Computer chess

Source: Wikipedia, the free encyclopedia.
1990s pressure-sensory chess computer with LCD screen

Computer chess includes both hardware (dedicated computers) and software capable of playing chess. Computer chess provides opportunities for players to practice even in the absence of human opponents, and also provides opportunities for analysis, entertainment and training. Computer chess applications that play at the level of a chess grandmaster or higher are available on hardware from supercomputers to smart phones. Standalone chess-playing machines are also available. Stockfish, Leela Chess Zero, GNU Chess, Fruit, and other free open source applications are available for various platforms.

Computer chess applications, whether implemented in hardware or software, utilize different strategies than humans to choose their moves: they use heuristic methods to build, search and evaluate trees representing sequences of moves from the current position and attempt to execute the best such sequence during play. Such trees are typically quite large, thousands to millions of nodes. The computational speed of modern computers, capable of processing tens of thousands to hundreds of thousands of nodes or more per second, along with extension and reduction heuristics that narrow the tree to mostly relevant nodes, make such an approach effective.

The first chess machines capable of playing chess or reduced chess-like games were software programs running on digital computers early in the vacuum-tube computer age (1950s). The early programs played so poorly that even a beginner could defeat them. Within 40 years, in 1997, chess engines running on super-computers or specialized hardware were capable of defeating even the best human players. By 2006, programs running on desktop PCs had attained the same capability. In 2006, Monty Newborn, Professor of Computer Science at McGill University, declared: "the science has been done". Nevertheless, solving chess is not currently possible for modern computers due to the game's extremely large number of possible variations.[1]

Computer chess was once considered the "Drosophila of AI", the edge of knowledge engineering. The field is now considered a scientifically completed paradigm, and playing chess is a mundane computing activity.[2]

Availability and playing strength

Computer chess IC bearing the name of developer Frans Morsch (see Mephisto)

Chess machines/programs are available in several different forms: stand-alone chess machines (usually a microprocessor running a software chess program, but sometimes as a specialized hardware machine), software programs running on standard PCs, web sites, and apps for mobile devices. Programs run on everything from super-computers to smartphones. Hardware requirements for programs are minimal; the apps are no larger than a few megabytes on disk, use a few megabytes of memory (but can use much more, if it is available), and any processor 300Mhz or faster is sufficient. Performance will vary modestly with processor speed, but sufficient memory to hold a large transposition table (up to several gigabytes or more) is more important to playing strength than processor speed.

Most available commercial chess programs and machines can play at super-grandmaster strength (Elo 2700 or more), and take advantage of multi-core and hyperthreaded computer CPU architectures. Top programs such as

Chessbase
. Playing strength, time controls, and other performance-related settings are adjustable from the GUI. Most GUIs also allow the player to set up and to edit positions, to reverse moves, to offer and to accept draws (and resign), to request and to receive move recommendations, and to show the engine's analysis as the game progresses.

There are thousands of

Fruit, Leela Chess Zero and GNU Chess which can be downloaded (or source code otherwise obtained) from the Internet
free of charge.

Types and features of chess software

Perhaps the most common type of chess software are programs that simply play chess. A human player makes a move on the board, the AI calculates and plays a subsequent move, and the human and AI alternate turns until the game ends. The

Elo rating of the engine (via UCI's uci_limitstrength and uci_elo parameters). Some versions of Fritz have a Handicap and Fun mode for limiting the current engine or changing the percentage of mistakes it makes or changing its style. Fritz
also has a Friend Mode where during the game it tries to match the level of the player.

Chess, a component of macOS

Chess databases allow users to search through a large library of historical games, analyze them, check statistics, and formulate an opening repertoire.

Chessbase (for PC) is a common program for these purposes amongst professional players, but there are alternatives such as Shane's Chess Information Database (Scid) [3] for Windows, Mac or Linux, Chess Assistant[4] for PC,[5] Gerhard Kalab's Chess PGN Master for Android[6] or Giordano Vicoli's Chess-Studio for iOS.[7]

Programs such as Playchess allow players to play against one another over the internet.

Chess training programs teach chess.

Chessbase has Fritz and Chesster
for children. Convekta provides a large number of training apps such as CT-ART and its Chess King line based on tutorials by GM Alexander Kalinin and Maxim Blokh.

There is also software for handling chess problems.

Computers versus humans

After discovering refutation screening—the application of

Eliot Hearst of Indiana University wrote that "the only way a current computer program could ever win a single game against a master player would be for the master, perhaps in a drunken stupor while playing 50 games simultaneously, to commit some once-in-a-year blunder".[9]

In the late 1970s chess programs suddenly began defeating highly skilled human players.

Chess 4.7, but it achieved the first computer victory against a Master-class player at the tournament level by winning one of the six games.[10] In 1980, Belle began often defeating Masters. By 1982 two programs played at Master level and three were slightly weaker.[9]

The sudden improvement without a theoretical breakthrough was unexpected, as many did not expect that Belle's ability to examine 100,000 positions a second—about eight plies—would be sufficient. The Spracklens, creators of the successful microcomputer program Sargon, estimated that 90% of the improvement came from faster evaluation speed and only 10% from improved evaluations. New Scientist stated in 1982 that computers "play terrible chess ... clumsy, inefficient, diffuse, and just plain ugly", but humans lost to them by making "horrible blunders, astonishing lapses, incomprehensible oversights, gross miscalculations, and the like" much more often than they realized; "in short, computers win primarily through their ability to find and exploit miscalculations in human initiatives".[9]

By 1982, microcomputer chess programs could evaluate up to 1,500 moves a second and were as strong as mainframe chess programs of five years earlier, able to defeat a majority of amateur players. While only able to look ahead one or two plies more than at their debut in the mid-1970s, doing so improved their play more than experts expected; seemingly minor improvements "appear to have allowed the crossing of a psychological threshold, after which a rich harvest of human error becomes accessible", New Scientist wrote.

BYTE wrote that "Computers—mainframes, minis, and micros—tend to play ugly, inelegant chess", but noted Robert Byrne's statement that "tactically they are freer from error than the average human player". The magazine described SPOC as a "state-of-the-art chess program" for the IBM PC with a "surprisingly high" level of play, and estimated its USCF rating as 1700 (Class B).[11]

At the 1982

Deep Blue that Kasparov lost his first game to a computer at tournament time controls in Deep Blue versus Kasparov, 1996, game 1. This game was, in fact, the first time a reigning world champion had lost to a computer using regular time controls. However, Kasparov regrouped to win three and draw
two of the remaining five games of the match, for a convincing victory.

