Chess

Early on, the pieces in shatranj — the predecessor of the European chess — had limited movement; elephants (bishops) could only move by jumping exactly two spaces diagonally, the counselor (queen) could move only one space diagonally, pawns could not move two spaces on their first move, and there was no castling. Pawns could only promote to a counselor.^[7] In addition to checkmate, player could win by capturing all of the opponent's pieces (except the king) and a stalemate was not a draw.^[8]

By the end of the 15th century, the modern rules for the basic moves had been adopted in Italy^[9] (or in Spain according to other sources^[10]): pawns gained the option of moving two squares on their first move and the en passant capture therewith, bishops acquired their modern move, and the queen was made the most powerful piece; consequently modern chess was referred to as "Queen's Chess" or "Mad Queen Chess".^[11] The game in Europe since that time has been almost the same as is played today.^[12]

Chess, with its new rules, started to develop a theory. The oldest preserved printed chess book, Repetición de Amores y Arte de Ajedrez (Repetition of Love and the Art of Playing Chess) by leading Spanish chess player Luis Ramirez de Lucena was published in Salamanca in 1497.^[13] Lucena and later masters of the 16th and 17th century like Portuguese Pedro Damiano, Italians Giovanni Leonardo Di Bona, Giulio Cesare Polerio and Gioacchino Greco or Spanish bishop Ruy López de Segura developed elements of some chess openings, e.g. Italian Game, King's Gambit or Ruy Lopez, and started to analyze simple endgames.

In the 18th century the center of European chess life moved from South-European countries to France. The two most important French masters were François-André Danican Philidor, a musician by profession, who discovered the importance of pawns for chess strategy, and later Louis-Charles Mahé de La Bourdonnais who won a famous series of matches with the strongest British master of the time, Alexander McDonnell from Ireland, in 1834.^[14] Centers of the chess life in this period were coffee houses in big European cities like Café de la Régence in Paris^[15] and Simpson's Divan in London.^[16]

During the 19th century, chess organization developed quickly. Many chess clubs, chess books and chess journals appeared. There were correspondence matches between cities, for example London Chess Club vs Edinburgh Chess Club in 1824.^[17] Chess problems, at the top level composed for example by Bernhard Horwitz, Josef Kling or Samuel Loyd, became regular part of 19th century newspapers. In the mid of the century, the first comprehensive manual of chess theory appeared, Handbuch des Schachspiels (Handbook of Chess) written by German masters Paul Rudolf von Bilguer and Tassilo von Heydebrand und der Lasa and first published in 1843.

[edit] Birth of a sport (1850—1945)

The "Immortal game" Anderssen-Kieseritzky 1851

The first modern chess tournament was held in London in 1851 and was surprisingly won by German Adolf Anderssen, relatively unknown by the time. Anderssen was hailed as the leading chess master and his brilliant, energetic — but from today's viewpoint strategically shallow — attacking style became typical for the time.^[18] Sparkling games like Anderssen's Immortal game or Morphy's Opera game — both short casual games with many sacrifices — were regarded as the highest possible summon of the chess art.^[19]

Deeper insight into the nature of chess battle came with two younger players. American Paul Morphy, an extraordinary chess prodigy, won over all important competitors including Anderssen during his short chess career between 1857 and 1863. Morphy won not only because he was able to attack brilliantly, but also because of the strategical soundness of his moves — he intuitively knew how to prepare the attack in advance.^[20] This secret was later re-invented and described by another strong master and theoretician, Prague-born Wilhelm Steinitz, who later settled in Vienna, in London and died in the USA.^[21]

Besides his theoretical successes, Steinitz founded another important tradition: His won match against the leading German master Johannes Zukertort in 1886 is regarded as the first official World Chess Championship, and Steinitz the first champion. He lost his crown in 1894 to much younger German mathematician Emanuel Lasker, who maintained this title for 27 years, the longest tenure of all World Champions.^[22]

The prodigy from Cuba, José Raúl Capablanca (World champion 1921—1927), who ended the German-speaking dominance in chess, loved simple positions and endgames and was very hard to beat — he lost no single tournament game during eight years around 1920. His follower was Russian-French Alexander Alekhine, a strong attacking player, who died as the World champion in 1946, having lost the title for a short time to Dutch player Max Euwe, but regaining it again.^[23]

Between the two World wars, chess was revolutionized by the new theoretical school of so-called hypermodernists like Aron Nimzowitsch or Richard Réti. They denied simple principles of older positional school of Steinitz and Tarrasch and advocated controlling the center of the board with distant pieces rather than with pawns, thus inviting the opponent to occupy the center with pawns which can then become objects of attack.

