Hubbry Logo
Chess theoryChess theoryMain
Open search
Chess theory
Community hub
Chess theory
logo
8 pages, 0 posts
0 subscribers
Be the first to start a discussion here.
Be the first to start a discussion here.
Chess theory
Chess theory
Chess theory
View on Wikipedia
from Wikipedia
Chess initial position

The game of chess is commonly divided into three phases: the opening, middlegame, and endgame.[1] There is a large body of theory regarding how the game should be played in each of these phases, especially the opening and endgame. Those who write about chess theory, who are often also eminent players, are referred to as "chess theorists" or "chess theoreticians".

"Opening theory" commonly refers to consensus, broadly represented by current literature on the openings.[2] "Endgame theory" consists of statements regarding specific positions, or positions of a similar type, though there are few universally applicable principles.[3] "Middlegame theory" often refers to maxims or principles applicable to the middlegame.[4] The modern trend, however, is to assign paramount importance to analysis of the specific position at hand rather than to general principles.[5]

The development of theory in all of these areas has been assisted by the vast literature on the game. In 1913, preeminent chess historian H. J. R. Murray wrote in his 900-page magnum opus A History of Chess that, "The game possesses a literature which in contents probably exceeds that of all other games combined."[6] He estimated that at that time the "total number of books on chess, chess magazines, and newspapers devoting space regularly to the game probably exceeds 5,000".[7] In 1949, B. H. Wood estimated that the number had increased to about 20,000.[8][9] David Hooper and Kenneth Whyld wrote in 1992 that, "Since then there has been a steady increase year by year of the number of new chess publications. No one knows how many have been printed..."[8] The world's largest chess library, the John G. White Collection[10] at the Cleveland Public Library, contains over 32,000 chess books and serials, including over 6,000 bound volumes of chess periodicals.[11][12] Chess players today also avail themselves of computer-based sources of information.

Opening theory

[edit]
This section uses algebraic notation to describe chess moves.
Further information: Chess opening
Early printed work on chess theory by Luis Ramirez de Lucena c. 1497

The earliest printed work on chess theory whose date can be established with some exactitude is Repeticion de Amores y Arte de Ajedrez by the Spaniard Luis Ramirez de Lucena, published c. 1497, which included among other things analysis of eleven chess openings. Some of them are known today as the Giuoco Piano, Ruy Lopez, Petrov's Defense, Bishop's Opening, Damiano's Defense, and Scandinavian Defense, though Lucena did not use those terms.[13]

The authorship and date of the Göttingen manuscript are not established,[14][15] and its publication date is estimated as being somewhere between 1471 and 1505.[16] It is not known whether it or Lucena's book was published first.[14] The manuscript includes examples of games with the openings now known as Damiano's Defence, Philidor's Defense, the Giuoco Piano, Petrov's Defense, the Bishop's Opening, the Ruy Lopez, the Ponziani Opening, the Queen's Gambit Accepted, 1.d4 d5 2.Bf4 Bf5 (a form of the London System), Bird's Opening, and the English Opening.[17] Murray observes that it "is no haphazard collection of commencements of games, but is an attempt to deal with the Openings in a systematic way."[18]

Fifteen years after Lucena's book, Portuguese apothecary Pedro Damiano published the book Questo libro e da imparare giocare a scachi et de la partiti (1512) in Rome. It includes analysis of the Queen's Gambit Accepted, showing what happens when Black tries to keep the gambit pawn with ...b5.[19] Damiano's book "was, in contemporary terms, the first bestseller of the modern game."[20] Harry Golombek writes that it "ran through eight editions in the sixteenth century and continued on into the next century with unflagging popularity."[21] Modern players know Damiano primarily because his name is attached to the weak opening Damiano's Defense (1.e4 e5 2.Nf3 f6?), although he condemned rather than endorsed it.[22]

These books and later ones discuss games played with various openings, opening traps, and the best way for both sides to play. Certain sequences of opening moves began to be given names, some of the earliest being Damiano's Defense, the King's Gambit (1.e4 e5 2.f4), the Queen's Gambit (1.d4 d5 2.c4), and the Sicilian Defense (1.e4 c5).[23]

Damiano's book was followed by general treatises on chess play by Ruy López de Segura (1561), Giulio Cesare Polerio (1590), Pietro Carrera (1617), Gioachino Greco (c. 1625), Joseph Bertin (1735), and François-André Danican Philidor (1749).[24][25]

The first author to attempt a comprehensive survey of the openings then known was Aaron Alexandre in his 1837 work Encyclopédie des Échecs.[26] According to Hooper and Whyld, "[Carl] Jaenisch produced the first openings analysis on modern lines in his Analyse nouvelle des ouvertures (1842-43)."[27] In 1843, Paul Rudolf von Bilguer published the German Handbuch des Schachspiels, which combined the virtues of Alexandre and Jaenisch's works.[27] The Handbuch, which went through several editions, last being published in several parts in 1912–16, was one of the most important opening references for many decades.[28] The last edition of the Handbuch was edited by Carl Schlechter, who had drawn a match for the World Championship with Emanuel Lasker in 1910. International Master William Hartston called it "a superb work, perhaps the last to encase successfully the whole of chess knowledge within a single volume."[29]

The English master Howard Staunton, perhaps the world's strongest player from 1843 to 1851,[30] included over 300 pages of analysis of the openings in his 1847 treatise The Chess Player's Handbook.[31] That work immediately became the standard reference work in English-speaking countries,[32][33] and was reprinted 21 times by 1935.[34] However, "as time passed a demand arose for more up-to-date works in English".[35] Wilhelm Steinitz, the first World Champion, widely considered the "father of modern chess,"[36][37][38][39] extensively analyzed various double king-pawn openings (beginning 1.e4 e5) in his book The Modern Chess Instructor, published in 1889 and 1895.[40] Also in 1889, E. Freeborough and C. E. Ranken published the first edition of Chess Openings Ancient and Modern; later editions were published in 1893, 1896, and 1910.[41] In 1911, R. C. Griffith and J. H. White published the first edition of Modern Chess Openings. It is now the longest-published opening treatise in history; the fifteenth edition (commonly called MCO-15), by Grandmaster Nick de Firmian, was published in April 2008.[42]

According to Hooper and Whyld, the various editions of Modern Chess Openings, the last edition of the Handbuch, and the fourth edition of Ludvig Collijn's Lärobok i Schack ("Textbook of Chess") in Swedish, with groundbreaking contributions by Rubinstein, Reti, Spielmann and Nimzowitch, "were the popular reference sources for strong players between the two world wars."[35] In 1937–39 former World Champion Max Euwe published a twelve-volume opening treatise, De theorie der schaakopeningen, in Dutch. It was later translated into other languages.[43]

