Editing Computer chess (section)

=== 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 (game theory)|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).

==== Minimax search====
{{further|Alpha–beta pruning|minimax}}

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 pawn]]s on seventh [[rank (chess)|rank]], etc.). These selective search heuristics have to be used very carefully however. If the program overextends, it wastes too much time looking at uninteresting positions. If too much is pruned or reduced, there is a risk of cutting out interesting nodes.

==== Monte Carlo tree search ====
{{further|Monte Carlo tree search}}

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 [[batch processing|batching]] on [[graphics processing units]] in order to calculate their [[evaluation function]]s and policy (move selection), and therefore require a [[parallel computing|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, [[transposition table]]s are used to record positions that have been previously evaluated, to save recalculation of them. [[Refutation table]]s 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&nbsp;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.

==== History ====
The [[Claude Shannon#Shannon's computer chess program|first paper]] on chess search was by [[Claude Shannon]] in 1950.<ref name="wheland197810">{{cite news | url=https://archive.org/stream/byte-magazine-1978-10/1978_10_BYTE_03-10_Chess_for_the_Microcomputer#page/n167/mode/2up | title=A Computer Chess Tutorial | work=BYTE | date=October 1978 | access-date=17 October 2013 | author=Wheland, Norman D. | page=168}}</ref> He predicted the two main possible search strategies which would be used, which he labeled "Type A" and "Type B",<ref name="shannon">{{Harvcol|Shannon|1950}}</ref> before anyone had programmed a computer to play chess.

Type A programs would use a "[[brute-force search|brute force]]" approach, examining every possible position for a fixed number of moves using a pure naive [[minimax|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 10<sup>9</sup> positions involved in looking three moves ahead for both sides (six [[Ply (game theory)|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 (chess)|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:
# Employ a [[quiescence search]].
# 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 [[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.