Since the end of 19th century, the number of annually held master tournaments and matches quickly grew. In 1914, the title of chess grandmaster was first formally conferred by Russian Tsar Nicholas II, who awarded it to five finalists of a tournament in Saint Petersburg (Lasker, Capablanca, Alekhine, Tarrasch and Marshall). This tradition was later continued by FIDE, The Fédération Internationale des Échecs or World Chess Federation, founded in 1924 in Paris. In 1927, a World Champion title for women was established, whose first bearer was Czech-English master Vera Menchik.^[24]

[edit] Post-war era (1945 and later)

After the death of Alekhine, a new World champion was sought in a tournament of elite players ruled by FIDE, who since then controlled the title for decades. The winner of the 1948 tournament, Russian Mikhail Botvinnik, started an era of Soviet dominance in the chess world — since then until the end of Soviet Union, there was only one champion other than Soviet, American Bobby Fischer (champion 1972-1975). All others were Soviet citizens.^[25]

In place of the previous informal system, in which the holder of the World Champion title decided about challengers, who were thus forced to seek sponsors for the match, a new system of qualifying tournaments and matches was arranged. The world's strongest players were seeded into "Interzonal tournaments", where they were joined by players who had qualified from "Zonal tournaments". The leading finishers in these Interzonals would go on the "Candidates" stage, which was initially a tournament, later a series of knock-out matches. The winner of the Candidates would then play a match against the reigning champion for the championship. If a champion was defeated, he had a right to play a rematch. This system worked on a three-year cycle.

Mikhail Botvinnik was involved in championship matches over a period of fifteen years. He won the world championship tournament in 1948 and retained the title in tied matches in 1951 and 1954. In 1957 he lost it to the strong universal player Vasily Smyslov, but he regained the title in a rematch in 1958. In 1960 he lost the title to the Latvian prodigy Mikhail Tal, accomplished tactician and attacking player. Botvinnik again regained the title in a rematch in 1961. Then FIDE abolished the right of a deposed champion to a rematch, and the next champion Armenian Tigran Petrosian, a genius of defense and strong positional player, was able to hold the title for two cycles, 1963–1969. His follower Boris Spassky from Russia (1969–1972) was an universal master able to win in both positional and sharp tactical style.^[26]

The next championship, so-called Match of the Century, saw the first non-Soviet finalist since before World War II, American Bobby Fischer, who defeated his Candidates opponents by unheard-of margins (both six wins to zero, no draws) and clearly won also the world championship match (12½ to 8½). In 1975, however, Fischer refused to defend his title against Soviet Anatoly Karpov when his demands were not met and Karpov therefore obtained the title by default. Karpov defended his title twice against Viktor Korchnoi and dominated the 1970s and 1980s with a string of tournament successes.^[27]

Karpov eventually lost his title to younger Garry Kasparov in 1984, who then dominated the chess world for another two decades.^[28] In 1993, Garry Kasparov and Nigel Short broke with FIDE to organize their own match for the title and formed a competing Professional Chess Association (PCA). From then until 2006 there were two simultaneous World Champions and World Championships: the PCA or Classical champion extending the Steinitzian tradition in which the current champion plays a challenger in match format (a series of many games); the other following FIDE's new format of a tournament with many players competing. Kasparov lost his Classical title in 2000 to Vladimir Kramnik. Reunification of the two lineages happened in 2006 in the FIDE World Chess Championship 2006 when Kramnik beat the FIDE World Champion Veselin Topalov and became the undisputed World Chess Champion.^[29]

[edit] Place in culture

Main article: Chess in the arts and literature

[edit] Pre-modern

In the Middle Ages and during the Renaissance, chess was a part of noble culture;^[30] it was used as a means of teaching war strategy and was dubbed the "King's Game". Gentlemen are "to be meanly seene in the play at Chestes," says the overview at the beginning of Baldassare Castiglione's The Book of the Courtier (1528, English 1561 by Sir Thomas Hoby), but chess should not be a gentleman's main passion. Castiglione explains it further:

And what say you to the game at chestes?