In the late 1930s to early 1950s Reuben Fine, one of the world's strongest players,[44] also became one of its leading theoreticians, publishing important works on the opening, middlegame, and endgame. These began with his revision of Modern Chess Openings, which was published in 1939.[45] In 1943, he published Ideas Behind the Chess Openings, which sought to explain the principles underlying the openings.[46] In 1948, he published his own opening treatise, Practical Chess Openings, a competitor to MCO.[47] In 1964, International Master I.A. Horowitz published the 789-page tome Chess Openings: Theory and Practice, which in addition to opening analysis includes a large number of illustrative games.[24]

In 1966, the first volume of Chess Informant was published in Belgrade, Yugoslavia, containing 466 annotated games from the leading chess tournaments and matches of the day.[48] The hugely influential Chess Informant series has revolutionized opening theory. Its great innovation is that it expresses games in languageless figurine algebraic notation and annotated them using no words, but rather seventeen symbols, whose meanings were explained at the beginning of the book in six different languages. This enabled readers around the world to read the same games and annotations, thus greatly accelerating the dissemination of chess ideas and the development of opening theory. The editors of Chess Informant later introduced other publications using the same principle, such as the five-volume Encyclopedia of Chess Openings and Encyclopedia of Chess Endings treatises. Chess Informant was originally published twice a year, and since 1991 has been published thrice annually. Volume 100 was published in 2007.[49] It now uses 57 symbols, explained in 10 languages, to annotate games (see Punctuation (chess)), and is available in both print and electronic formats. In 2005, former World Champion Garry Kasparov wrote, "We are all Children of the Informant."[50]

In the 1990s and thereafter, the development of opening theory has been further accelerated by such innovations as extremely strong chess engines such as Fritz and Rybka, software such as ChessBase, and the sale of multi-million-game databases such as ChessBase's Mega 2013 database, with over 5.4 million games.[51] Today, the most important openings have been analyzed over 20 moves deep,[52] sometimes well into the endgame,[53][54] and it is not unusual for leading players to introduce theoretical novelties on move 25 or even later.[55][56][57]

Thousands of books have been written on chess openings. These include both comprehensive openings encyclopedias such as the Encyclopedia of Chess Openings and Modern Chess Openings; general treatises on how to play the opening such as Mastering the Chess Openings (in four volumes), by International Master John L. Watson;[58] and myriad books on specific openings, such as Understanding the Grünfeld[59] and Chess Explained: The Classical Sicilian.[60] "Books and monographs on openings are popular, and as they are thought to become out of date quickly there is a steady supply of new titles."[61] According to Andrew Soltis, "Virtually all the new information about chess since 1930 has been in the opening."[62]

Middlegame theory

[edit]
Further information: Chess middlegame
Aron Nimzowitsch

Middlegame theory is considerably less developed than either opening theory or endgame theory.[63] Watson writes, "Players wishing to study this area of the game have a limited and rather unsatisfactory range of resources from which to choose."[64]

One of the earliest theories to gain attention was that of William Steinitz, who posited that a premature attack against one's opponent in an equal position could be repelled by skillful defence, and so a player's best bet was to slowly maneuver with the goal of accumulating small advantages. Emanuel Lasker in Lasker's Manual of Chess and Max Euwe in The Development of Chess Style outlined theories that they attributed to Steinitz.

Leading player and theorist Aron Nimzowitsch's[65] influential books, My System (1925),[66] Die Blockade (1925) (in German),[67] and Chess Praxis (1936),[68][69] are among the most important works on the middlegame.[64] Nimzowitsch called attention to the possibility of letting one's opponent occupy the centre with pawns while you exert control with your pieces as in the Nimzo-Indian or Queen's Indian defences. He pointed out how in positions with interlocking pawn chains, one could attack the chain at its base by advancing one's own pawns and carrying out a freeing move (pawn break). He also drew attention to the strategy of occupying open files with one's rooks in order to later penetrate to the seventh rank where they could attack the enemy pawns and hem in the opponent's king. Another of his key concepts was prophylaxis, moves aimed at limiting the opponent's mobility to the point where he would no longer have any useful moves.

In 1952, Fine published the 442-page The Middle Game in Chess, perhaps the most comprehensive treatment of the subject up until that time.[70] The mid-20th century also saw the publication of The Middle Game, volumes 1 and 2, by former World Champion Max Euwe and Hans Kramer,[71][72] and a series of books by the Czechoslovak-German grandmaster Luděk Pachman: three volumes of Complete Chess Strategy,[73][74][75] Modern Chess Strategy,[76] Modern Chess Tactics,[77] and Attack and Defense in Modern Chess Tactics.[78]

Another key turning point in middlegame theory came with the release of Alexander Kotov's book Think like a Grandmaster in 1971. Kotov outlined how a player calculates by developing a tree of variations in his head, and recommended that players only examine each branch of the tree once. He also noted how some players seem to fall victim to what is now known as Kotov's Syndrome: they calculate out a large range of different lines, become dissatisfied with the result, and realizing that they are short on time, play a completely new candidate move without even checking whether it is sound. More recently, Jonathan Tisdall, John Nunn and Andrew Soltis have elaborated on Kotov's tree theory further.

In 1999, Watson's Secrets of Modern Chess Strategy: Advances Since Nimzowitsch was published, in which Watson discusses the revolution in middlegame theory that has occurred since Nimzowitsch's time.[79]

Many books on specific aspects of the middlegame exist, such as The Art of Attack in Chess by Vladimir Vuković,[80] The Art of Sacrifice in Chess by Rudolf Spielmann,[81] The Art of the Checkmate by Georges Renaud and Victor Kahn,[82] The Basis of Combination in Chess by J. du Mont,[83] and The Art of Defense in Chess by Andrew Soltis.[84]

Endgame theory

[edit]
Further information: Chess endgame

Many significant chess treatises, beginning with the earliest works, have included some analysis of the endgame. Lucena's book (c. 1497) concluded with 150 examples of endgames and chess problems.[85]

The second edition (1777) of Philidor's Analyse du jeu des Échecs devoted 75 pages of analysis to various endgames.[86] These included a number of theoretically important endings, such as rook and bishop versus rook, queen versus rook, queen versus rook and pawn, and rook and pawn versus rook. Certain positions in the endings of rook and bishop versus rook, rook and pawn versus rook, and queen versus rook have become known as Philidor's position. Philidor concluded his book with two pages of (in the English translation), "Observations on the ends of parties", in which he set forth certain general principles about endings, such as: "Two knights alone cannot mate" (see Two knights endgame), the ending with a bishop and rook pawn whose queening square is on the opposite color from the bishop is drawn (see Wrong rook pawn § Bishop and pawn), and a queen beats a bishop and knight (see Pawnless chess endgame § Queen versus two minor pieces).[87]