In May 1997, an updated version of Deep Blue defeated Kasparov 3½–2½ in a return match. A documentary mainly about the confrontation was made in 2003, titled Game Over: Kasparov and the Machine.

abcdefgh
8
h7 white rook
f6 black queen
h6 black king
d5 white queen
g5 white knight
d4 black pawn
a3 white pawn
b3 white pawn
f3 black pawn
g3 white pawn
h3 white pawn
f2 black knight
h2 white king
e1 black rook
8
77
66
55
44
33
22
11
abcdefgh
Final position

With increasing processing power and improved evaluation functions, chess programs running on commercially available workstations began to rival top-flight players. In 1998,

blitz games (five minutes plus five seconds Fischer delay for each move); these Rebel won 3–1. Two were semi-blitz games (fifteen minutes for each side) that Rebel won as well (1½–½). Finally, two games were played as regular tournament games (forty moves in two hours, one hour sudden death); here it was Anand who won ½–1½.[13]
In fast games, computers played better than humans, but at classical time controls – at which a player's rating is determined – the advantage was not so clear.

In the early 2000s, commercially available programs such as Junior and Fritz were able to draw matches against former world champion Garry Kasparov and classical world champion Vladimir Kramnik.

In October 2002, Vladimir Kramnik and Deep Fritz competed in the eight-game Brains in Bahrain match, which ended in a draw. Kramnik won games 2 and 3 by "conventional" anti-computer tactics – play conservatively for a long-term advantage the computer is not able to see in its game tree search. Fritz, however, won game 5 after a severe blunder by Kramnik. Game 6 was described by the tournament commentators as "spectacular". Kramnik, in a better position in the early middlegame, tried a piece sacrifice to achieve a strong tactical attack, a strategy known to be highly risky against computers who are at their strongest defending against such attacks. True to form, Fritz found a watertight defense and Kramnik's attack petered out leaving him in a bad position. Kramnik resigned the game, believing the position lost. However, post-game human and computer analysis has shown that the Fritz program was unlikely to have been able to force a win and Kramnik effectively sacrificed a drawn position. The final two games were draws. Given the circumstances, most commentators still rate Kramnik the stronger player in the match.[citation needed]

In January 2003, Kasparov played Junior, another chess computer program, in New York City. The match ended 3–3.

In November 2003, Kasparov played X3D Fritz. The match ended 2–2.

In 2005, Hydra, a dedicated chess computer with custom hardware and sixty-four processors and also winner of the 14th IPCCC in 2005, defeated seventh-ranked Michael Adams 5½–½ in a six-game match (though Adams' preparation was far less thorough than Kramnik's for the 2002 series).[14]

In November–December 2006, World Champion Vladimir Kramnik played Deep Fritz. This time the computer won; the match ended 2–4. Kramnik was able to view the computer's opening book. In the first five games Kramnik steered the game into a typical "anti-computer" positional contest. He lost one game (

overlooking a mate in one), and drew the next four. In the final game, in an attempt to draw the match, Kramnik played the more aggressive Sicilian Defence
and was crushed.

There was speculation that interest in human–computer chess competition would plummet as a result of the 2006 Kramnik-Deep Fritz match.[15] According to Newborn, for example, "the science is done".[16]

Human–computer chess matches showed the best computer systems overtaking human chess champions in the late 1990s. For the 40 years prior to that, the trend had been that the best machines gained about 40 points per year in the

Elo rating while the best humans only gained roughly 2 points per year.[17] The highest rating obtained by a computer in human competition was Deep Thought's USCF rating of 2551 in 1988 and FIDE no longer accepts human–computer results in their rating lists. Specialized machine-only Elo pools have been created for rating machines, but such numbers, while similar in appearance, are not directly compared.[18] In 2016, the Swedish Chess Computer Association rated computer program Komodo
at 3361.

Hiarcs 13 running inside Pocket Fritz 4 on the mobile phone HTC Touch HD won the Copa Mercosur tournament in Buenos Aires, Argentina with 9 wins and 1 draw on August 4–14, 2009.[19] Pocket Fritz 4 searches fewer than 20,000 positions per second.[20]
This is in contrast to supercomputers such as Deep Blue that searched 200 million positions per second.

Advanced Chess
is a form of chess developed in 1998 by Kasparov where a human plays against another human, and both have access to computers to enhance their strength. The resulting "advanced" player was argued by Kasparov to be stronger than a human or computer alone. This has been proven in numerous occasions, such as at Freestyle Chess events.

Players today are inclined to treat chess engines as analysis tools rather than opponents.[21] Chess grandmaster Andrew Soltis stated in 2016 "The computers are just much too good" and that world champion Magnus Carlsen won't play computer chess because "he just loses all the time and there's nothing more depressing than losing without even being in the game."[22]

Computer methods

Since the era of mechanical machines that played rook and king endings and electrical machines that played other games like hex in the early years of the 20th century, scientists and theoreticians have sought to develop a procedural representation of how humans learn, remember, think and apply knowledge, and the game of chess, because of its daunting complexity, became the "Drosophila of artificial intelligence (AI)".[Note 1] The procedural resolution of complexity became synonymous with thinking, and early computers, even before the chess automaton era, were popularly referred to as "electronic brains". Several different schema were devised starting in the latter half of the 20th century to represent knowledge and thinking, as applied to playing the game of chess (and other games like checkers):

Using "ends-and-means" heuristics a human chess player can intuitively determine optimal outcomes and how to achieve them regardless of the number of moves necessary, but a computer must be systematic in its analysis. Most players agree that looking at least five moves ahead (ten plies) when necessary is required to play well. Normal tournament rules give each player an average of three minutes per move. On average there are more than 30 legal moves per chess position, so a computer must examine a quadrillion possibilities to look ahead ten plies (five full moves); one that could examine a million positions a second would require more than 30 years.[9]

The earliest attempts at procedural representations of playing chess predated the digital electronic age, but it was the stored program digital computer that gave scope to calculating such complexity. Claude Shannon, in 1949, laid out the principles of algorithmic solution of chess. In that paper, the game is represented by a "tree", or digital data structure of choices (branches) corresponding to moves. The nodes of the tree were positions on the board resulting from the choices of move. The impossibility of representing an entire game of chess by constructing a tree from first move to last was immediately apparent: there are an average of 36 moves per position in chess and an average game lasts about 35 moves to resignation (60-80 moves if played to checkmate, stalemate, or other draw). There are 400 positions possible after the first move by each player, about 200,000 after two moves each, and nearly 120 million after just 3 moves each.

