalyzer was used - as the input mechanism - to compare against manual entry into StockFish which was also the chess engine used in the app. The results validate the hypothesis that both for sparse and dense chessboard populations, ARChessAnalyzer was faster than manual entry with p-value < 0.005. This app and technologies underneath will help chess learners improve their game and hopefully will be widely used in chess clubs.

FinalGen revisited: new discoveries

Romero’s FINALGEN of 2012 creates designer endgame tables for specific chess positions that feature no more than one non-pawn piece per side. Larger hard discs and faster solid-state discs have extended the reach of this software and encouraged its greater use. Some new discoveries illustrate here what is now feasible and how FINALGEN may be combined with other tools to reach definitive and likely truths.

Five Chess Positions to Learn Law and Legal Argumentation

Five Chess Positions to Learn Law and Legal Argumentation

On the Ecological Validity of Memory Research: Generalization to Memory for Chess Positions

Abstract Although there is often a tradeoff between experimental control and ecological validity, there are good arguments that the study of memory for chess positions allows a high level of both. For example, chess is a very complex game, and remembering chess positions is in many ways comparable to the memory involved in real-world tasks. Accordingly, chess has been called the Drosophila of cognitive science. This article reviews several key findings in memory and assesses whether they generalize to memory for chess positions. Specifically, research on the role of thinking and comprehension on memory, memory’s reconstructive nature, contextual effects on memory, and the effects of encoding instructions on memory are reviewed. In each of these cases, established memory phenomena generalize to the chess domain. This demonstrates that key findings from experimental memory studies hold in contexts outside the ones in which they were discovered and supports the ecological validity and generality of these findings.

Decreasing Operational Distortion and Surrogation Through Narrative Reporting

ABSTRACTPrior research finds that agents who are compensated on an imperfect measure of performance tend to distort their operational decisions and believe that the measure is more reflective of reality than it actually is (i.e., they surrogate). I find that agents distort decisions less and surrogate less when they can provide unverifiable narrative explanations for their actions. In my experiment, experienced chess players place bets on and write explanations about in-progress chess games. I manipulate whether participants give their explanations to their boss (who allocates a subjective bonus) when working as an agent. Participants who give explanations are more likely to make bets that reflect all dimensions of a chess position, rather than making bets that favor only the objective measure. They are also less likely to surrogate and are more likely to write about unmeasurable aspects of the games when subsequently making bets on their own behalf.

Decreasing Operational Distortion and Surrogation through Narrative Reporting

Prior research finds that agents who are compensated on an imperfect measure of performance tend to distort their operational decisions and believe that the measure is more reflective of reality than it actually is (i.e. they surrogate). I find that agents distort decisions less and surrogate less when they can provide unverifiable narrative explanations for their actions. In my experiment, experienced chess players place bets on and write explanations about in-progress chess games. I manipulate whether or not participants give their explanations to their boss (who allocates a subjective bonus) when working as an agent. Participants who give explanations are more likely to make bets that reflect all dimensions of a chess position, rather than making bets that favor only the objective measure. They are also less likely to surrogate and are more likely to write about unmeasurable aspects of the games when subsequently making bets on their own behalf.

Chess knowledge predicts chess memory even after controlling for chess experience: Evidence for the role of high-level processes.

The expertise effect in memory for chess positions is one of the most robust effects in cognitive psychology. One explanation of this effect is that chess recall is based on the recognition of familiar patterns and that experts have learned more and larger patterns. Template theory and its instantiation as a computational model are based on this explanation. An alternative explanation is that the expertise effect is due, in part, to stronger players having better and more conceptual knowledge, with this knowledge facilitating memory performance. Our literature review supports the latter view. In our experiment, a sample of 79 chess players were given a test of memory for chess positions, a test of declarative chess knowledge, a test of fluid intelligence, and a questionnaire concerning the amount of time they had played nontournament chess and the amount of time they had studied chess. We determined the numbers of tournament games the players had played from chess databases. Chess knowledge correlated .67 with chess memory and accounted for 16% of the variance after controlling for chess experience. Fluid intelligence accounted for an additional 13% of the variance. These results support the conclusion that both high-level conceptual processing and low-level recognition of familiar patterns play important roles in memory for chess positions.

Assessing Human Error Against a Benchmark of Perfection

An increasing number of domains are providing us with detailed trace data on human decisions in settings where we can evaluate the quality of these decisions via an algorithm. Motivated by this development, an emerging line of work has begun to consider whether we can characterize and predict the kinds of decisions where people are likely to make errors. To investigate what a general framework for human error prediction might look like, we focus on a model system with a rich history in the behavioral sciences: the decisions made by chess players as they select moves in a game. We carry out our analysis at a large scale, employing datasets with several million recorded games, and using chess tablebases to acquire a form of ground truth for a subset of chess positions that have been completely solved by computers but remain challenging for even the best players in the world. We organize our analysis around three categories of features that we argue are present in most settings where the analysis of human error is applicable: the skill of the decision-maker, the time available to make the decision, and the inherent difficulty of the decision. We identify rich structure in all three of these categories of features, and find strong evidence that in our domain, features describing the inherent difficulty of an instance are significantly more powerful than features based on skill or time.

Confirmation Bias as a Default Heuristic in Novice Chess Players' Problem Solving

Confirmation bias, the compiling of cases verifying one’s beliefs, as opposed to cases to falsify one’s beliefs (falsification), has been linked to inefficient and systematic error in human thinking. Previous research has suggested that when task-specific information is lacking or cognitive demands are high, reasoners will rely on a confirmation strategy as a heuristic when engaging in hypothesis testing. To investigate this hypothesis a combined think aloud-retrospective method was adopted to examine levels of confirmation at novice and expert levels of chess expertise. Ten chess novices and ten experts were instructed to think aloud while choosing a move in given chess positions. Verbalised move sequences were recorded and called back to the chess player to elicit whether they led to a positive (confirming) outcome or negative (falsifying) outcome. It was predicted that novices who do not typically possess substantial amounts of chess specific knowledge would rely on a confirming strategy as a heuristic to select a move in a game of chess. Chess experts have been found to possess large repositories of chess specific knowledge in long-term memory. Access to such knowledge was predicted to reduce cognitive load when choosing a chess move so that experts confirm to a lesser extent and falsify to a greater extent than novices when selecting chess moves. Significant evidence was found to support the use of a confirmation strategy by novices when choosing a move. Experts where found to falsify to a greater extent than confirm when compared to novices as predicted.