Chess Problems Research Articles

EEG acquisition and processing for cognitive brain mapping during chess problem solving

Owing to its compact and controlled environment, chess has provided in the last few decades a fruitful domain for fundamental questions about human reasoning and promoted the development of several research papers in different areas of scientific knowledge. This paper describes and implements a computational framework for acquiring and processing electroencephalography signals of players with different levels of experience with the goal of identifying distinct patterns of cognitive brain mapping during specific well-known chess problems. Our experimental results have showed a neural organisation consistent with the activity performed by the sample groups of volunteers who took part in this study, highlighting discriminant differences in cortical brain areas between beginners and specialists ranked by their proficiency levels. We believe that such information would be helpful for the formulation of more efficient methodologies to teaching and learning chess.

Chess Training and Mathematical Problem-Solving: The Role of Teaching Heuristics in Transfer of Learning

Background:The introduction of including chess into school activities has recently attracted the attention of policy makers, teachers and researchers. Chess has been claimed to be an effective tool to enhance children’s mathematical abilities, because the game – similarly to mathematical tasks – demands children the use of heuristics to correctly interpret problem situations, and select the appropriate course of actions.Material and methods:In this study, 931 primary school pupils were recruited and assigned to either one of two treatment groups attending chess lessons, or a control group, and all were tested on their mathematical problem-solving abilities. The two treatment groups differed with regard to the teaching method adopted: The trainers (chess instructors) of one group taught the pupils heuristics to solve chess problems, whereas the trainers (school teachers) of the other group did not teach any chess-specific problem-solving heuristic.Results:The results showed that the chess instructors’ group outperformed the other two groups in mathematical problem-solving ability, whereas no difference was found between the school teachers' and the control groups.Conclusions:These results foster the hypothesis that a specific type of chess training improves children’s mathematical skills, and uphold the idea that teaching general heuristics is an effective way to promote transfer of learning.

Expert vs. novice differences in the detection of relevant information during a chess game: evidence from eye movements.

The present study explored the ability of expert and novice chess players to rapidly distinguish between regions of a chessboard that were relevant to the best move on the board, and regions of the board that were irrelevant. Accordingly, we monitored the eye movements of expert and novice chess players, while they selected white's best move for a variety of chess problems. To manipulate relevancy, we constructed two different versions of each chess problem in the experiment, and we counterbalanced these versions across participants. These two versions of each problem were identical except that a single piece was changed from a bishop to a knight. This subtle change reversed the relevancy map of the board, such that regions that were relevant in one version of the board were now irrelevant (and vice versa). Using this paradigm, we demonstrated that both the experts and novices spent more time fixating the relevant relative to the irrelevant regions of the board. However, the experts were faster at detecting relevant information than the novices, as shown by the finding that experts (but not novices) were able to distinguish between relevant and irrelevant information during the early part of the trial. These findings further demonstrate the domain-related perceptual processing advantage of chess experts, using an experimental paradigm that allowed us to manipulate relevancy under tightly controlled conditions.

Analysis of Performance of Consultation Methods in Computer Chess

The performance of consultation methods, i.e., majority voting, the optimistic selection rule, and the pseudo-random number (PRN) ensemble method, are examined in computer chess using 2180 chess problems. Here, the optimistic selection rule selects a program that returns the highest search value, and the PRN ensemble consists of multiple individual copies of one base program, and each copy is diversified by adding random numbers to the evaluation function of the base program. We carried out empirical experiments by using state-of-the-art chess-program Crafty as the base program. We found that the percentage of correct answers increased from 55.6 to 57.1% using optimistic selection from the PRN ensemble. The experimental results indicated that the consultation methods allowed simple yet effective distributed computing in chess.

The appearance of the characteristic features of the mathematical thinking in the thinking of a chess player

It is more and more important in 21st century's education that not only facts and subject knowledge should be taught but also the ways and methods of thinking should be learnt by students. Thinking is a human specificity which is significant both in mathematics and chess. The exercises aimed at beginner chess players are appropriate to demonstrate to students the mathematical thinking of 12-14 year-old students. Playing chess is an abstract activity. During the game we use abstract concepts (e.g. sacrifice, stalemate). When solving a chess problem we use logical quantifiers frequently (e.g. in the case of any move of white, black has a move that...). Among the endgames we find many examples (e.g. exceptional draw options) that state impossibility. Affirmation of existence is frequent in a mate position with many moves. We know there is a mate but the question in these cases is how it can be delivered. We present the chess problem on beginners' level although these exercises appear in the game of advanced players and chess masters too, in a more complex form. We chose the mathematical tasks from arithmetic, number theory, geometry and the topic of equations. Students encounter these in classes, admission exams and student circles. Revealing the common features of mathematical and chess thinking shows how we can help the development of students' mathematical skills with the education of chess.