So a limited lookahead (search) to some depth, followed by using domain-specific knowledge to evaluate the resulting terminal positions was proposed. A kind of middle-ground position, given good moves by both sides, would result, and its evaluation would inform the player about the goodness or badness of the moves chosen. Searching and comparing operations on the tree were well suited to computer calculation; the representation of subtle chess knowledge in the evaluation function was not. The early chess programs suffered in both areas: searching the vast tree required computational resources far beyond those available, and what chess knowledge was useful and how it was to be encoded would take decades to discover.

The developers of a chess-playing computer system must decide on a number of fundamental implementation issues. These include:

  • Graphical user interface (GUI) – how moves are entered and communicated to the user, how the game is recorded, how the time controls are set, and other interface considerations
  • Board representation
    – how a single position is represented in data structures;
  • Search techniques – how to identify the possible moves and select the most promising ones for further examination;
  • Leaf evaluation – how to evaluate the value of a board position, if no further search will be done from that position.

masters and beginners look at around forty to fifty positions before deciding which move to play. What makes the former much better players is that they use pattern recognition
skills built from experience. This enables them to examine some lines in much greater depth than others by simply not considering moves they can assume to be poor. More evidence for this being the case is the way that good human players find it much easier to recall positions from genuine chess games, breaking them down into a small number of recognizable sub-positions, rather than completely random arrangements of the same pieces. In contrast, poor players have the same level of recall for both.

The equivalent of this in computer chess are evaluation functions for leaf evaluation, which correspond to the human players' pattern recognition skills, and the use of machine learning techniques in training them, such as Texel tuning, stochastic gradient descent, and reinforcement learning, which corresponds to building experience in human players. This allows modern programs to examine some lines in much greater depth than others by using forwards pruning and other selective heuristics to simply not consider moves the program assume to be poor through their evaluation function, in the same way that human players do. The only fundamental difference between a computer program and a human in this sense is that a computer program can search much deeper than a human player could, allowing it to search more nodes and bypass the horizon effect to a much greater extent than is possible with human players.

Graphical user interface

Computer chess programs usually support a number of common de facto standards. Nearly all of today's programs can read and write game moves as

algebraic chess notation
.

Starting in the late 1990s, programmers began to develop separately engines (with a command-line interface which calculates which moves are strongest in a position) or a graphical user interface (GUI) which provides the player with a chessboard they can see, and pieces that can be moved. Engines communicate their moves to the GUI using a protocol such as the Chess Engine Communication Protocol (CECP) or Universal Chess Interface (UCI). By dividing chess programs into these two pieces, developers can write only the user interface, or only the engine, without needing to write both parts of the program. (See also chess engine.)

Developers have to decide whether to connect the engine to an opening book and/or endgame

tablebases
or leave this to the GUI.

Board representations

The

position evaluation. Methods include pieces stored in an array ("mailbox" and "0x88"), piece positions stored in a list ("piece list"), collections of bit-sets for piece locations ("bitboards"), and huffman coded
positions for compact long-term storage.

Search techniques

Computer chess programs consider chess moves as a game tree. In theory, they examine all moves, then all counter-moves to those moves, then all moves countering them, and so on, where each individual move by one player is called a "ply". This evaluation continues until a certain maximum search depth or the program determines that a final "leaf" position has been reached (e.g. checkmate).

One particular type of search algorithm used in computer chess are minimax search algorithms, where at each ply the "best" move by the player is selected; one player is trying to maximize the score, the other to minimize it. By this alternating process, one particular terminal node whose evaluation represents the searched value of the position will be arrived at. Its value is backed up to the root, and that evaluation becomes the valuation of the position on the board. This search process is called minimax.

A naive implementation of the minimax algorithm can only search to a small depth in a practical amount of time, so various methods have been devised to greatly speed the search for good moves. Alpha–beta pruning, a system of defining upper and lower bounds on possible search results and searching until the bounds coincided, is typically used to reduce the search space of the program.

In addition, various selective search heuristics, such as

rank
, etc.). These selective search heuristics have to be used very carefully however. Over extend and the program wastes too much time looking at uninteresting positions. If too much is pruned or reduced, there is a risk cutting out interesting nodes.

Monte Carlo tree search (MCTS) is a heuristic search algorithm which expands the search tree based on random sampling of the search space. A version of Monte Carlo tree search commonly used in computer chess is PUCT, Predictor and Upper Confidence bounds applied to Trees.

DeepMind's

graphics processing units in order to calculate their evaluation functions and policy (move selection), and therefore require a parallel
search algorithm as calculations on the GPU are inherently parallel. The minimax and alpha-beta pruning algorithms used in computer chess are inherently serial algorithms, so would not work well with batching on the GPU. On the other hand, MCTS is a good alternative, because the random sampling used in Monte Carlo tree search lends itself well to parallel computing, and is why nearly all engines which support calculations on the GPU use MCTS instead of alpha-beta.

Other optimizations

Many other optimizations can be used to make chess-playing programs stronger. For example,

pondering
, searching to deeper levels on the opponent's time, similar to human beings, to increase their playing strength.

Of course, faster hardware and additional memory can improve chess program playing strength. Hyperthreaded architectures can improve performance modestly if the program is running on a single core or a small number of cores. Most modern programs are designed to take advantage of multiple cores to do parallel search. Other programs are designed to run on a general purpose computer and allocate move generation, parallel search, or evaluation to dedicated processors or specialized co-processors.

History

The first paper on search was by Claude Shannon in 1950.[23] He predicted the two main possible search strategies which would be used, which he labeled "Type A" and "Type B",[24] before anyone had programmed a computer to play chess.

Type A programs would use a "brute force" approach, examining every possible position for a fixed number of moves using a pure naive minimax algorithm. Shannon believed this would be impractical for two reasons.

First, with approximately thirty moves possible in a typical real-life position, he expected that searching the approximately 109 positions involved in looking three moves ahead for both sides (six plies) would take about sixteen minutes, even in the "very optimistic" case that the chess computer evaluated a million positions every second. (It took about forty years to achieve this speed. A later search algorithm called alpha–beta pruning, a system of defining upper and lower bounds on possible search results and searching until the bounds coincided, reduced the branching factor of the game tree logarithmically, but it still was not feasible for chess programs at the time to exploit the exponential explosion of the tree.

Second, it ignored the problem of quiescence, trying to only evaluate a position that is at the end of an exchange of pieces or other important sequence of moves ('lines'). He expected that adapting minimax to cope with this would greatly increase the number of positions needing to be looked at and slow the program down still further. He expected that adapting type A to cope with this would greatly increase the number of positions needing to be looked at and slow the program down still further.