Staunton's The Chess-Player's Handbook (1847) includes almost 100 pages of analysis of endgames.[88] Some of Staunton's analysis, such as his analysis of the very rare rook versus three minor pieces endgame, is surprisingly sophisticated. At page 439, he wrote, "Three minor Pieces are much stronger than a Rook, and in cases where two of them are Bishops will usually win without much difficulty, because the player of the Rook is certain to be compelled to lose him for one of his adversary's Pieces. If, however, there are two Knights and one Bishop opposed to a Rook, the latter may generally be exchanged for the Bishop, and as two Knights are insufficient of themselves to force checkmate, the game will be drawn." Modern-day endgame tablebases confirm Staunton's assessments of both endings.[89] Yet Reuben Fine, 94 years after Staunton, erroneously wrote on page 521 of Basic Chess Endings that both types of rook versus three minor piece endings "are theoretically drawn." Grandmaster Pal Benko, an authority on the endgame and like Fine a world-class player at his peak, perpetuated Fine's error in his 2003 revision of Basic Chess Endings.[90] Grandmaster Andrew Soltis in a 2004 book expressly disagreed with Staunton, claiming that the rook versus two bishops and knight ending is drawn with correct play.[91] At the time Benko and Soltis offered their assessments (in 2003 and 2004, respectively), endgame tablebases had already proven that Staunton was correct, and that Fine, Benko, and Soltis were wrong, although the ending can take up to 68 moves to win.[92]

Staunton's conclusions on these endgames were anticipated by the British master George Walker, who wrote in 1846 (and perhaps earlier):

Although the two Bishops and Kt win, as a general proposition, against Rook, yet the two Knights with a Bishop cannot expect the same success; and the legitimate result of such conflict would be a draw. The Bishops, united, are stronger than the Knights, as they strike from a greater distance. When the two Knights are left with a Bishop, the Rook has also the chance of exchanging for the latter, which can hardly be avoided by his adversary, and the two Knights, alone, have not the mating power.[93]

In 1941 Reuben Fine published his monumental 573-page treatise Basic Chess Endings, the first attempt at a comprehensive treatise on the endgame.[94] A new edition, revised by Pal Benko, was published in 2003.[95] Soviet writers published an important series of books on specific endings: Rook Endings by Grigory Levenfish and Vasily Smyslov,[96] Pawn Endings by Yuri Averbakh and I. Maizelis,[97] Queen and Pawn Endings by Averbakh,[98] Bishop Endings by Averbakh,[99] Knight Endings by Averbakh and Vitaly Chekhover,[100] Bishop v. Knight Endings by Yuri Averbakh,[101] Rook v. Minor Piece Endings by Averbakh,[102] and Queen v. Rook/Minor Piece Endings by Averbakh, Chekhover, and V. Henkin.[103] These books by Averbakh and others were collected into the five-volume Comprehensive Chess Endings in English.

In recent years, computer-generated endgame tablebases have revolutionized endgame theory, conclusively showing best play in many complicated endgames that had vexed human analysts for over a century, such as queen and pawn versus queen. They have also overturned human theoreticians' verdicts on a number of endgames; for example by proving that the two bishops versus knight ending, which had been thought drawn for over a century, can be a win for the bishops (see Pawnless chess endgame § Minor pieces only and Chess endgame § Effect of tablebases on endgame theory).

Several important works on the endgame have been published in recent years, among them Dvoretsky's Endgame Manual,[104] Fundamental Chess Endings by Karsten Müller and Frank Lamprecht,[89] Basic Endgames: 888 Theoretical Positions by Yuri Balashov and Eduard Prandstetter,[105] Chess Endgame Lessons by Benko,[106] and Secrets of Rook Endings[107] and Secrets of Pawnless Endings by John Nunn.[108] Some of these have been aided by analysis from endgame tablebases.

See also

[edit]

References

[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Chess theory

View on Grokipedia
from Grokipedia
Chess theory encompasses the systematic study and accumulated principles of chess play, focusing on optimal decision-making across the game's phases—openings, middlegame, and endgame—to achieve strategic advantages and ultimately victory or a draw. Central to chess theory is the evaluation of positions through five key elements: material balance (the relative value of pieces), (the configuration and potential of pawns), (control over squares on the board), time (development and ), and king safety (protection of the monarch). These elements inform both tactical combinations—short-term sequences exploiting immediate opportunities—and long-range strategies that shape the game's course. In the opening phase, theory emphasizes initial moves to control , develop pieces efficiently, and safeguard the king, with variations classified in authoritative references like the Encyclopedia of Chess Openings (ECO), which organizes thousands of lines into a standardized coding system for analysis and study. The middlegame builds on these foundations, integrating tactics such as pins, forks, and discovered attacks with positional motifs like outposts and weak squares, often guided by honed through extensive practice. Endgame theory, by contrast, deals with simplified positions where precise calculation becomes paramount, relying on techniques for pawn promotion, activity, and opposition, as explored through to determine winning probabilities in specific configurations. Historical development traces back to the , when François-André Philidor advanced the idea that "pawns are the soul of chess," prioritizing central control, a concept refined by 19th-century innovators like , who formalized positional principles as the foundation of modern theory. Today, chess theory evolves with computational tools and , enabling deeper analysis while underscoring the procedural rationality of human play—balancing limited search depth with vast stored knowledge—amid the game's immense of approximately 10^120 possible games.

Introduction

Definition and Scope

Chess theory constitutes the systematic body of knowledge regarding optimal moves and strategies in chess, derived from rigorous analysis of positions across the game's three primary phases: opening, middlegame, and endgame. This encompasses principles for achieving and maintaining advantages, informed by centuries of player experiences and analytical scrutiny rather than mere . The scope of chess theory includes analytical methods like exhaustive variation , for identifying recurring tactical and strategic motifs, and the formulation of evaluation functions to quantify positional merits. Unlike casual play, which relies on decisions, or psychological elements such as bluffing and pressure tactics, chess theory prioritizes objective assessment of board states to guide decision-making. Central to this framework are evaluations divided into static and dynamic components: static factors assess enduring features like material imbalance and , which influence long-term control and weaknesses; dynamic factors, including initiative, development tempo, and piece activity, capture transient opportunities that can shift momentum rapidly.

