Board representations
The data structure used to represent each chess position is key to the performance of move generation and 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.
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 quiescence search, forward pruning, search extensions and search reductions, are also used as well. These heuristics are triggered based on certain conditions in an attempt to weed out obviously bad moves (history moves) or to investigate interesting nodes (e.g. check extensions, passed pawns on seventh 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 AlphaZero and Leela Chess Zero uses MCTS instead of minimax. Such engines use batching on 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.
Many other optimizations can be used to make chess-playing programs stronger. For example, transposition tables are used to record positions that have been previously evaluated, to save recalculation of them. Refutation tables record key moves that "refute" what appears to be a good move; these are typically tried first in variant positions (since a move that refutes one position is likely to refute another). The drawback is that transposition tables at deep ply depths can get quite large – tens to hundreds of millions of entries. IBM's Deep Blue transposition table in 1996, for example was 500 million entries. Transposition tables that are too small can result in spending more time searching for non-existent entries due to threshing than the time saved by entries found. Many chess engines use 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.
The first paper on chess 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:
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 quiescence search, null move pruning, and other modern selective search heuristics. These heuristics had far fewer mistakes than earlier heuristics did, and was found to be worth the extra time it saved because it could search deeper and widely adopted by many engines. While many modern programs do use 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.
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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 FRC (same time control but Chess960).[Note 2] Pondering (or permanent brain) is switched off and timing is adjusted to the AMD64 X2 4600+ (2.4 GHz) CPU by using Crafty 19.17 BH as a benchmark. Generic, neutral opening books are used (as opposed to the engine's own book) up to a limit of 12 moves into the game alongside 4 or 5 man tablebases.[40][41][42]
The idea of creating a chess-playing machine dates back to the eighteenth century. Around 1769, the chess playing automaton called The Turk, created by Hungarian inventor Farkas Kempelen, became famous before being exposed as a hoax. Before the development of 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.
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Computer hardware and software capable of playing chess
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, use 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]
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