This led naturally to what is referred to as "selective search" or "type B search", using chess knowledge (heuristics) to select a few presumably good moves from each position to search, and prune away the others without searching. Instead of wasting processing power examining bad or trivial moves, Shannon suggested that type B programs would use two improvements:

  1. Employ a quiescence search.
  2. Employ forward pruning; i.e. only look at a few good moves for each position.

This would enable them to look further ahead ('deeper') at the most significant lines in a reasonable time. However, early attempts at selective search often resulted in the best move or moves being pruned away. As a result, little or no progress was made for the next 25 years dominated by this first iteration of the selective search paradigm. The best program produced in this early period was Mac Hack VI in 1967; it played at the about the same level as the average amateur (C class on the United States Chess Federation rating scale).

Meanwhile, hardware continued to improve, and in 1974, brute force searching was implemented for the first time in the Northwestern University Chess 4.0 program. In this approach, all alternative moves at a node are searched, and none are pruned away. They discovered that the time required to simply search all the moves was much less than the time required to apply knowledge-intensive heuristics to select just a few of them, and the benefit of not prematurely or inadvertently pruning away good moves resulted in substantially stronger performance.

In the 1980s and 1990s, progress was finally made in the selective search paradigm, with the development of

alpha-beta search
as a substrate for their search algorithm, these additional selective search heuristics used in modern programs means that the program no longer does a "brute force" search. Instead they heavily rely on these selective search heuristics to extend lines the program considers good and prune and reduce lines the program considers bad, to the point where most of the nodes on the search tree are pruned away, enabling modern programs to search very deep.

In 2006, Rémi Coulom created Monte Carlo tree search, another kind of type B selective search. In 2007, an adaption of Monte Carlo tree search called Upper Confidence bounds applied to Trees or UCT for short was created by Levente Kocsis and Csaba Szepesvári. In 2011, Chris Rosin developed a variation of UCT called Predictor + Upper Confidence bounds applied to Trees, or PUCT for short. PUCT was then used in AlphaZero in 2017, and later in Leela Chess Zero in 2018.

Knowledge versus search (processor speed)

In the 1970s, most chess programs ran on super computers like Control Data Cyber 176s or Cray-1s, indicative that during that developmental period for computer chess, processing power was the limiting factor in performance. Most chess programs struggled to search to a depth greater than 3 ply. It was not until the hardware chess machines of the 1980s, that a relationship between processor speed and knowledge encoded in the evaluation function became apparent.

It has been estimated that doubling the computer speed gains approximately fifty to seventy Elo points in playing strength (Levy & Newborn 1991:192).

Leaf evaluation

For most chess positions, computers cannot look ahead to all possible final positions. Instead, they must look ahead a few plies and compare the possible positions, known as leaves. The algorithm that evaluates leaves is termed the "evaluation function", and these algorithms are often vastly different between different chess programs. Evaluation functions typically evaluate positions in hundredths of a pawn (called a centipawn), where by convention, a positive evaluation favors White, and a negative evaluation favors Black. However, some evaluation function output win/draw/loss percentages instead of centipawns.

Historically, handcrafted evaluation functions consider material value along with other factors affecting the strength of each side. When counting up the material for each side, typical values for pieces are 1 point for a pawn, 3 points for a knight or bishop, 5 points for a rook, and 9 points for a queen. (See Chess piece relative value.) The king is sometimes given an arbitrarily high value such as 200 points (Shannon's paper) to ensure that a checkmate outweighs all other factors (Levy & Newborn 1991:45). In addition to points for pieces, most handcrafted evaluation functions take many factors into account, such as pawn structure, the fact that a pair of bishops are usually worth more, centralized pieces are worth more, and so on. The protection of kings is usually considered, as well as the phase of the game (opening, middle or endgame). Machine learning techniques such as Texel turning, stochastic gradient descent, or reinforcement learning are usually used to optimise handcrafted evaluation functions.

Most modern evaluation functions make use of

deep neural networks in their evaluation function. Neural networks are usually trained using some reinforcement learning algorithm, in conjunction with supervised learning or unsupervised learning
.

The output of the evaluation function is a single scalar, quantized in centipawns or other units, which is, in the case of handcrafted evaluation functions, a weighted summation of the various factors described, or in the case of neural network based evaluation functions, the output of the head of the neural network. The evaluation putatively represents or approximates the value of the subtree below the evaluated node as if it had been searched to termination, i.e. the end of the game. During the search, an evaluation is compared against evaluations of other leaves, eliminating nodes that represent bad or poor moves for either side, to yield a node which by convergence, represents the value of the position with best play by both sides.

Endgame tablebases

Endgame play had long been one of the great weaknesses of chess programs because of the depth of search needed. Some otherwise master-level programs were unable to win in positions where even intermediate human players could force a win.

To solve this problem, computers have been used to analyze some

Ken Thompson
was a pioneer in this area.

The results of the computer analysis sometimes surprised people. In 1977 Thompson's Belle chess machine used the endgame tablebase for a king and rook against king and queen and was able to draw that theoretically lost ending against several masters (see Philidor position#Queen versus rook). This was despite not following the usual strategy to delay defeat by keeping the defending king and rook close together for as long as possible. Asked to explain the reasons behind some of the program's moves, Thompson was unable to do so beyond saying the program's database simply returned the best moves.

Most grandmasters declined to play against the computer in the queen versus rook endgame, but Walter Browne accepted the challenge. A queen versus rook position was set up in which the queen can win in thirty moves, with perfect play. Browne was allowed 2½ hours to play fifty moves, otherwise a draw would be claimed under the fifty-move rule. After forty-five moves, Browne agreed to a draw, being unable to force checkmate or win the rook within the next five moves. In the final position, Browne was still seventeen moves away from checkmate, but not quite that far away from winning the rook. Browne studied the endgame, and played the computer again a week later in a different position in which the queen can win in thirty moves. This time, he captured the rook on the fiftieth move, giving him a winning position (Levy & Newborn 1991:144–48), (Nunn 2002:49).

Other positions, long believed to be won, turned out to take more moves against perfect play to actually win than were allowed by chess's fifty-move rule. As a consequence, for some years the official FIDE rules of chess were changed to extend the number of moves allowed in these endings. After a while, the rule reverted to fifty moves in all positions – more such positions were discovered, complicating the rule still further, and it made no difference in human play, as they could not play the positions perfectly.