Historical Development

The historical development of chess theory began in 15th- and 16th-century , where informal studies and modish play among laid the groundwork for systematic analysis. The earliest printed on modern chess rules and appeared in 1497 with Luis Ramírez de Lucena's Repetiçión de Amores y Artes de Axedrez, which included 101 sample games and emphasized tactical maneuvers in the emerging variant of the game that had spread from . This work marked the transition from medieval to the queen's gambit-influenced European chess, fostering initial theoretical exploration through practical examples rather than abstract principles. By the , chess theory shifted toward positional understanding, exemplified by François-André Philidor's groundbreaking Analyse du jeu des Échecs (1749), which introduced the iconic maxim "pawns are the soul of chess." Philidor advocated for pawn structures as the foundation of strategy, prioritizing solid formation over aggressive attacks and influencing defensive play for generations. The ushered in the romantic era, characterized by a tactical focus on brilliant combinations and sacrifices, as seen in the games of , whose rapid development and open lines exemplified the era's emphasis on initiative over accumulation. This period's flair gave way to Wilhelm Steinitz's codification of positional principles in The Modern Chess Instructor (1889), where he outlined accumulation of small advantages, control of the center, and development as enduring laws, establishing the classical school that dominated subsequent theory. In the early , the hypermodern school challenged classical dogma by promoting flexible development and control of from afar, as articulated in Aron Nimzowitsch's My System (), which explored concepts like overprotection and to counter occupation. Post-World War II, Soviet theorists asserted dominance through rigorous, scientific approaches, with Alexander Kotov's Think Like a Grandmaster () introducing the "candidate moves" method and analysis tree for objective position evaluation, reflecting the state's emphasis on systematic training that produced multiple world champions.

Fundamental Principles

Positional Concepts

Positional concepts in chess theory revolve around the static and enduring features of a position that influence long-term , emphasizing the achievement of and balance among all elements on the board. These ideas, foundational to evaluation across all game phases, prioritize structural advantages over immediate threats, allowing players to build sustainable edges that can be converted into winning chances. Key among them are space control, , piece coordination, and king safety, each contributing to a cohesive positional framework. Space control refers to the ability to dominate key areas of the board, particularly the central squares, which restricts the opponent's piece mobility and facilitates one's own development. In classical theory, as articulated by , controlling space involves directly occupying the center with pawns on e4 and d4 to establish a strong foothold and cramp the opponent's forces. In contrast, hypermodern approaches, pioneered by , advocate influencing the center indirectly from the flanks using pieces, such as through fianchettoed bishops that exert long-range pressure without immediate pawn advances, allowing for flexible counterplay. This duality in center control theories highlights the tension between aggressive occupation and prophylactic influence, with hypermodern ideas proving effective in openings like the Nimzo-Indian Defense. Pawn structure forms the backbone of positional evaluation, dictating the potential strengths and vulnerabilities of the position. Isolated pawns, lacking support from adjacent pawns, are often weak targets for attack as they cannot be defended by other pawns, though they can control important central squares if advanced. Doubled pawns, situated on the same file, typically hinder piece development by blocking lines and creating exploitable gaps, but they may gain strength in closed positions where they form a passed pawn duo upon capture. Passed pawns, unopposed by enemy pawns on their path to promotion, represent a dynamic asset that can become decisive if supported by pieces, often warranting material sacrifices to advance them. Nimzowitsch emphasized overprotection in pawn structures, where key pawns are defended multiple times to enable aggressive piece play elsewhere. Piece coordination involves harmonizing the activities of one's forces to maximize their collective impact, ensuring that bishops, knights, rooks, and the queen work in tandem rather than in isolation. For instance, placing rooks on open files while knights outpost on supported squares enhances control and pressure, preventing the opponent from reorganizing effectively. safety, meanwhile, demands sheltering the monarch from checks and threats, often by early and avoiding pawn weaknesses around it; an exposed invites tactical disasters, undermining even superior structures. Evaluation principles in positional play account for material imbalances through compensatory features, such as the bishop pair—two bishops operating on opposite colors—which is typically valued at approximately 0.5 pawns higher than two or a bishop and in open positions, due to their ability to control both color complexes and exploit long diagonals. This edge diminishes in crowded boards with many pawns but grows in endgames with reduced material. Prophylaxis, a cornerstone concept introduced by Nimzowitsch, entails anticipating and thwarting the opponent's intended plans before they develop, such as advancing a pawn to block a potential break or repositioning a piece to deny key squares. This preventive mindset contrasts with reactive play, fostering gradual accumulation of advantages. Complementing it is the exploitation of weaknesses, where players fix and target structural flaws—like isolated pawns or unsecured files—through consistent pressure, transforming static inferiorities into concrete gains. These principles apply directly to middlegame by guiding the identification of imbalances for strategic exploitation.

Tactical Elements

Tactical elements in chess theory refer to short-term sequences of forcing moves that exploit immediate opportunities on the board to gain , positional advantage, or , often transforming static positions into dynamic imbalances. These maneuvers rely on precise and , distinguishing them from broader strategic planning by their calculable, threat-based nature. Fundamental tactics form the building blocks, while more complex combinations integrate multiple motifs to overwhelm the opponent. Among the core tactical devices are forks, where a single piece attacks two or more enemy pieces simultaneously, forcing the opponent to choose which to save. Pins immobilize an enemy piece by threatening a more valuable one behind it, preventing movement without exposing the higher-value target; absolute pins target the , while relative pins affect other pieces. Skewers function similarly but in reverse, attacking a valuable piece that must move, thereby exposing a less valuable one behind it to capture. Discovered attacks occur when one piece moves away, uncovering an attack from another piece on the same line, often combining with checks for added force. Deflections lure a defender away from its post, allowing an attack on a newly unprotected target, such as drawing a king or rook from guarding a . Combinations elevate these basics into multi-move sequences, frequently involving to dismantle defenses. The Greek gift sacrifice exemplifies this, where a is offered on h7 (or h2) against a castled , typically followed by and queen involvement to pry open the kingside. forces the opponent into a position where any move worsens their situation, often arising in restricted spaces to compel loss of material or . Interference disrupts enemy lines by blocking a defender's path, such as placing a piece to cut off a rook's support for a pawn chain, enabling breakthroughs elsewhere. Key tactical motifs contextualize these tools, such as overloading, where a single defender guards multiple threats and must abandon one to address another, leading to material loss. Back-rank weaknesses exploit confined kings on the first or eighth rank, vulnerable to rook or queen checks along the rank if no escape squares exist, a motif amplified by pawn structures sealing the rank. These patterns demand vigilant analysis, as players train recognition through repeated exposure to sharpen intuitive calculation during games. A classic recognition pattern is the Arabian mate, where a rook delivers check along the seventh rank while a knight controls escape squares near the cornered king, often concluding simplified positions with decisive force.