It is truely an honest kynde of enterteynmente and wittie, quoth Syr Friderick. But me think it hath a fault, whiche is, that a man may be to couning at it, for who ever will be excellent in the playe of chestes, I beleave he must beestowe much tyme about it, and applie it with so much study, that a man may assoone learne some noble scyence, or compase any other matter of importaunce, and yet in the ende in beestowing all that laboure, he knoweth no more but a game. Therfore in this I beleave there happeneth a very rare thing, namely, that the meane is more commendable, then the excellency.^[31]

Beautiful chess sets used by the aristocracy of the time are mostly lost, but some of the surviving examples, like the 12th century Lewis chessmen, are of high artistic quality.

At the same time, chess was often used as a basis of sermons on morality. An example is Liber de moribus hominum et officiis nobilium sive super ludo scacchorum ('Book of the customs of men and the duties of nobles or the Book of Chess'), written by an Italian Dominican monk Jacobus de Cessolis circa 1300. The popular work was translated into many other languages (first printed edition at Utrecht in 1473) and was the basis for William Caxton's The Game and Playe of the Chesse (1474), one of the first books printed in English.^[32] Different chess pieces were used as metaphors for different classes of people, and human duties were derived from the rules of the game or from visual properties of the chess pieces.^[33]

The knyght ought to be made alle armed upon an hors in suche wyse that he haue an helme on his heed and a spere in his ryght hande/ and coueryd wyth his sheld/ a swerde and a mace on his lyft syde/ Cladd wyth an hawberk and plates to fore his breste/ legge harnoys on his legges/ Spores on his heelis on his handes his gauntelettes/ his hors well broken and taught and apte to bataylle and couerid with his armes/ whan the knyghtes ben maad they ben bayned or bathed/ that is the signe that they shold lede a newe lyf and newe maners/ also they wake alle the nyght in prayers and orysons vnto god that he wylle gyue hem grace that they may gete that thynge that they may not gete by nature/ The kynge or prynce gyrdeth a boute them a swerde in signe/ that they shold abyde and kepe hym of whom they take theyr dispenses and dignyte.^[34]

On the other side, political and religious authorities in many places forbade chess as frivolous or as a sort of gambling.

Known in the circles of clerics, students and merchants, chess entered into the popular culture of Middle Ages. An example is the 209th song of Carmina Burana from the 13th century, which starts with the names of chess pieces, Roch, pedites, regina...^[35]

[edit] Modern

To the Age of Enlightenment, chess appeared mainly as a means of self-improvement. Benjamin Franklin, in his article "The Morals of Chess" (1750), wrote:

"The Game of Chess is not merely an idle amusement; several very valuable qualities of the mind, useful in the course of human life, are to be acquired and strengthened by it, so as to become habits ready on all occasions; for life is a kind of Chess, in which we have often points to gain, and competitors or adversaries to contend with, and in which there is a vast variety of good and ill events, that are, in some degree, the effect of prudence, or the want of it. By playing at Chess then, we may learn:

1st, Foresight, which looks a little into futurity, and considers the consequences that may attend an action ...

2nd, Circumspection, which surveys the whole Chess-board, or scene of action: - the relation of the several Pieces, and their situations; ...

3rd, Caution, not to make our moves too hastily...."^[36]

With these or similar hopes, chess is taught to children in schools around the world today and used in armies to train minds of cadets and officers.^[37]

Moreover, chess is often depicted in the arts, used for example as a metaphor of a struggle of two, as a symbol of cold logic, or - in the spirit of mediaeval moralists - as an allegory of society's life. Significant works, where chess plays a key role, range from Thomas Middleton's A Game at Chess over Through the Looking-Glass by Lewis Carroll to The Royal Game by Stefan Zweig or Vladimir Nabokov's The Defense.

Chess is also present in the contemporary popular culture. For example, J. K. Rowling's Harry Potter plays "Wizard's Chess" while the characters of Star Trek prefer "Tri-Dimensional Chess" and the hero of Searching for Bobby Fischer struggles against adopting the aggressive and misanthropic views of a real chess Grandmaster.

[edit] Notation for recording moves

Main article: Chess notation

Chess games and positions are recorded using a chess notation, most often the algebraic chess notation.^[38] The abbreviated (or short) algebraic notation generally records moves in the format abbreviation of the piece moved - file where it moved - rank where it moved, e.g. Qg5 means "Queen moved to file g and rank 5 (that is, to the field g5). If there are two pieces of the same type, which can move to the same field, one more letter or number is added to indicate the file or rank from which the piece moved, e.g. Ngf3 means "Knight from the file g moved to the field f3". Letter P indicating a pawn is usually dropped, so that e4 means "Pawn moved to the field e4".