The Mechanisms and Boundary Conditions of the Einstellung Effect in Chess: Evidence from Eye Movements

In a wide range of problem-solving settings, the presence of a familiar solution can block the discovery of better solutions (i.e., the Einstellung effect). To investigate this effect, we monitored the eye movements of expert and novice chess players while they solved chess problems that contained a familiar move (i.e., the Einstellung move), as well as an optimal move that was located in a different region of the board. When the Einstellung move was an advantageous (but suboptimal) move, both the expert and novice chess players who chose the Einstellung move continued to look at this move throughout the trial, whereas the subset of expert players who chose the optimal move were able to gradually disengage their attention from the Einstellung move. However, when the Einstellung move was a blunder, all of the experts and the majority of the novices were able to avoid selecting the Einstellung move, and both the experts and novices gradually disengaged their attention from the Einstellung move. These findings shed light on the boundary conditions of the Einstellung effect, and provide convergent evidence for Bilalić, McLeod, & Gobet (2008)’s conclusion that the Einstellung effect operates by biasing attention towards problem features that are associated with the familiar solution rather than the optimal solution.

Nabokov as Translator: Passion and Precision

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What chess games and chess problems tell us about digital games and art

This article examines the relationship between chess games and chess problems (‘compositions’) in order to describe the chess problem as art. Arguing that the chess problem is a manipulation of game form guided by human aesthetic principles (e.g. Schiller's ‘beauty’ and Wimsatt's ‘human condition’), the article draws a parallel between art derived from games and art derived from nature. This parallel has important implications in circumstances where a natural world is replaced by a virtual world and nature is, in some sense, ‘lost’ to the artist. The article argues that, in such circumstances, the interactive and ‘concreative’ nature of digital media – particularly digital games – allows for unabated aesthetic production.

The role of intuition and deliberative thinking in experts’ superior tactical decision-making

Current theories argue that human decision making is largely based on quick, automatic, and intuitive processes that are occasionally supplemented by slow controlled deliberation. Researchers, therefore, predominantly studied the heuristics of the automatic system in everyday decision making. Our study examines the role of slow deliberation for experts who exhibit superior decision-making outcomes in tactical chess problems with clear best moves. Our study uses advanced computer software to measure the objective value of actions preferred at the start versus the conclusion of decision making. It finds that both experts and less skilled individuals benefit significantly from extra deliberation regardless of whether the problem is easy or difficult. Our findings have important implications for the role of training for increasing decision making accuracy in many domains of expertise.

Knowledge Discovery in Chess Using an Aesthetics Approach

Computational aesthetics is a relatively new subfield of artificial intelligence (AI). It includes research that enables computers to “recognize” (and evaluate) beauty in various domains such as visual art, music, and games. Aside from the benefit this gives to humans in terms of creating and appreciating art in these domains, there are perhaps also philosophical implications about the nature and “mechanics” of aesthetic perception in humans. We can, potentially, learn more about ourselves as we replicate or simulate this ability in machines. My original intention or objective was to develop an aesthetics model or method for computers to recognize beauty in the game of chess since it is greatly appreciated by human players1—there is even an entire subdomain devoted to it in the form of chess compositions2—and because it has other promising applications, such as improving computer chess heuristics, for example, in solving complex chess problems. My intention was also that this model should correlate positively and reasonably well with human player aesthetic assessment. Both were achieved with better experimentally validated success than previous approaches.3 A computer program called CHESTHETICA (see appendix) was developed to aid in the complex calculations involved. It can identify beautiful combinations4 in large databases of chess games based on the aesthetics model.5

Reduced caudate volume and enhanced striatal-DMN integration in chess experts

The superior capability of chess experts largely depends on quick automatic processing skills which are considered to be mediated by the caudate nucleus. We asked whether continued practice or rehearsal of the skill over a long period of time can lead to structural changes in this region. We found that, comparing to novice controls, grandmaster and master level Chinese chess players (GM/Ms), who had a mean period of over 10years of tournament and training practice, exhibited significant smaller gray-matter volume in the bilateral caudate nuclei. When these regions were used as seeds in functional connectivity analysis in resting-state fMRI, significantly enhanced integration was found in GM/Ms between the caudate and the default mode network (DMN), a constellation of brain areas important for goal-directed cognitive performance and theory of mind. These findings demonstrate the structural changes in the caudate nucleus in response to its extensive engagement in chess problem solving, and its enhanced functional integration with widely distributed circuitry to better support high-level cognitive control of behavior.