Opening Theory

Principles of Development

In the opening phase of a chess game, the principles of development guide players toward establishing a strong position by mobilizing their forces efficiently, laying the groundwork for subsequent play. These guidelines emphasize rapid activation of pieces while minimizing vulnerabilities, ensuring that the player gains initiative without overextending resources. A core principle is controlling the center of the board, typically squares e4, d4, e5, and d5, using pawns and pieces to restrict the opponent's mobility and enhance one's own piece activity. This control maximizes the potential of knights and bishops, allowing them to influence more squares and support future attacks or defenses. Developing minor pieces—knights and bishops—quickly follows, prioritizing their placement toward the center before moving the queen or rooks, as early knight development often precedes bishops to avoid blocking central pawns. Castling early, ideally within the first seven to ten moves, secures the king while activating a rook toward the center, promoting overall coordination. Finally, connecting the rooks by clearing the back rank through piece development and appropriate queen placement enables their potential for file control later in the game. Time serves as a critical resource in the opening, where each move should contribute to development rather than waste on non-essential actions. Excessive pawn moves, particularly on the flanks, can hinder piece mobilization by obstructing lines or creating weaknesses without gaining central influence. Players must balance pawn advances with piece activity to avoid falling behind in development, as the side that coordinates its forces first often seizes the initiative. Common errors undermine these principles, such as premature queen moves that expose the powerful piece to harassment, costing valuable tempi while the opponent develops further. Unnecessary pawn captures early on similarly squander time, as recapturing or responding diverts focus from piece development and may weaken without strategic gain. The theoretical foundation for these principles traces to , the first World Chess Champion, who advocated harmonious development over premature aggressive attacks in his seminal work, emphasizing coordinated piece activity to build lasting positional advantages before launching offensives. This approach shifted chess from romantic-era tactics to modern strategy, influencing opening play by prioritizing sustainable initiative.

Common Openings and Variations

Common chess openings and their variations are systematically classified using the Encyclopedia of Chess Openings (ECO) codes, a standardized alphanumeric system that organizes thousands of lines into five volumes (A–E) based on initial moves, facilitating analysis and study. Open Games, arising after 1.e4 e5 (ECO C20–C99), emphasize rapid development and central control, with White targeting Black's e5 pawn early. The (2.Nf3 Nc6 3.Bc4; ECO C50–C59) focuses on quick piece activity and kingside castling, allowing White to build a strong center while pressuring f7; its main line (3...Bc5 4.c3) supports a future d4 push for space advantage. Historically introduced by 16th-century Italian masters and refined by 19th-century players like , it balances tactical opportunities with solid structure. The (2.Nf3 Nc6 3.Bb5; ECO C60–C99) extends this theme by pinning the knight on c6 to undermine e5 support, promoting long-term pressure on Black's center; it has endured for over 500 years, featuring in modern World Championships like Anand-Carlsen 2013. Key lines include the Closed Defense (3...a6 4.Ba4 Nf6 5.O-O Be7), where Black develops harmoniously but faces White's spatial edge, and the Berlin Defense (3...Nf6 4.O-O Nxe4 5.d4), a solid endgame-oriented variation popularized for its drawing tendencies at elite levels. Theoretical evolution has seen sub-variations like the Zaitsev and Breyer, adapting to White's advances in central play. In Semi-Open Games, Black responds to 1.e4 with alternatives to e5 (ECO B00–B99), seeking asymmetry for counterplay. The Sicilian Defense (1...c5; ECO B20–B99) is Black's most dynamic choice, challenging White's center directly and enabling queenside expansion; it leads to unbalanced positions where Black aims for piece activity over pawn symmetry. The Najdorf Variation (2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 a6) emphasizes flexibility, with Black using ...a6 to control b5 and prepare ...b5 advances, while White often targets kingside weaknesses via 6.Be3 or 6.Bg5 setups. The Dragon Variation (5...g6) fianchettoes the bishop on g7 for diagonal pressure and kingside defense, inviting sharp White attacks like the Yugoslav (6.Be3 Bg7 7.f3), but rewarding Black's counterattacking potential on the queenside. Closed Games follow 1.d4 d5 (ECO D00–D69), promoting symmetrical pawn structures and gradual maneuvering. The (2.c4 e6) sees Black solidify the center with ...e6 while retaining options for development; its flexibility allows transpositions to lines like the Slav or even the Grunfeld, prioritizing a solid pawn chain over immediate equality. White gains space but must navigate Black's potential ...c5 breaks for counterplay. The (2...c6) supports d5 more actively with the c-pawn, enabling free piece development and avoiding the passivity sometimes associated with ...e6 setups; it suits players seeking robust queenside counterchances while maintaining a supported center. Indian Defenses are hypermodern openings (ECO E00–E99) in which Black controls the center indirectly through pieces rather than immediate pawn occupation. The Nimzo-Indian (1.d4 Nf6 2.c4 e6 3.Nc3 Bb4) pins the knight to disrupt White's development, often leading to doubled c-pawns after 4.a3 Bxc3+ but granting Black dynamic dark-square control and counterattacks via ...c5 or ...d5; introduced by , it exemplifies ideas for long-term pressure. The King's Indian (1.d4 Nf6 2.c4 g6) es the kingside bishop, allowing White a broad center before striking with ...e5; Black pursues aggressive kingside assaults (e.g., ...f5 pawn storm), contrasting White's queenside expansion, in a hypermodern framework that influenced 20th-century theory through players like . Opening theory evolved significantly post-1850s, shifting from Romantic-era gambits—speculative sacrifices for rapid attacks, as championed by —to solid, positional lines emphasizing accumulation of small advantages, pioneered by . This transition reflected growing understanding of over tactical fireworks.

Middlegame Theory

Strategic planning in the middlegame involves formulating long-term objectives based on positional imbalances, such as superior , minor piece activity, space advantages, or material considerations, to guide piece maneuvers and pawn advances toward favorable outcomes. Players assess these imbalances to determine which side of the board to emphasize, prioritizing plans that exploit weaknesses like isolated or backward pawns while restricting the opponent's counterplay. For instance, identifying open files allows rooks to infiltrate enemy territory, doubling on semi-open files to pressure pawn weaknesses, as emphasized in classical positional . Weak squares, undefended by pawns and controllable by pieces, serve as outposts for knights or bishops to establish long-term pressure, often dictating the direction of the attack. Pawn breaks are central to plan formulation, aiming to disrupt the opponent's pawn chain and open lines for piece activity; these breaks are timed to coincide with favorable piece placement, creating dynamic imbalances that favor the initiator. Piece redeployment plays a key role in executing these plans, focusing on improving the worst-placed piece—such as rerouting a knight from a cramped edge to a central outpost or transferring a rook to an active file—to target identified weaknesses and enhance overall coordination. This maneuver often involves multi-move transfers across the board, ensuring pieces align with the strategic goals derived from imbalances. Managing the initiative requires balancing aggressive pressure with timely consolidation; players seize the initiative through forcing moves that limit opponent responses but transition to defensive consolidation when threats are neutralized, preventing overextension and preserving advantages for later exploitation. In the , the minority attack exemplifies this by advancing White's queenside pawns (b4-b5, followed by captures) against Black's majority, weakening Black's structure to create isolated pawns and open the c-file for rooks, often leading to long-term pressure despite numerical inferiority. Similarly, in closed positions like the King's Indian Defense, a kingside via pawn storm (...f5, ...g5, ...h5) breaks through White's castled position after a locked center, coordinating pieces like the fianchettoed and rerouted to open files and deliver threats. Tactical execution supports these plans but remains secondary to the underlying strategic framework.