If the piece captures, "x" is inserted behind the abbreviation of the piece, e.g. Bxf3 means "Bishop captured on f3". When a pawn makes a capture, the file from which the pawn departed is used in place of a piece initial. For example, exd5 (pawn on the e-file captures the piece on d5).

The "Scholar's mate"

If a pawn moves to its last rank, achieving promotion, the piece chosen is indicated after the move, for example e1Q. Castling is indicated by the special notations 0-0 for kingside castling and 0-0-0 for queenside. A move which places the opponent's king in check usually has the notation "+" added. Checkmate can be indicated "#" (some use "++"). At the end of the game, "1-0" means "White won", "0-1" means "Black won" and "½-½" indicates draw.

Chess moves can be commented by punctuation. For example ! indicates a good move, !! an excellent move, ? a mistake, ?? a blunder, !? an interesting move that may not be best or ?! a dubious move, but not easily refuted.

For example, one variant of a simple trap known as the Scholar's mate, animated in the picture rights, can be recorded:
1. e4 e5
2. Qh5?! Nc6
3. Bc4 Nf6??
4. Qxf7# 1-0

[edit] Strategy and tactics

Chess strategy is about how to set and achieve long-term goals during the game - for example, where to place different pieces - while tactics concentrates on immediate maneuvers. These two sides of chess thinking cannot be completely separated, because strategic goals are mostly achieved by the means of tactics, while the tactical opportunities are based on the previous sound strategy of play.

Because of different strategic and tactical patterns, a game of chess is usually divided into three distinct phases: Opening, usually the first 10 to 25 moves, when players develop their armies and set up the stage for the coming battle; middlegame, the developed phase of the game; and endgame, when most of pieces are gone and kings start to take an active part in the struggle.

[edit] Fundamentals of strategy

Main article: Chess strategy

Chess strategy is concerned with evaluation of chess positions and with setting up goals and long-term plans for the future play. During the evaluation, players must take into account the value of pieces on board, pawn structure, king safety, space, and control of key squares and groups of squares (for example, diagonals, open-files, and dark or light squares).

A chess position (Tarrasch - Euwe, 1922)...

...and its pawn skeleton ("The Rauzer formation")

The most basic task is to count the total value of pieces of both sides.^[39] The point values used for this purpose are based on experience; usually pawns are considered worth one point, knights and bishops about three points each, rooks about five points (the value difference between a rook and a bishop being known as the exchange), and queens about nine points. The fighting value of the king in the endgame is equivalent to about four points. These basic values are then modified by other factors like position of the piece (for example, advanced pawns are usually more valuable than those on initial positions), coordination between pieces (for example, a pair of bishops usually coordinates better than the pair bishop + knight), or type of position (knights are generally better in closed positions with many pawns while bishops are more powerful in open positions).

Another important factor in the evaluation of chess positions is the pawn structure (sometimes known as the pawn skeleton), or the configuration of pawns on the chessboard.^[40] Pawns being the least mobile of the chess pieces, the pawn structure is relatively static, and largely determines the strategic nature of the position. Weaknesses in the pawn structure, such as isolated, doubled or backward pawns and holes, once created, are usually permanent. Care must therefore be taken to avoid them unless they are compensated by another valuable asset (for example, by the possibility to develop an attack).

[edit] Fundamentals of tactics

Main article: Chess tactics

In chess, tactics in general concentrate on short-term actions - so short-term that they can be calculated in advance by a human player or by a computer. The possible depth of calculation depends on the player's ability or speed of the processor. In quiet positions with many possibilities on both sides, a deep calculation is not possible, while in "tactical" positions with a limited number of forced variants, it is possible to calculate very long sequences of moves.

Simple one-move or two-move tactical actions - threats, exchanges of material, double attacks etc. - can be combined into more complicated variants, tactical maneuvers, often forced from one side or from both. Theoreticians described many elementary tactical methods and typical maneuvers, for example pins, forks, skewers, discovered attacks (especially discovered checks), zwischenzugs, deflections, decoys, sacrifices, underminings, overloadings and interferences.^[41]

A forced variant which is connected with a sacrifice and usually results in a tangible gain is named a combination.^[42] Brilliant combinations - such as those in the Immortal game - are usually described as beautiful and are admired by chess lovers. Finding a combination is also a common type of chess puzzle aimed at development of player's skills.