Over the years, other

Shredder and Fritz. Tablebases for all positions with six pieces are available.[25] Some seven-piece endgames have been analyzed by Marc Bourzutschky and Yakov Konoval.[26] Programmers using the Lomonosov supercomputers in Moscow have completed a chess tablebase for all endgames with seven pieces or fewer (trivial endgame positions are excluded, such as six white pieces versus a lone black king).[27][28]
In all of these endgame databases it is assumed that castling is no longer possible.

Many tablebases do not consider the fifty-move rule, under which a game where fifty moves pass without a capture or pawn move can be claimed to be a draw by either player. This results in the tablebase returning results such as "Forced mate in sixty-six moves" in some positions which would actually be drawn because of the fifty-move rule. One reason for this is that if the rules of chess were to be changed once more, giving more time to win such positions, it will not be necessary to regenerate all the tablebases. It is also very easy for the program using the tablebases to notice and take account of this 'feature' and in any case if using an endgame tablebase will choose the move that leads to the quickest win (even if it would fall foul of the fifty-move rule with perfect play). If playing an opponent not using a tablebase, such a choice will give good chances of winning within fifty moves.

The Nalimov tablebases, which use state-of-the-art

TB of storage space.[29]

Endgame databases featured prominently in 1999, when Kasparov played an exhibition match on the Internet against the rest of the world. A seven piece Queen and pawn endgame was reached with the World Team fighting to salvage a draw. Eugene Nalimov helped by generating the six piece ending tablebase where both sides had two Queens which was used heavily to aid analysis by both sides.

The most popular endgame tablebase is syzygy which is used by most top computer programs like Stockfish, Leela Chess Zero, and Komodo. It is also significantly smaller in size than other formats, with 7-piece tablebases taking only 18.4 TB.[30]

For a current state-of-the art chess engine like Stockfish, a table base only provides a very minor increase in playing strength (approximately 3 Elo points for syzygy 6men as of Stockfish 15).[31]

Opening book

Chess engines, like human beings, may save processing time as well as select strong variations as expounded by the masters, by referencing an opening book stored in a disk database. Opening books cover the opening moves of a game to variable depth, depending on opening and variation, but usually to the first 10-12 moves (20-24 ply). Since the openings have been studied in depth by the masters for centuries, and some are known to well into the middle game, the valuations of specific variations by the masters will usually be superior to the general heuristics of the program.

While at one time, playing an out-of-book move in order to put the chess program onto its own resources might have been an effective strategy because chess opening books were selective to the program's playing style, and programs had notable weaknesses relative to humans, that is no longer true today.[when?] The opening books stored in computer databases are most likely far more extensive than even the best prepared humans, and playing an early out-of-book move may result in the computer finding the unusual move in its book and saddling the opponent with a sharp disadvantage. Even if it does not, playing out-of-book may be much better for tactically sharp chess programs than for humans who have to discover strong moves in an unfamiliar variation over the board.

In modern engine tournaments, opening books are used to force the engines to play intentionally unbalanced openings to reduce the draw rate and to add more variety to the games.[32]

Computer chess rating lists

CEGT,[33] CSS,[34] SSDF,[35] WBEC,[36] REBEL,[37] FGRL,[38] and IPON[39] maintain rating lists allowing fans to compare the strength of engines. Various versions of Stockfish, Komodo, Leela Chess Zero, and Fat Fritz dominate the rating lists in the early 2020s.

CCRL (Computer Chess Rating Lists) is an organisation that tests computer chess engines' strength by playing the programs against each other. CCRL was founded in 2006 to promote computer-computer competition and tabulate results on a rating list.[40]

The organisation runs three different lists: 40/40 (40 minutes for every 40 moves played), 40/4 (4 minutes for every 40 moves played), and 40/4

tablebases.[40][41][42]

History

Pre-computer age

El Ajedrecista

The idea of creating a chess-playing machine dates back to the eighteenth century. Around 1769, the chess playing

digital computing, serious trials based on automata such as El Ajedrecista of 1912, built by Spanish engineer Leonardo Torres Quevedo
, which played a king and rook versus king ending, were too complex and limited to be useful for playing full games of chess. The field of mechanical chess research languished until the advent of the digital computer in the 1950s.

Early software age: selective search and Botvinnik

Since then, chess enthusiasts and

World Chess Champion Mikhail Botvinnik, who wrote several works on the subject. Botvinnik’s interest in Computer Chess started in the 50s, favouring chess algorithms based on Shannon's selective type B strategy, as discussed along with Max Euwe 1958 in Dutch Television. Working with relatively primitive hardware available in the Soviet Union in the early 1960s, Botvinnik had no choice but to investigate software move selection techniques; at the time only the most powerful computers could achieve much beyond a three-ply full-width search, and Botvinnik had no such machines. In 1965 Botvinnik was a consultant to the ITEP team in a US-Soviet computer chess match which won a correspondence chess match against the Kotok-McCarthy-Program led by John McCarthy in 1967.(see Kotok-McCarthy
). Later he advised the team that created the chess program Kaissa at Moscow’s Institute of Control Sciences. Botvinnik had his own ideas to model a Chess Master's Mind. After publishing and discussing his early ideas on attack maps and trajectories at Moscow Central Chess Clubin 1966, he found Vladimir Butenko as supporter and collaborator. Butenko first implemented the 15x15 vector attacks board representation on a M-20 computer, determining trajectories. After Botvinnik introduced the concept of Zones in 1970, Butenko refused further cooperation and began to write his own program, dubbed Eureka. In the 70s and 80s, leading a team around Boris Stilman, Alexander Yudin, Alexander Reznitskiy, Michael Tsfasman and Mikhail Chudakov, Botvinnik worked on his own project 'Pioneer' - which was an Artificial Intelligence based chess project. In the 90s, Botvinnik already in his 80s, he worked on the new project 'CC Sapiens'.

One developmental milestone occurred when the team from Northwestern University, which was responsible for the Chess series of programs and won the first three ACM Computer Chess Championships (1970–72), abandoned type B searching in 1973. The resulting program, Chess 4.0, won that year's championship and its successors went on to come in second in both the 1974 ACM Championship and that year's inaugural World Computer Chess Championship, before winning the ACM Championship again in 1975, 1976 and 1977. The type A implementation turned out to be just as fast: in the time it used to take to decide which moves were worthy of being searched, it was possible just to search all of them. In fact, Chess 4.0 set the paradigm that was and still is followed essentially by all modern Chess programs today, and that had been successfully started by the Russian ITEP in 1965.

Rise of chess machines

In 1978, an early rendition of Ken Thompson's hardware chess machine Belle, entered and won the North American Computer Chess Championship over the dominant Northwestern University Chess 4.7.

