The minimax algorithm finds the best move, and alpha-beta pruning prevents it from going into branches of the game tree that cannot produce a better result than previous branches already have. However, the chess game tree is too large to be completely examined.

1. Chess Algorithm Formula
2. Computer Chess Algorithm

1990s pressure-sensory chess computer with LCD screen Computer chess is encompassing and capable of playing autonomously without human guidance. Computer chess acts as solo entertainment (allowing players to practice and to better themselves when no sufficiently strong human opponents are available), as aids to chess analysis, for computer chess competitions, and as research to provide insights into human. Current are able to defeat even the strongest human players under normal conditions. Whether computation could ever remains an open question. Computer chess IC bearing the name of developer Frans Morsch (see also ) Chess-playing computers are now accessible to the average consumer. From the mid-1970s to the present day, dedicated chess computers have been available for purchase. There are many such as, and that can be downloaded from the for free.

These engines are able to play a game that, when run on an up-to-date, can defeat most master players under tournament conditions. Top programs such as the or or the program Stockfish have surpassed even world champion caliber players at and short. In October 2008 was rated top in the, and rating lists and has won many recent official computer chess tournaments such as CCT 8 and 9, the 2006 Dutch Open Computer Championship, the 16th, and the 15th. As of 3 February 2016, Stockfish is the top rated chess program on the rating list. Computer Chess Rating Lists CCRL (Computer Chess Rating Lists) is an organisation that tests computer ' by playing the programs against each other. CCRL was founded in 2006 by Graham Banks, Ray Banks, Sarah Bird, and Charles Smith, and as of June 2012 its members are Graham Banks, Ray Banks (who only participates in, or Fischer Random Chess), Shaun Brewer, Adam Hair, Aser Huerga, Kirill Kryukov, Denis Mendoza, Charles Smith and Gabor Szots. 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 (same time control but Chess960).

Pondering (or ) is switched off and timing is adjusted to the AMD64 X2 4600+ (2.4 GHz) by using as a benchmark. Generic, neutral 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. Computers versus humans. Main article: 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 (five ) 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. After discovering refutation screening—the application of to optimizing move evaluation—in 1957, a team at predicted that a computer would defeat the world human champion by 1967. It did not anticipate the difficulty of determining the right order to evaluate branches. Researchers worked to improve programs' ability to identify, unusually high-scoring moves to reexamine when evaluating other branches, but into the 1970s most top chess players believed that computers would not soon be able to play at a level. In 1968 that no chess computer would be able to beat him within ten years, and in 1976 and professor of psychology Eliot Hearst of 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'. In the late 1970s chess programs suddenly began defeating top human players.

The year of Hearst's statement, 's at the American Chess Championship's level became the first to win a human tournament. Levy won his bet in 1978 by beating, but it achieved the first computer victory against a Master-class player at the tournament level by winning one of the six games. In 1980 began often defeating Masters. By 1982 two programs played at Master level and three were slightly weaker. The sudden improvement without a theoretical breakthrough surprised humans, who 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, estimated that 90% of the improvement came from faster evaluation speed and only 10% from improved evaluations. 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'.

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 almost all 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. While reviewing SPOC in 1984, wrote that 'Computers—mainframes, minis, and micros—tend to play ugly, inelegant chess', but noted '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). At the 1982, predicted that a chess program could become world champion within five years; tournament director and International Master predicted ten years; the Spracklens predicted 15; predicted more than 20; and others predicted that it would never happen.

The most widely held opinion, however, stated that it would occur around the year 2000. In 1989, Levy was defeated by in an exhibition match. Deep Thought, however, was still considerably below World Championship Level, as the then reigning world champion demonstrated in two strong wins in 1989. It was not until a 1996 match with that Kasparov lost his first game to a computer at tournament time controls in.

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 two of the remaining five games of the match, for a convincing victory. In May 1997, an updated version of defeated Kasparov 3½–2½ in a return match. A documentary mainly about the confrontation was made in 2003, titled. IBM keeps a web site of.

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, defeated, who at the time was ranked second in the world, by a score of 5–3. However most of those games were not played at normal time controls. Out of the eight games, four were games (five minutes plus five seconds Fischer delay (see ) 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. 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 and were able to draw matches against former world champion Garry Kasparov and classical world champion. In October 2002, and competed in the eight-game match, which ended in a draw. Kramnik won games 2 and 3 by 'conventional' – 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, 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.

In January 2003, Garry Kasparov played, another chess computer program, in. The match ended 3–3.

In November 2003, Garry Kasparov played. The match ended 2–2. In 2005, a dedicated chess computer with custom hardware and sixty-four processors and also winner of the 14th in 2005, defeated seventh-ranked 5½–½ in a six-game match (though Adams' preparation was far less thorough than Kramnik's for the 2002 series). In November–December 2006, World Champion played. 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 , and drew the next four. In the final game, in an attempt to draw the match, Kramnik played the more aggressive 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. According to Newborn, for example, 'the science is done'. 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 while the best humans only gained roughly 2 points per year. The highest rating obtained by a computer in human competition was '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, should not be directly compared. In 2016, the rated computer program at 3361.