[edit] Opening

Main article: Chess opening

A chess opening is the group of initial moves of a game (the "opening moves"). Recognized sequences of opening moves are referred to as openings or defenses, and have been given names such as the Ruy Lopez or Sicilian Defense, and are catalogued in reference works such as the Encyclopedia of Chess Openings. There are dozens of different openings, varying widely in character from quiet positional play (e.g. the Réti Opening) to wild tactical play (e.g. the Latvian Gambit). In some opening lines, the moves considered best for both sides have been worked out to 30-35 moves or more.^[43] Professional players spend years studying openings, and continue doing so throughout their careers, as opening theory continues to evolve.

Although a variety of moves can be played in the opening, the fundamental strategical aims are similar:^[44]

• Development: To place (develop) the pieces on useful squares where they will have an impact on the game. For example, knights are often developed to f3, c3, f6 and c6 (or sometimes e2, d2, e7 or d7).
• Control of the center: Control of the central squares allows pieces to be moved to any part of the board relatively easily, and can also have a cramping effect on the opponent.
• King safety: enhanced via castling, for example.
• Pawn structure: Players strive to avoid the creation of pawn weaknesses such as isolated, doubled and backward pawns, and pawn islands.

Apart from these ideas, other strategic plans or tactical sequences may also appear in the opening.

[edit] Middlegame

Main article: Middlegame

The middlegame is the part of the game when most pieces have been developed. Because the opening theory has ended, players have to assess the position, to form plans based on the features of the positions, and at the same time to take into account the tactical possibilities in the position.^[45]

Typical plans or strategical themes — for example the minority attack, that is the attack of queenside pawns against an opponent who has more pawns on the queenside — are often appropriate just for some pawn structures, resulting from a specific group of openings. The study of openings should therefore be connected with the preparation of plans typical for resulting middlegames.

Middlegame is also the phase in which most combinations occur. Middlegame combinations are often connected with the attack against the opponent's king; some typical patterns have their own names, for example the Boden's Mate or the Lasker-Bauer combination.

Another important strategical question in the middlegame is whether and how to reduce material and transform into an endgame. For example, minor material advantages can generally be transformed into victory only in an endgame, and therefore the stronger side must choose an appropriate way to achieve an ending. Not every reduction of material is good for this purpose; for example, if one side keeps a light-squared bishop and the opponent has a dark-squared one, the transformation into a bishops and pawns ending is usually advantageous for the weaker side only, because an endgame with bishops on opposite colors is likely to be a draw, even with an advantage of one or two pawns.

[edit] Endgame

Main article: Endgame

The endgame (or end game or ending) is the stage of the game when there are few pieces left on the board. There are three main strategic differences between earlier stages of the game and endgame:^[46]

• During the endgame, pawns become more important; endgames often revolve around attempting to promote a pawn by advancing it to the eighth rank.
• The king, which has to be protected in the middlegame owing to the threat of checkmate, becomes a strong piece in the endgame and it is often advisable to bring it to the center of the board where it can protect its own pawns and attack the pawns of opposite color.
• Zugzwang, a disadvantage because the player has to make a move, is often a factor in endgames and rarely in other stages of the game.

Endgames can be classified according to the type of pieces that remain on board. Basic checkmates are positions in which one side has only a king and the other side has one or two pieces and can checkmate the opposing king, with the pieces working together with their king. King and pawn endgames involve only kings and pawns on one or both sides and the task of the stronger side is to promote one of the pawns. Other more complicated endings are classified according to the pieces on board other than kings, e.g. "rook and pawn versus rook".

[edit] Chess composition

Main article: Chess problem

Chess composition is the art of creating chess problems (these problems themselves are sometimes also called chess compositions); that is, puzzles using chess pieces on a chess board. For instance, a position might be given with the instruction that white is to move first, and checkmate black in two moves against any possible defense. A person who creates such problems is known as a chess composer.^[47]

Most chess problems exhibit the following features:

• The position is composed, that is, it has not been taken from an actual game, but has been invented for the specific purpose of providing a problem.
• There is a specific stipulation, that is, a goal to be achieved; for example, to checkmate black within a specified number of moves.
• There is a theme (or combination of themes) that the problem has been composed to illustrate: chess problems typically instantiate particular ideas. Many of these themes have their own names, often by persons who used them first, for example Novotny or Lacny theme.
• The problem exhibits economy in its construction: no greater force is employed than that required to guarantee that the problem's intended solution is indeed a solution and that it is the problem's only solution.
• The problem has aesthetic value. Problems are experienced not only as puzzles but as objects of beauty. This is closely related to the fact that problems are organized to exhibit clear ideas in as economical a manner as possible.