Microcomputer revolution

Technological advances by orders of magnitude in processing power have made the brute force approach far more incisive than was the case in the early years. The result is that a very solid, tactical AI player aided by some limited positional knowledge built in by the evaluation function and pruning/extension rules began to match the best players in the world. It turned out to produce excellent results, at least in the field of chess, to let computers do what they do best (calculate) rather than coax them into imitating human thought processes and knowledge. In 1997

Deep Blue
, a brute-force machine capable of examining 500 million nodes per second, defeated World Champion Garry Kasparov, marking the first time a computer has defeated a reigning world chess champion in standard time control.

Super-human chess

In 2016, NPR asked experts to characterize the playing style of computer chess engines. Murray Campbell of IBM stated that "Computers don't have any sense of aesthetics... They play what they think is the objectively best move in any position, even if it looks absurd, and they can play any move no matter how ugly it is." Grandmasters Andrew Soltis and Susan Polgar stated that computers are more likely to retreat than humans are.[22]

Neural network revolution

While

neural networks have been used in the evaluation functions of chess engines since the late 1980s, with programs such as NeuroChess, Morph, Blondie25, Giraffe, AlphaZero, and MuZero,[43][44][45][46][47] neural networks did not become widely adopted by chess engines until the arrival of efficiently updatable neural networks in the summer of 2020. Efficiently updatable neural networks were originally developed in computer shogi in 2018 by Yu Nasu,[48][49] and had to be first ported to a derivative of Stockfish called Stockfish NNUE on 31 May 2020,[50] and integrated into the official Stockfish engine on 6 August 2020,[51][52]
before other chess programmers began to adopt neural networks into their engines.

Some people, such as the

central processing units, and computing and processing information on the GPUs require special libraries in the backend such as Nvidia's CUDA, which none of the engines had access to. Thus the vast majority of chess engines such as Komodo and Stockfish continued to use handcrafted evaluation functions until efficiently updatable neural networks were ported to computer chess in 2020, which did not require either the use of GPUs or libraries like CUDA at all. Even then, the neural networks used in computer chess are fairly shallow, and the deep reinforcement learning
methods pioneered by AlphaZero are still extremely rare in computer chess.

Timeline

abcdef
6a6 black rookb6 black knightc6 black queend6 black kinge6 black knightf6 black rook6
5a5 black pawnb5 black pawnc5 black pawnd5 black pawne5 black pawnf5 black pawn5
4a4b4c4d4e4f44
3a3b3c3d3e3f33
2a2 white pawnb2 white pawnc2 white pawnd2 white pawne2 white pawnf2 white pawn2
1a1 white rookb1 white knightc1 white queend1 white kinge1 white knightf1 white rook1
abcdef
Los Alamos chess. This simplified version of chess was played in 1956 by the MANIAC I computer.
Released in 1977, Boris was one of the first chess computers to be widely marketed. It ran on a Fairchild F8 8-bit microprocessor with only 2.5 KiB ROM and 256 byte RAM.

Categorizations

Dedicated hardware

These chess playing systems include custom hardware with approx. dates of introduction (excluding dedicated microcomputers):

  • Belle 1976
  • Bebe, a strong
    bit-slice processor
    1980
  • HiTech 1985
  • ChipTest 1985
  • Deep Thought 1987
  • Deep Thought 2 (Deep Blue prototype)~1994
  • Deep Blue
    1996, 1997
  • Hydra, predecessor was called Brutus 2002
  • AlphaZero 2017 (used Google's Tensor Processing Units for neural networks, but the hardware is not specific to Chess or games)
    • MuZero 2019 (similar hardware to its predecessor AlphaZero, non-specific to Chess or e.g. Go), learns the rules of Chess

Commercial dedicated computers

Boris Diplomat (1979) travel chess computer
Fidelity Voice Chess Challenger (1979), the first talking chess computer
Speech output from Voice Chess Challenger
Milton Bradley Grandmaster (1983), the first commercial self-moving chess computer
Novag Super Constellation (1984), known for its human-like playing style
DGT Centaur (2019), a modern chess computer based on Stockfish running on a Raspberry Pi

In the late 1970s to early 1990s, there was a competitive market for dedicated chess computers. This market changed in the mid-1990s when computers with dedicated processors could no longer compete with the fast processors in personal computers.

Recently, some hobbyists have been using the Multi Emulator Super System to run the chess programs created for Fidelity or Hegener & Glaser's Mephisto computers on modern 64-bit operating systems such as Windows 10.[74] The author of Rebel, Ed Schröder has also adapted three of the Hegener & Glaser Mephisto's he wrote to work as UCI engines.[75]

DOS programs

These programs can be run on MS-DOS, and can be run on 64-bit Windows 10 via emulators such as

Qemu:[76]

Notable theorists

Well-known computer chess theorists include:

  • Georgy Adelson-Velsky, a Soviet and Israeli mathematician and computer scientist
  • Hans Berliner, American computer scientist and world correspondence chess champion, design supervisor of HiTech (1988)
  • Mikhail Botvinnik, Soviet electrical engineer and world chess champion, wrote Pioneer
  • Alexander Brudno, Russian computer scientist, first elaborated the alphabeta pruning algorithm
  • Feng-hsiung Hsu, the lead developer of Deep Blue (1986–97)
  • Professor Robert Hyatt developed Cray Blitz and Crafty[77]
  • Danny Kopec, American Professor or Computer Science and International Chess Master, developed Kopec-Bratko test
  • Alexander Kronrod
    , Soviet computer scientist and mathematician
  • Professor
    Monroe Newborn
    , chairman of the computer chess committee for the Association for Computing Machinery
  • Claude E. Shannon
    , American computer scientist and mathematician
  • Alan Turing, English computer scientist and mathematician

Solving chess

The prospects of completely

EXPTIME-complete,[79]
meaning that determining the winning side in an arbitrary position of generalized chess provably takes exponential time in the worst case; however, this theoretical result gives no lower bound on the amount of work required to solve ordinary 8x8 chess.

Martin Gardner's Minichess, played on a 5×5 board with approximately 1018 possible board positions, has been solved; its game-theoretic value is 1/2 (i.e. a draw can be forced by either side), and the forcing strategy to achieve that result has been described.

Progress has also been made from the other side: as of 2012, all 7 and fewer pieces (2 kings and up to 5 other pieces) endgames have been solved.