Famous puzzles of great mathematicians

This entertaining book presents a collection of 180 famous mathematical puzzles and intriguing elementary problems that great mathematicians have posed, discussed, and/or solved. The selected problems do not require advanced mathematics, making this book accessible to a variety of readers. Mathematical recreations offer a rich playground for both amateur and professional mathematicians. Believing that creative stimuli and aesthetic considerations are closely related, great mathematicians from ancient times to the present have always taken an interest in puzzles and diversions. The goal of this book is to show that famous mathematicians have all communicated brilliant ideas, methodological approaches, and absolute genius in mathematical thoughts by using recreational mathematics as a framework. Concise biographies of many mathematicians mentioned in the text are also included. The majority of the mathematical problems presented in this book originated in number theory, graph theory, optimization, and probability. Others are based on combinatorial and chess problems, while still others are geometrical and arithmetical puzzles. This book is intended to be both entertaining as well as an introduction to various intriguing mathematical topics and ideas. Certainly, many stories and famous puzzles can be very useful to prepare classroom lectures, to inspire and amuse students, and to instill affection for mathematics.

Introduction

I n t r o d u c t i o n David H. J. Larmour T E X A S T E C H U N I V E R S I T Y These were images that Franz usually held at bay but that always kept swarming in the background of his life greeting with ahysterical spasm any new impression that was kin to them. After ashock of that sort in those still recent days he would throw himself prone on his bed and try to fight off the fit of nausea. Vladimir Nabokov, King, Queen, Knave In this collection of articles by four eminent scholars who have distinguished themselves in both Nabokovian studies and Russian literature we present read¬ ings of The Defense (1930) by Catharine Nepomnyashchy, of Pnin (1957) by Irene Masing-Delic, of Lolita (1955) by Zsuzsa Het^nyi, and of Pale Fire (1962) in con¬ junction with Nabokov’s translation of Eugene Onegin (1964) by Julia Trubikhina. Anumber of other texts are brought into consideration by these authors, ranging from Freud’s “The Uncanny” {Das Unheimlich), which in turn treats E. T.A. Hoff¬ mann’s “The Sandman,” through Pushkin’s Tsar Saltan and The Tales of Belkin, to Virgil’sAeneid,theHomericHymntoDemeter,andthecorpusofGreekmythol¬ ogy.EacharticleproceedsbydrawingoneofNabokov’smostcelebratednovels into aclose and revealing association with other texts—from elsewhere in this author’s compendious oeuvre and from sources of pointed intertextual rele¬ vance—as well as with the analyses of several well-known Nabokovian critics. In her “King, Queen, Sui-mate: Nabokov’s Defense against Freud’s ‘Uncanny,’” Catharine Nepomnyashchy takes up the long-running controversy surrounding Nabokov’s attitude to Freud. Nabokov himself chose to bring this issue to the fore, by means of his frequent expressions of hostility to “the Viennese Quack” and his followers.QuotingfromthePrefacetoTheDefense,vnthitssymptomatic“words ofencouragementtotheViennesedelegation,”Nepomnyashchymovesbeyond the obvious—that such statements guarantee the “infection of the Nabokovian text by Freud”—to set the author’s attempts to inoculate both himself and his texts inthecontextofthehermeneuticchallengesposedbyFreudandotherstothe authority of the modernist author. She then looks for evidence that Nabokov may have read Freud’s “Das Unheimlich,” published in 1919 and goes on to make the casethatTheDefenseof1929canbereadasa“serious,ifanxiousandambivalent” responsetothatessay.WhenLuzhinexperiencestheUncanny,hehasthedefinite sense that he is repeating apast action, that somehow “this has all happened before”—for example, when he reveals to his father his skill in chess and is taken uptotheattictofindthechessboard.Nepomnyashchyhomesinonthepassagein Intertcxts,Vo\. 12,No. 1-2 2008 ©Texas Tech Univcrsir)'Press I N T E R T E X T S 4 Nabokov’s Preface to the English translation of The Defense, in which the struc¬ tural exploitation of chess designs in the novel is made clear: “The entire sequence of moves in these three central chapters reminds me—or should remind one—of acertain kind of chess problem where the point is not merely the finding of a mate in so many moves, but what is termed ‘retrograde analysis’ [. ..]” This “ret¬ rograde analysis,’’-she argues, is analogous to Freud’s nachtrdglichkeit and suggests that Nabokov’s peach stone—“the stone of the peach Iplucked in my own walled garden” (Preface, 11) which he “gave” to Luzhin and which reappears when he turns out his pockets (252)—is “a metonym for the incarnation of unrepeatable individuahty in the very texture of literature.” This peach kernel, according to Irene Masing-Delic in her “Belkin, Belochkiny, and Belka Chudo-Divo: Pushkin’s ‘The Fairytale of Czar Saltan’ in Nabokov’s Pnin” “would seem to be the ‘object’ that the squirrel holds in its paws on the screen contemplated by the sick boy Pnin” during his bout of influenza (Pnin, 312). As such, it figures as acritical point of entry into the complex web of allusions to squirrels in that novel, while simultaneously recalling The Defense (which was published in English translation, with the added Introduction in 1964) and its walled garden of the author’s secrets. In an echo of the “retrograde analysis” discussed by Nepomnyashchy, Masing-Delic shows how Pnin attempts to unravel the meaning of the pattern of squirrel references in the text, thereby inviting the reader to do the same. Noting the symbolism of the name Mira Belochkina (who perished in...