Tactical Combinations

Tactical combinations in the middlegame represent intricate sequences of forcing moves that exploit accumulated positional tensions, frequently resulting in material gains, positional superiority, or . These maneuvers demand precise and foresight, distinguishing them from simpler tactical motifs by their multi-move nature and reliance on the opponent's constrained responses. Unlike straightforward exploits, combinations unfold over several turns, often involving sacrifices to create unstoppable threats that resolve stalled or balanced positions. Among advanced combinations, the windmill tactic involves a series of discovered checks by a rook or queen along a file or rank, compelling the to shuttle back and forth while the attacking side captures unprotected pieces along the way. This rare but devastating , sometimes termed a "seesaw," maximizes material harvest through repeated checks that limit defensive options. The , or intermediate move, introduces an unexpected counter-threat during an opponent's anticipated recapture or response, disrupting their plans and often securing a net advantage such as an extra pawn or piece. pursuits, conversely, aim to force a draw by establishing a cycle of inescapable checks, particularly useful when defending an inferior position by targeting the opponent's exposed . Effective execution of these combinations hinges on deep , modeled as a tree search where players branch through main lines and variations to evaluate outcomes up to 5-10 moves ahead. This process includes candidate move identification, opponent reply anticipation, and safety checks to prune unsafe paths, thereby minimizing blunders like overlooking counterattacks. Blunder avoidance emphasizes verifying forcing sequences for tactical soundness, such as confirming no intermediate escapes for the opponent, which can turn a promising into a loss. A seminal historical example is the Immortal Game between and in 1851, where Anderssen unleashed a series of queen and rook sacrifices in a sacrificial tactic that dismantled Kieseritzky's position, culminating in despite being down significant . This encounter exemplifies how bold combinations can shatter defensive setups through calculated risks. In the middlegame, such tactics play a pivotal role in breaking deadlocked positions by introducing forcing lines that compel responses, transforming static equilibria into dynamic imbalances favorable to the initiator. Positional preparation, as outlined in , often sets the stage for these breakthroughs by creating the necessary imbalances.

Endgame Theory

Basic Endgames

Basic endgames in chess theory revolve around simplified positions involving , pawns, and minor pieces or rooks, where mastery of fundamental techniques like opposition and pawn promotion decides wins or draws. These scenarios emphasize the 's newfound activity in the endgame, contrasting its defensive role earlier, and require precise calculation to exploit material imbalances up to minor pieces. In and pawn versus endgames, the attacking side aims to promote the pawn while the defender seeks to capture it or block promotion. A core concept is opposition, defined as the mutual confrontation of kings on the same rank, file, or diagonal with an odd number of empty squares between them, allowing the player who does not move first to control key areas. For instance, in linear opposition, kings separated by one square enable the side with the move to force the opponent away from the pawn's path. Rectangular opposition, where kings occupy diagonally opposite corners of a same-colored square , also applies, such as in positions like Ke6 versus Kg2. Key squares are critical positions the attacking king must occupy to force promotion, typically the squares immediately in front of the pawn and adjacent ones two ranks ahead, like d6 and e6 for a pawn on d4. Controlling these allows the king to gain opposition or the defender, ensuring the pawn advances safely. The rule of the square provides a quick assessment when the attacking king is distant: imagine a square extending from the pawn to its promotion square (e.g., a 4x4 square for a pawn four files away); if the defending king is outside this square, the pawn promotes without interference, as the king cannot enter in time. Rook endgames introduce more complexity, particularly with a rook and pawn against a lone rook, where positions like and Philidor define winning and drawing strategies. The , a winning setup for the side with the pawn, features the attacking rook shielding its from checks while the pawn advances, achieved by first driving the enemy king from the promotion file (e.g., with Rd1+) and then building a "bridge" by placing the rook on the fourth rank (e.g., Rd4) to protect the king on the sixth rank. This allows the king to approach the pawn safely. Conversely, the Philidor defense offers a drawing resource for the defender in similar rook and pawn versus rook positions, by placing the rook on the third rank to restrict the attacking king's advance and control the promotion file. The key idea is to maintain the rook on the third rank (e.g., Rh3) while the king stays close to the pawn, preventing the attacker from gaining space; for example, after 1. Ke5 Rh5+ 2. Ke4 Rh4+, the rook checks force the king back without allowing progress. This setup, effective against non-rook pawns, can draw even if the attacker has the opposition initially. Minor piece endgames, such as versus , highlight piece preferences based on board structure. The generally outperforms the in open positions, as its long-range mobility allows control over promotion paths and distant squares, whereas the excels in closed or blocked setups where its jumping ability targets weak pawns on the opposite color. For example, in an open endgame, a can dominate by restricting the 's squares and supporting passed pawns. A notable drawing motif in bishop and pawn versus king endgames is the wrong-color bishop, where the bishop cannot control the promotion square of its own pawn—typically occurring with rook pawns (a- or h-file) and a light-squared trying to promote on a dark square. In such cases, the defender's can reach the promotion square first, capturing the pawn or stalemating to , as the attacks only opposite-colored squares and cannot intervene effectively. This loss arises because the pawn's queening square lies on the wrong color for the 's influence, turning a theoretically won position into a . Across basic endgames, general principles guide play: the active king must centralize and support pawn advances or opposition maneuvers to maximize its reach, often by entering the game aggressively rather than passively. In pawn promotion races, the side with the faster or more advanced typically wins unless the opponent can capture or block en route; calculation involves comparing pawn distances while accounting for support, as simultaneous promotions often favor the attacker due to potential captures post-queening. The 50-move rule implies draws in prolonged positions without pawn moves or captures, affecting theoretical evaluations in rook endgames like , where wins may require over 50 moves, but practical play rarely invokes it as shorter paths exist.