Continue to improve. In 2009, chess engines running on slower hardware have reached the level. A won a 6 tournament with a performance rating 2898: chess engine 13 running inside 4 on the mobile phone won the Copa Mercosur tournament in with 9 wins and 1 draw on August 4–14, 2009. Pocket Fritz 4 searches fewer than 20,000 positions per second. This is in contrast to supercomputers such as Deep Blue that searched 200 million positions per second. 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, although this has not been proven. Players today are inclined to treat chess engines as analysis tools rather than opponents. Implementation issues The developers of a chess-playing computer system must decide on a number of fundamental implementation issues. These include:. – 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.

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 (PGN), and can read and write individual positions as (FEN). Older chess programs often only understood, but today users expect chess programs to understand standard. Most computer chess programs are divided into an engine (which computes the best move given a current position) and a user interface. Most engines are separate programs from the user interface, and the two parts communicate to each other using a public communication protocol.

The most popular protocol is the (CECP). Another open alternate chess communication protocol is the (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.) Implementers also need to decide if they will use endgame databases or other, and often implement common de facto chess standards.

Board representations. Main article: The used to represent each chess position is key to the performance of move generation and.

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 ('), and positions for compact long-term storage. Search techniques The was by in 1950. He predicted the two main possible search strategies which would be used, which he labeled 'Type A' and 'Type B', before anyone had programmed a computer to play chess. Type A programs would use a ' approach, examining every possible position for a fixed number of moves using the. 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 9 positions involved in looking three moves ahead for both sides (six ) 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.) Second, it ignored the problem of quiescence, trying to only evaluate a position that is at the end of an of pieces or other important sequence of moves ('lines').

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. Instead of wasting processing power examining bad or trivial moves, Shannon suggested that 'type B' programs would use two improvements:. Employ a. 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. The test of time has borne out the first approach; all modern programs employ a terminal quiescence search before evaluating positions.

The second approach (now called forward pruning) has been dropped in favor of search extensions. Interviewed a number of chess players of varying strengths, and concluded that both 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 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 problem with type B is that it relies on the program being able to decide which moves are good enough to be worthy of consideration ('plausible') in any given position and this proved to be a much harder problem to solve than speeding up type A searches with superior hardware and search extension techniques.

One of the few chess grandmasters to devote himself seriously to computer chess was former, who wrote several works on the subject. He also held a doctorate in electrical engineering. Working with relatively primitive hardware available in the 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.

Chess Algorithm Formula

In 1965 Botvinnik was a consultant to the ITEP team in a US-Soviet computer chess match (see ). One developmental milestone occurred when the team from, which was responsible for the series of programs and won the first three (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, before winning the ACM Championship again in 1975, 1976 and 1977.

One reason they gave for the switch was that they found it less stressful during competition, because it was difficult to anticipate which moves their type B programs would play, and why. They also reported that type A was much easier to debug in the four months they had available and 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. Chess 4.0 type programs won out for the simple reason that their programs played better chess. Such programs did not try to mimic human thought processes, but relied on full width and searches. Most such programs (including all modern programs today) also included a fairly limited selective part of the search based on quiescence searches, and usually extensions and pruning (particularly null move pruning from the 1990s onwards) which were triggered based on certain conditions in an attempt to weed out or reduce obviously bad moves (history moves) or to investigate interesting nodes (e.g.

Check extensions, on seventh, etc.). Extension and pruning triggers 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, there is a risk cutting out interesting nodes. Chess programs differ in terms of how and what types of pruning and extension rules are included as well as in the evaluation function. Some programs are believed to be more selective than others (for example was known to be less selective than most commercial programs because they could afford to do more complete full width searches), but all have a base full width search as a foundation and all have some selective components (Q-search, pruning/extensions). Though such additions meant that the program did not truly examine every node within its search depth (so it would not be truly brute force in that sense), the rare mistakes due to these selective searches was found to be worth the extra time it saved because it could search deeper.

In that way Chess programs can get the best of both worlds. Furthermore, 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 defeated World Champion Garry Kasparov, marking the first time a computer has defeated a reigning world chess champion in standard time control. Computer chess programs consider chess moves as a.

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 '. This evaluation continues until a certain maximum search depth or the program determines that a final 'leaf' position has been reached (e.g. A naive implementation of this approach 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. For more information, see:.

algorithm. Leaf evaluation For most chess positions, computers cannot look ahead to all possible final positions. Instead, they must look ahead a few and compare the possible positions, known as leaves. The algorithm that evaluates leaves is termed the ', and these algorithms are often vastly different between different chess programs. Evaluation functions typically evaluate positions in hundredths of a pawn (called a centipawn), and 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, 3 points for a or, 5 points for a, and 9 points for a. (See.) The is sometimes given an arbitrary high value such as 200 points or 1,000,000,000 points (1961 USSR program) to ensure that a checkmate outweighs all other factors (:45).