There are many types of chess problems. The two most important are:

• Directmates: white to move first and checkmate black within a specified number of moves against any defense. These are often referred to as "mate in n", where n is the number of moves within which mate must be delivered - for example "mate in three" (a three-mover).
• Studies: orthodox problems in which the stipulation is that white to play must win or draw. Almost all studies are endgame positions.

Chess composition is a distinct branch of chess sport, and tournaments (or tourneys) exist for both the composition and solving of chess problems.

[edit] Competitive play

[edit] Organization of competitions

Contemporary chess is an organized sport with structured international and national leagues, tournaments and congresses. Chess's international governing body is FIDE (Fédération Internationale des Échecs). Most countries have a national chess organization as well, which in turn is a member of FIDE. FIDE is a member of the International Olympic Committee (IOC), but the game of chess has never been part of the Olympic Games; chess does have its own Olympiad, held every two years as a team event.

The current World Chess Champion is Vladimir Kramnik,^[48] and the reigning Women's World Champion is Xu Yuhua from China. However, the world's highest rated female player Judit Polgar has never participated in the Women's World Chess Championship, instead preferring to compete with the leading men.

Other competitions for individuals include the World Junior Chess Championship, the European Individual Championship and the National Chess Championships. Other elite tournament include Spain's Linares event, Monte Carlo's Melody Amber tournament, the Dortmund Sparkassen meeting and Wijk aan Zee's Corus tournament.

Regular team chess events include the aforementioned Chess Olympiad and the European Team Championship. The 37th Chess Olympiad was held 2006 in Turin, Italy; Armenia won the gold in the unrestricted event, and Ukraine took the top medal for the women. The World Chess Solving Championship and World Correspondence Chess Championships are both team and individual events.

Besides these prestigious competitions, there are thousands of other chess tournaments, matches and festivals held around the world every year, which cater to players of all levels, from beginners to experts.

[edit] Titles and rankings

The best players can be awarded specific lifetime titles by the world chess organization FIDE:^[49]

• International Grandmaster (shortened: Grandmaster, GM or IGM) is awarded to world-class chess masters. Apart from World Champion, Grandmaster is the highest title a chess player can attain. Before FIDE will confer the title on a player, the player must have an ELO chess rating (see below) of at least 2500 at one time and two favorable results (called norms) in tournaments involving other Grandmasters, including some from countries other than the applicant's. There are also other milestones a player can achieve to attain the title, such as winning the World Junior Championship.
• International Master (shortened: IM). The conditions are similar to GM, but less demanding. The minimum rating for the IM title is 2400.
• FIDE Master (shortened: FM). The usual way for a player to qualify for the FIDE Master title is by achieving a FIDE Rating of 2300 or more.
• Candidate Master (shortened: CM). Similar to FM, but with a FIDE Rating of at least 2200.

All the titles are open to men and women. Separate women-only titles, such as Woman Grandmaster (WGM), are also available. In 1991, Susan Polgar became the first woman to earn the GM title under the same conditions as men, and most of the top ten women in 2006 hold the unrestricted GM title.^[50]

International titles are awarded to composers and solvers of chess problems, and to correspondence chess players (by the International Correspondence Chess Federation). Moreover, national chess organizations may also award titles, usually to the advanced players still under the level needed for international titles; an example is the Chess expert title used in the USA.

In order to rank players, FIDE, ICCF and national chess organizations use the Elo rating system developed by Arpad Elo. Elo is a statistical system based on assumption that the chess performance of each player in his games is a random variable. Arpad Elo thought of a player's true skill as the average of that player's performance random variable, and showed how to estimate the average from results of player's games. The US Chess Federation implemented Elo's suggestions in 1960, and the system quickly gained recognition as being both fairer and more accurate than older systems; it was adopted by FIDE in 1970.^[51]

The highest ever FIDE rating was 2851, which Garry Kasparov had on the July 1999 and January 2000 lists.^[52]

[edit] Mathematics and computers

Main articles: Computer chess, List of mathematicians who studied chess