Advanced Endgame Techniques

In queen endgames, the defending side often relies on to secure a draw, where the queen repeatedly attacks the opponent's without allowing capture, forcing a repetition of moves. This defensive resource becomes critical when the attacker holds a material advantage but cannot prevent the checks without losing or exposing the . Triangulation, a technique to lose a , enables the attacking to gain the opposition—building on basic opposition principles—allowing it to approach key squares or support a effectively. As detailed in Mark Dvoretsky's analysis, such maneuvers are essential in queen versus pawn scenarios, where precise play can turn a drawn position into a win by exploiting defensive stalemates or pawn weaknesses. Multi-piece pawnless endgames introduce combinatorial complexity, such as rook and bishop versus rook, which is generally a draw with accurate defense but can favor the superior side if the lone rook's king is confined to an unfavorable corner. The defender must centralize the king and use the rook to check and restrict the bishop's mobility, avoiding pins that expose the king. Fortresses represent another defensive bastion in these scenarios, where the inferior side establishes an impregnable zone—often with a king and minor pieces blocking invasion routes—rendering the opponent's extra material ineffective despite prolonged efforts. Classic examples include bishop and knight versus rook configurations, where the defenders coordinate to seal off the board, as explored in theoretical studies. Theoretical milestones in endgame analysis include the completion of 7-piece tablebases, which exhaustively solve all positions with up to seven pieces on the board, revealing distances to win or draw in moves. The Lomonosov tablebases, generated in 2012 using supercomputing, marked a breakthrough by covering 140 terabytes of data and confirming that many intuitively drawable positions require up to 549 moves to resolve. As of 2025, progress on 8-piece tablebases continues, with partial computations uncovering even longer sequences, such as wins requiring up to 584 moves. These databases have revolutionized understanding of multi-piece interactions, identifying exceptions like certain queen and rook endings that were previously misjudged as wins. Practical techniques in advanced endgames emphasize , particularly outside passed pawns, which distract the enemy to the flank, allowing the attacker's to advance central pawns or capture opposition forces. In works by Karsten Müller and Frank Lamprecht, such pawns are highlighted as decisive assets when supported by activity, often tipping balanced positions toward promotion. emerges as a pivotal tool, forcing the opponent into moves that weaken their structure or concede key squares, such as in rook endgames where the defender must abandon a defensive post. Dvoretsky illustrates how in pawnless scenarios, like opposite-colored bishops, can convert theoretical draws into wins by restricting the opponent's last viable options.

Modern Developments

Computer-Assisted Analysis

The landmark event in computer-assisted chess analysis occurred in 1997 when IBM's Deep Blue defeated world champion in a six-game match by a score of 3.5–2.5, marking the first time a computer bested a reigning champion under standard tournament conditions. This victory, achieved through evaluating up to 200 million positions per second via specialized hardware and algorithms, demonstrated the potential of computational power to challenge human intuition and propelled the development of chess engines as analytical tools. Subsequent advancements led to open-source engines like , a community-driven program that has dominated championships such as the Top Chess Engine Championship (TCEC) since its inception in 2008, consistently ranking as one of the strongest engines. A arrived in 2017 with DeepMind's , which, through , surpassed in a 100-game match, winning 28, drawing 72, and losing none, without relying on human-generated data. Inspired by , (Lc0) emerged as an open-source counterpart, leveraging for training and achieving superhuman performance in positional evaluation. Historically, traditional engines employed hand-crafted evaluation functions that assign scores in centipawns—a unit representing 1/100th of a pawn's value—to assess material, position, and king safety, enabling precise quantification of advantages as small as 0.01 pawns. However, since 2020, has integrated (Efficiently Updatable Neural Network), a hybrid approach combining evaluation with traditional alpha-beta search for greater efficiency and accuracy. In contrast, -based systems such as Lc0 and use to output probabilistic s, including win/draw/loss probabilities and policy vectors for move suggestions, capturing subtle imbalances beyond explicit rules. These tools have profoundly impacted chess theory by rigorously testing and refuting variations once deemed viable; for instance, deep analysis with engines like Houdini has classified the as structurally inferior for White due to Black's ability to secure a lasting advantage in key lines. Engines have also uncovered novelties, such as AlphaZero's innovative pawn sacrifices in closed positions, which human players later adopted to refine middlegame strategies. Through , AI systems like have revealed positional insights transcending human intuition, such as prioritizing hypermodern control over central space and favoring quiet maneuvers that accumulate long-term advantages, as evidenced by its acquisition of novel concepts like "space advantage without occupation." This approach not only challenges classical principles but has enriched theoretical understanding by highlighting imbalances in endgame transitions previously overlooked.

Theoretical Databases

Theoretical databases in chess serve as comprehensive repositories of game data and precomputed evaluations, enabling players and analysts to study positions across all phases of the game with unprecedented depth and accuracy. These databases compile millions of recorded games, often annotated with engine-derived evaluations, to reveal patterns in openings, middlegames, and endgames. Key examples include , established in 1986 by Matthias Wüllenweber and Frederic Friedel, which offers the Mega Database containing over 11 million games from historical and modern tournaments. Similarly, the Opening Explorer provides free access to a vast collection of master games alongside billions of user-submitted games from the platform, allowing exploration of opening lines through interactive trees. Another prominent resource is 365Chess, which maintains a database exceeding 4.2 million games, primarily from master-level play, with tools for searching specific openings and variations. These databases typically include annotations such as move evaluations in centipawns, win/draw/loss statistics, and performance data by player rating, covering everything from rare gambits in the opening to complex rook endgames. A specialized subset of theoretical databases consists of endgame tablebases, which precompute perfect play for positions with few pieces remaining on the board. The Nalimov tablebases, developed by Eugene Nalimov and completed in 2005, cover all 3- to 6-piece endgames, storing outcomes like wins, draws, or losses along with the distance to mate, totaling about 1.2 terabytes for the full 6-piece set. More recent advancements include the Syzygy tablebases, created by Ronald de Man starting in 2013, which extend to 7-piece endgames in a more compact format using distance-to-zeroing-move metrics and supporting the 50-move rule; these are freely available online and comprise approximately 18 terabytes of data for 7-piece positions. Tablebases ensure exhaustive analysis by enumerating every legal position, eliminating errors in simplified endgames that might otherwise require manual calculation. In chess theory, these play a pivotal role by facilitating statistical analysis of win rates and move popularity, helping theorists identify reliable lines and avoid transposition errors where similar positions arise via different move orders. For instance, querying a database might reveal that a particular opening variation yields a 55% win rate for in master games above 2500 Elo, guiding preparation toward high-performance choices. By integrating with chess engines for dynamic querying, allow real-time evaluation of novel ideas against historical , though the core value lies in their static compilation of verified outcomes.