Evaluation of Economy in a Zero-sum Perfect Information Game

A zero-sum perfect information game is one where every player knows all the moves. Chess is a good example where the object is to checkmate or capture the enemy king. One important feature of checkmates, especially in chess problem composition, is economy. This paper proposes a computational function to evaluate the economy of checkmate configurations on the chessboard. Several experiments were performed comparing chess compositions and regular games to validate the function. The results suggest that the proposed evaluation function is able to correctly discern economical differences in checkmate positions to a high degree of statistical significance and correlates positively with the perception of human chess players. This evaluation function can therefore be useful in increasing the versatility of chess database search engines, as a component in aesthetic models of chess and aiding judges in chess composition tournaments.

How to beat Capablanca

We consider the chess problem of checkmating a king with a king and a rook on an m × n board at a specific starting position. We analyze the fastest way to checkmate.

A DEEP IMPROVER OF TWO-MOVE CHESS MATE PROBLEMS

Computer composition of high-quality chess mate problems is relatively an uninvestigated research domain. A previous model, called an Improver of Chess Problems, which is based on a hill-climbing search, improved slightly the quality of 10 out of 36 known problems (about 28%). In this article, we describe an improved model, called Deep Improver of Chess Problems. This model uses an improved version of Bounded Depth First Search. The experiment, we carry out on the same problems, show that the quality of 32 problems (about 89%) has been improved. Moreover, some of the improvements are meaningful and impressive.

Planning abilities and chess: A comparison of chess and non‐chess players on the Tower of London task

Playing chess requires problem-solving capacities in order to search through the chess problem space in an effective manner. Chess should thus require planning abilities for calculating many moves ahead. Therefore, we asked whether chess players are better problem solvers than non-chess players in a complex planning task. We compared planning performance between chess ( N=25) and non-chess players ( N=25) using a standard psychometric planning task, the Tower of London (ToL) test. We also assessed fluid intelligence (Raven Test), as well as verbal and visuospatial working memory. As expected, chess players showed better planning performance than non-chess players, an effect most strongly expressed in difficult problems. On the other hand, they showed longer planning and movement execution times, especially for incorrectly solved trials. No differences in fluid intelligence and verbal/visuospatial working memory were found between both groups. These findings indicate that better performance in chess players is associated with disproportionally longer solution times, although it remains to be investigated whether motivational or strategic differences account for this result.

Evaluating and Choosing Journals and Editors – A Guide for Authors

Evaluating and Choosing Journals and Editors – A Guide for Authors

New Directions in Enumerative Chess Problems

Normally a chess problem must have a unique solution, and is deemed unsound even if there are alternatives that differ only in the order in which the same moves are played. In an enumerative chess problem, the set of moves in the solution is (usually) unique but the order is not, and the task is to count the feasible permutations via an isomorphic problem in enumerative combinatorics. Almost all enumerative chess problems have been "series-movers"$\!$, in which one side plays an uninterrupted series of moves, unanswered except possibly for one move by the opponent at the end. This can be convenient for setting up enumeration problems, but we show that other problem genres also lend themselves to composing enumerative problems. Some of the resulting enumerations cannot be shown (or have not yet been shown) in series-movers.

Chess Tableaux

A chess tableau is a standard Young tableau in which, for all $i$ and $j$, the parity of the entry in cell $(i,j)$ equals the parity of $i+j+1$. Chess tableaux were first defined by Jonas Sjöstrand in his study of the sign-imbalance of certain posets, and were independently rediscovered by the authors less than a year later in the completely different context of composing chess problems with interesting enumerative properties. We prove that the number of $3\times n$ chess tableaux equals the number of Baxter permutations of $n-1$, as a corollary of a more general correspondence between certain three-rowed chess tableaux and certain three-rowed Dulucq-Guibert nonconsecutive tableaux. The correspondence itself is proved by means of an explicit bijection. We also outline how lattice paths, or rat races, can be used to obtain generating functions for chess tableaux. We conclude by explaining the connection to chess problems, and raising some unanswered questions, e.g., there are striking numerical coincidences between chess tableaux and the Charney-Davis statistic; is there a combinatorial explanation?