Chess engines

A "chess engine" is software that calculates and orders which moves are the strongest to play in a given position. Engine authors focus on improving the play of their engines, often just importing the engine into a

Chessbase has its own proprietary protocol, and at one time Millennium 2000 had another protocol used for ChessGenius
. Engines designed for one operating system and protocol may be ported to other OS's or protocols.

Chess engines are regularly matched against each other at dedicated chess engine tournaments.

Chess web apps

In 1997, the

Chessbase/Playchess has long had a downloadable client, and added a web-based client in 2013.[84]

Another popular web app is tactics training. The now defunct Chess Tactics Server opened its site in 2006,

Chessbase added a tactics trainer web app in 2015.[88]

Chessbase by releasing a NICBase program for Windows 3.x, but eventually, decided to give up on software, and instead focus on their online database starting in 2002.[91]

One could play against the engine

Chessbase added a play Fritz web app,[93] as well as My Games for storing one's games.[94]

Starting in 2007, Chess.com offered the content of the training program, Chess Mentor, to their customers online.[95] Top GMs such as Sam Shankland and Walter Browne have contributed lessons.

See also

Notes

  1. ^ What this means is that chess, like the common fruit fly, is a simple and more accessible and familiar paradigm to experiment with technology that can be used to produce knowledge about other, more complex systems.
  2. ^ The first number refers to the number of moves which must be made by each engine, the second number refers to the number of minutes allocated to make all of these moves. The repeating time control means that the time is reset after each multiple of this number of moves is reached. For example, in a 40/4 time control, each engine would have 4 minutes to make 40 moves, then a new 4 minutes would be allocated for the next 40 moves and so on, until the game was complete.