References

  1. https://new.uschess.org/news/check-mail-analyzing-elements-part-one
  2. https://new.uschess.org/news/check-mail-examining-elements-pt-2
  3. https://www.nature.com/articles/s41598-023-31658-w
  4. https://iiif.library.cmu.edu/file/Simon_box00069_fld05354_bdl0001_doc0001/Simon_box00069_fld05354_bdl0001_doc0001.pdf
  5. https://en.chessbase.com/post/britannica-the-development-of-chess-theory-2
  6. https://www.paradise.caltech.edu/ist4/lectures/shannonchess1950.pdf
  7. https://link.springer.com/article/10.1007/BF01359218
  8. https://rosenberglab.stanford.edu/papers/LappoEtAl2023-ProcRSocB.pdf
  9. https://onlinelibrary.wiley.com/doi/10.1155/2023/7143943
  10. https://archive.org/details/repeticiondeamor0000luce
  11. https://museum.fide.com/exhibits/lanalyse-des-echecs
  12. https://publishing.cdlib.org/ucpressebooks/view?docId=ft438nb2b6&chunk.id=d0e889&toc.id=&brand=eschol
  13. https://chessify.me/blog/the-evolution-of-chess-openings
  14. https://archive.org/details/modernchessinstr00steirich
  15. https://archive.org/details/nimzowitsch-my-system
  16. https://www.chess.com/article/view/quotthink-like-a-grandmasterquot-by-alexander-kotov
  17. https://archive.org/details/kotov-soviet-chess-school-1961
  18. https://www.chess.com/article/view/how-to-play-positional-chess
  19. https://www.chess.com/article/view/steinitz-defense-openings-of-world-champions
  20. https://thechessworld.com/articles/general-information/10-things-to-learn-from-aron-nimzowitsch/
  21. https://www.chess.com/terms/hypermodern-chess
  22. https://www.chess.com/terms/types-of-pawns
  23. https://archive.org/details/my-system-2020
  24. https://www.chess.com/article/view/the-evaluation-of-material-imbalances-by-im-larry-kaufman
  25. https://www.chess.com/terms/prophylaxis-chess
  26. https://lichess.org/practice/fundamental-tactics/the-fork/Qj281y1p/uAoBhXY8
  27. https://www.chess.com/article/view/chess-tactics
  28. https://lichess.org/practice/fundamental-tactics/the-skewer/tuoBxVE5/DXc6bhG2
  29. https://lichess.org/practice/fundamental-tactics/discovered-attacks/MnsJEWnI/vV50tWGB
  30. https://lichess.org/practice/advanced-tactics/greek-gift/s5pLU7Of/uCkLsFs1
  31. https://chessfox.com/chess-tactics-list/
  32. https://www.chess.com/terms/back-rank-mate-chess
  33. https://new.uschess.org/news/inside-story-how-study-tactics
  34. https://www.chess.com/article/view/the-principles-of-the-opening
  35. https://www.chessworld.net/steinitz.asp
  36. https://www.365chess.com/eco.php
  37. https://www.365chess.com/chess-openings/Italian-Game
  38. https://www.365chess.com/chess-openings/Ruy-Lopez-Opening
  39. https://www.365chess.com/chess-openings/Sicilian-Defense
  40. https://www.365chess.com/chess-openings/Queens-Gambit-Declined
  41. https://www.simplifychess.com/slav-defense/index.html
  42. https://chesspathways.com/chess-openings/queens-pawn-opening/nimzo-indian-defense/
  43. https://www.chess.com/openings/Kings-Indian-Defense
  44. https://en.chessbase.com/post/britannica-the-development-of-chess-theory
  45. https://chessnook.files.wordpress.com/2010/12/how-to-reassess-your-chess-jeremy-silman.pdf
  46. https://www.chess.com/article/view/initiative-1
  47. https://www.chessnook.files.wordpress.com/2010/12/how-to-reassess-your-chess-jeremy-silman.pdf
  48. https://www.chess.com/terms/minority-attack-chess
  49. https://chesscheatsheets.com/blogs/chess-openings/kings-indian-pawn-storms-attacking-the-kingside
  50. https://www.chess.com/blog/GMTheDeepThinker/understanding-middlegame-tactics-key-patterns-and-ideas
  51. https://www.chess.com/blog/Gertsog/webinar-104-most-beautiful-tactic-windmill
  52. https://chesstempo.com/tactical-motifs
  53. https://www.chess.com/blog/GMTheDeepThinker/unlocking-the-tree-of-analysis-your-guide-to-mastering-chess-calculation
  54. https://www.chess.com/article/view/how-to-avoid-blunders-part-1
  55. https://www.chessgames.com/perl/chessgame?gid=1018910
  56. https://www.chess.com/blog/dovanngocson/the-middlegame-what-you-need-to-know
  57. https://www.chess.com/blog/RussBell/opposition
  58. https://www.ragchess.com/ultimate-guide-to-pawn-endgames/
  59. https://www.chess.com/blog/vinniethepooh/basic-rook-endgames-philidor-and-lucena
  60. https://www.ragchess.com/philidor-and-lucena-rook-endgames/
  61. https://www.chess.com/article/view/the-eternal-battle-bishops-vs-knights
  62. https://en.chessbase.com/post/the-wrong-bishop
  63. https://www.chess.com/article/view/pawn-races
  64. https://www.chess.com/terms/50-move-rule-chess
  65. https://www.chessstrategyonline.com/content/tutorials/introduction-to-chess-endgames-queen-endgames
  66. https://thechessworld.com/articles/endgame/chess-endgames-triangulation/
  67. https://matthewsadler.me.uk/the-endgame/rook-bishop-vs-rook-part-i/
  68. https://thechessworld.com/articles/endgame/chess-fortress-7-must-know-positions/
  69. https://www.chessprogramming.org/Endgame_Tablebases
  70. https://www.chess.com/blog/Rocky64/eight-piece-tablebases-a-progress-update-and-some-results
  71. https://thechessworld.com/articles/endgame/7-basic-pawn-structure-you-must-know/
  72. https://www.uscfsales.com/chess-blog/guide-to-zugzwang/
  73. https://www.ibm.com/history/deep-blue
  74. https://stockfishchess.org/
  75. https://arxiv.org/abs/1712.01815
  76. https://lczero.org/
  77. https://lczero.org/dev/wiki/technical-explanation-of-leela-chess-zero/
  78. https://en.chessbase.com/post/rajlich-busting-the-king-s-gambit-this-time-for-sure
  79. https://deepmind.google/blog/alphazero-shedding-new-light-on-chess-shogi-and-go/
  80. https://www.pnas.org/doi/10.1073/pnas.2206625119
  81. https://www.wired.com/story/deepmind-ai-chess/
  82. https://en.chessbase.com/post/chessbase-a-look-back-at-the-early-days
  83. https://shop.chessbase.com/en/shopping_advisor_Mega
  84. https://lichess.org/opening
  85. https://github.com/lichess-org/lila-openingexplorer
  86. https://www.365chess.com/
  87. https://www.chessprogramming.org/Nalimov_Tablebases
  88. https://en.chessbase.com/post/endgame-tablebases-a-short-history
  89. https://syzygy-tables.info/
  90. https://www.chessprogramming.org/Syzygy_Bases
  91. https://www.chess.com/blog/SamCopeland/databases-tips-tricks-and-recommendations
  92. https://chessify.me/blog/how-to-use-chess-databases-for-opening-preparation
Add your contribution
Related Hubs
User Avatar
No comments yet.