References

  1. ^ Sreedhar, Suhas (2 July 2007). "Checkers, Solved!". IEEE Spectrum. Institute of Electrical and Electronics Engineers.
  2. S2CID 968033
    .
  3. ^ http://scid.sourceforge.net SCID.
  4. ^ "Chess Assistant Chess Website:: About Us". www.convekta.com. Archived from the original on August 20, 2008.
  5. ^ http://www.exachess.com ExaChess for Mac
  6. ^ "Chess PGN Master".
  7. user-generated source
    ]
  8. . Retrieved 10 February 2018.
  9. ^ a b c d e f g Hapgood, Fred (23–30 December 1982). "Computer chess bad-human chess worse". New Scientist. pp. 827–830. Retrieved 22 January 2015.[permanent dead link]
  10. ^ a b c Douglas, J R (December 1978). "Chess 4.7 versus David Levy". BYTE. p. 84. Retrieved 17 October 2013.
  11. ^ Flock, Emil; Silverman, Jonathan (March 1984). "SPOC / The Chess Master". BYTE. pp. 288–294. Retrieved 8 September 2015.
  12. ^ Stinson, Craig (Jan 1982). "Chess Championship: Machines Play, People Watch". Softline. p. 6. Retrieved 13 July 2014.
  13. ^ "Rebel vs Anand". Rebel.nl. Retrieved 2010-04-03.
  14. ^ "Chess News – Adams vs Hydra: Man 0.5 – Machine 5.5". ChessBase.com. 28 June 2005. Retrieved 2010-04-03.
  15. ^ Once Again, Machine Beats Human Champion at Chess New York Times, December 5, 2006
  16. ^ "Once Again, Machine Beats Human Champion at Chess". The New York Times. 5 December 2006. Retrieved 30 April 2010.
  17. ^ Computer Chess: The Drosophila of AI October 30, 2002
  18. ^ Deep Thought wins Fredkin Intermediate Prize, Hans Berliner
  19. ^ a b "Pocket Fritz 4 wins Copa Mercosur". Chess.co.uk. Archived from the original on 2011-09-30. Retrieved 2010-04-03.
  20. ^ Stanislav Tsukrov, Pocket Fritz author. Pocket Fritz 4 searches less than 20,000 positions per second.
  21. ^ "World chess champion Magnus Carlsen: 'The computer never has been an opponent'". Deutsche Welle. 16 April 2016. Retrieved 26 August 2016.
  22. ^ a b "20 Years Later, Humans Still No Match For Computers On The Chessboard". NPR.org. 2016. Retrieved 28 June 2020.
  23. ^ Wheland, Norman D. (October 1978). "A Computer Chess Tutorial". BYTE. p. 168. Retrieved 17 October 2013.
  24. ^ (Shannon 1950)
  25. ^ Kirill Kryukov. "Endgame Tablebases Online". Kirill-kryukov.com. Retrieved 2010-04-03.
  26. ^ "Open chess diary 301–320". Xs4all.nl. Retrieved 2010-04-03.
  27. ^ http://tb7.chessok.com Lomonosov website allowing registered user to access 7-piece tablebase, and a forum with positions found.
  28. ^ "Who wins from this? (chess puzzle)" An example chess position found from the Lomonosov chess tablebase.
  29. ^ The Rybka Lounge / Computer Chess / Tablebase sizes, http://rybkaforum.net/cgi-bin/rybkaforum/topic_show.pl?tid=9380 Archived 2017-06-27 at the Wayback Machine, 19th June 2012
  30. ^ "7-piece Syzygy tablebases are complete". lichess.org. Retrieved 2023-10-02.
  31. ^ "Useful data". GitHub. Retrieved 2023-10-12.
  32. ^ "TCEC Openings FAQ". tcec-chess.com. Retrieved 2023-10-12.
  33. ^ CEGT 40/20, Chess Engines Grand Tournament, 12 October 2008, archived from the original on 1 March 2012, retrieved 21 October 2008
  34. ^ Computerschach und Spiele – Eternal Rating, Computerschach und Spiele, 18 March 2007, retrieved 21 May 2008
  35. ^ The SSDF Rating List, Swedish Chess Computer Association, 26 September 2008, retrieved 20 October 2008
  36. ^ BayesianElo Ratinglist of WBEC Ridderkerk, retrieved 20 July 2008
  37. ^ "Gambit Rating List". Home of the Dutch Rebel. January 30, 2021. Retrieved December 12, 2021.
  38. ^ "FGRL". FastGM's Rating List. Retrieved December 12, 2010.
  39. ^ "IPON". Ingo Bauer. November 16, 2016. Archived from the original on January 25, 2019. Retrieved February 3, 2016.
  40. ^ a b CCRL, http://ccrl.chessdom.com/ Archived 2022-01-21 at the Wayback Machine, 14 November 2021
  41. ^ CCRL Discussion Board, http://kirill-kryukov.com/chess/discussion-board/viewtopic.php?f=7&t=2808, 19 June 2012
  42. ^ Adam's Computer Chess Pages, http://adamsccpages.blogspot.co.uk/2012/05/ccrl.html, 19 June 2012
  43. ^ Thurn, Sebastian (1995), Learning to Play the Game of Chess (PDF), MIT Press, retrieved 12 December 2021
  44. ^ Levinson, Robert (1989), A Self-Learning, Pattern-Oriented Chess Program, vol. 12, ICCA Journal
  45. ].
  46. .
  47. ^ Yu Nasu (April 28, 2018). "Efficiently Updatable Neural-Network-based Evaluation Function for computer Shogi" (PDF) (in Japanese).
  48. ^ Yu Nasu (April 28, 2018). "Efficiently Updatable Neural-Network-based Evaluation Function for computer Shogi (Unofficial English Translation)" (PDF). GitHub.
  49. ^ Noda, Hisayori (30 May 2020). "Release stockfish-nnue-2020-05-30". Github. Retrieved 12 December 2021.
  50. ^ a b "Introducing NNUE Evaluation". 6 August 2020.
  51. ^ a b Joost VandeVondele (July 25, 2020). "official-stockfish / Stockfish, NNUE merge". GitHub.
  52. .
  53. ^ Chess, a subsection of chapter 25, Digital Computers Applied to Games, of Faster than Thought, ed. B. V. Bowden, Pitman, London (1953). Online.
  54. ^ A game played by Turing's chess algorithm
  55. ^ "Chessville – Early Computer Chess Programs – by Bill Wall – Bill Wall's Wonderful World of Chess". Archive.is. Archived from the original on 21 July 2012. Retrieved 1 December 2014.{{cite web}}: CS1 maint: bot: original URL status unknown (link)
  56. ^ David Bronstein v M-20, replay at Chessgames.com
  57. ^ Dennis Ritchie (June 2001). "Ken, Unix and Games". ICGA Journal. 24 (2).
  58. ^ "Appendix CHESS 4.5: Competition in 1976" (PDF).
  59. ^ "Oral History of Peter Jennings | Mastering the Game | Computer History Museum".
  60. ^ "New Restrictions". BYTE. January 1981. p. 292. Retrieved 18 October 2013.
  61. ^ "GNU's Bulletin, vol. 1 no. 2".
  62. ^ Hsu (2002) p. 292
  63. ^ Newborn (1997) p. 159
  64. ^ Selective Search. June 1990
  65. ^ International Paderborn Computer Chess Championship 2005
  66. ^ "Challenger uses supercomputer at the world chess championship". Chessbase. 25 May 2010.
  67. ^ "Rybka disqualified and banned from World Computer Chess Championships | ChessVibes". www.chessvibes.com. Archived from the original on 30 March 2014.
  68. ^ Riis, Dr. Søren (2 January 2012). "A Gross Miscarriage of Justice in Computer Chess (part one)". Chessbase News. Retrieved 19 February 2012.
  69. ^ Yu Nasu (2018). ƎUИИ Efficiently Updatable Neural-Network based Evaluation Functions for Computer Shogi. Ziosoft Computer Shogi Club, pdf (Japanese with English abstract)
  70. ^ https://cd.tcecbeta.club/archive.html?season=15&div=sf&game=1 TCEC season 15
  71. ^ Sousa, Ismenio. "Fidelity Chess Challenger 1 – World's First Chess Computer". Retrieved 25 September 2016.
  72. ^ van den Herik, H.J.; Herschberg, I. S. (1992). "The 7th World Computer-Chess Championship: Report on the tournament, Madrid, Spain, November 23-27, 1992". ICCA Journal. 15 (4): 208–209.
  73. ^ "Download | Home of the Dutch Rebel". Rebel13.nl. Retrieved 2022-08-31.
  74. ^ "Dedicated as UCI | Home of the Dutch Rebel". Rebel13.nl. Retrieved 2022-08-31.
  75. ^ "More DOS oldies". Archived from the original on 2018-12-03. Retrieved 2018-12-02.
  76. ^ "Dr. Robert Hyatt's home page". Cis.uab.edu. 2004-02-01. Retrieved 2010-04-03.
  77. ^ The size of the state space and game tree for chess were first estimated in Claude Shannon (1950), "Programming a Computer for Playing Chess" (PDF), Philosophical Magazine, 41 (314), archived from the original (PDF) on 6 July 2010, retrieved 30 December 2008 Shannon gave estimates of 1043 and 10120 respectively, smaller than the estimates in the Game complexity table, which are from Victor Allis's thesis. See Shannon number for details.
  78. ^ "CoffeeHouse: The Internet Chess Club Java Interface". Archived from the original on 1997-06-20. Retrieved 2019-07-08.
  79. ^ "FICS - Free Internet Chess Server". Archived from the original on 1998-12-12. Retrieved 2019-07-08.
  80. ^ "Archived copy". Archived from the original on 2004-08-31. Retrieved 2004-08-31.{{cite web}}: CS1 maint: archived copy as title (link)
  81. ^ "Play Daily (Correspondence) Chess". Archived from the original on 2007-10-06.
  82. ^ "Play Chess Online for Free". play.chessbase.com. Archived from the original on 17 December 2013. Retrieved 11 January 2022.
  83. ^ "Chess Tactics Server". Archived from the original on 2006-04-08. Retrieved 2006-04-08.
  84. ^ "Chess Tactics". Archived from the original on 2007-06-13. Retrieved 2007-06-13.
  85. ^ "Chess Puzzles - Improve Your Chess by Solving Tactics". Archived from the original on 2008-02-18. Retrieved 2008-02-18.
  86. ^ "Chess Tactics Online". Archived from the original on 2015-05-04.
  87. ^ "Chessbase Online, Searching a high quality database of Chessgames. Free Chess Games.ChessBase-Online". www.chessbase-online.com. Archived from the original on 11 May 2000. Retrieved 11 January 2022.
  88. ^ "Java chess games: Database search, analysis". Archived from the original on 1999-02-19. Retrieved 2019-07-08.
  89. ^ "NICBase Online". Archived from the original on 2002-10-08. Retrieved 2002-10-08.
  90. ^ "Play Chess Online - Shredder Chess". Archived from the original on 2006-12-05. Retrieved 2006-12-05.
  91. ^ "Home". fritz.chessbase.com.
  92. ^ "Home". mygames.chessbase.com.
  93. ^ "Chess Lessons - Learn with Online Courses". Archived from the original on 2007-12-14. Retrieved 2007-12-14.

 This article incorporates text by Chess Programming Wiki available under the CC BY-SA 3.0 license.

Sources

Further reading

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