By convention, a positive evaluation favors White, and a negative evaluation favors Black. In addition to points for pieces, most 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). Endgame tablebases. Main article: 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 can force a win.

Computer Chess Algorithm

To solve this problem, computers have been used to analyze some positions completely, starting with and against king. Such endgame tablebases are generated in advance using a form of, starting with positions where the final result is known (e.g., where one side has been mated) and seeing which other positions are one move away from them, then which are one move from those, etc. 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 against king and and was able to draw that theoretically lost ending against several masters (see ).

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 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.

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 (:144–48), (: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. Emil strainu - razboiul ingerilor pdf. 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 formats have been released including the Edward Tablebase, the De Koning Database and the Tablebase which is used by many chess programs such as, and. Tablebases for all positions with six pieces are available. Some seven-piece endgames have been analyzed by Marc Bourzutschky and Yakov Konoval.

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 ). 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 techniques, require 7.05 of hard disk space for all five-piece endings.

To cover all the six-piece endings requires approximately 1.2. It is estimated that a seven-piece tablebase requires between 50 and 200 of storage space.

Endgame databases featured prominently in 1999, when Kasparov played an exhibition match on the Internet against the. A seven piece and endgame was reached with the World Team fighting to salvage a draw. Helped by generating the six piece ending tablebase where both sides had two Queens which was used heavily to aid analysis by both sides. Other optimizations Many other optimizations can be used to make chess-playing programs stronger. For example, are used to record positions that have been previously evaluated, to save recalculation of them. 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).

Opening books aid computer programs by giving common openings that are considered good play (and good ways to counter poor openings). Many chess engines use to increase their strength. Of course, faster hardware and additional processors can improve chess-playing program abilities, and some systems (such as ) use specialized chess hardware instead of only software. Another way to examine more chess positions is to distribute the analysis of positions to many computers. The ChessBrain project was a chess program that distributed the search tree computation through the Internet. In 2004 the ChessBrain played chess using 2,070 computers. Playing strength versus computer speed It has been estimated that doubling the computer speed gains approximately fifty to seventy points in playing strength (:192).

Chess variants. Is an example of a game largely unaffected by chess computers or software. Chess engines have been developed to play some such as, but the engines are almost never directly integrated with specific hardware. Even for the software that has been developed, most will not play chess beyond a certain board size, so games played on an unbounded chessboard remain virtually untouched by both chess computers and software. Other chess software There are several other forms of chess-related, including the following:. Chess game viewers allow players to view a pre-recorded game on a computer.

Most chess-playing programs can also be used for this purpose, but some special-purpose software exists. Chess instruction software is designed to teach chess. Chess databases are systems which allow the searching of a large library of historical games.

(Scid) is an example of a database which may be used under, and. There are also commercial databases, such as and Chess Assistant for Windows and for Mac OS X. and clients Notable theorists Well-known computer chess theorists include:., International Master and Computer Science professor., three-time. D. Beal (Donald Francis Beal)., The Father of Deep Blue (IBM & Carnegie Mellon University)., author of open source chess program.

Solving chess. Main article: The prospects of completely chess are generally considered to be rather remote. It is widely conjectured that there is no computationally inexpensive method to solve chess even in the very weak sense of determining with certainty the value of the initial position, and hence the idea of solving chess in the stronger sense of obtaining a practically usable description of a strategy for perfect play for either side seems unrealistic today. However, it has not been proven that no computationally cheap way of determining the best move in a chess position exists, nor even that a traditional running on present-day computing hardware could not solve the initial position in an acceptable amount of time.

The difficulty in proving the latter lies in the fact that, while the number of board positions that could happen in the course of a chess game is huge (on the order of at least 10 43 to 10 47), it is hard to rule out with mathematical certainty the possibility that the initial position allows either side to force a mate or a after relatively few moves, in which case the search tree might encompass only a very small subset of the set of possible positions. It has been mathematically proven that generalized chess (chess played with an arbitrarily large number of pieces on an arbitrarily large chessboard) is, 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. Gardner's, played on a 5×5 board with approximately 10 18 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 piece (2 kings and up to 5 other pieces) endgames have been solved. Chronology The idea of creating a chess-playing machine dates back to the eighteenth century.

Around 1769, the chess playing called became famous before being exposed as a hoax. Before the development of, serious trials based on automata such as of 1912, 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. Since then, chess enthusiasts and have built, with increasing degrees of seriousness and success, chess-playing machines and computer programs. 1769 – builds the, in what becomes one of the greatest hoaxes of its period. 1868 – Charles Hooper presented the automaton — which also had a human chess player hidden inside. 1912 – builds a machine that could play.

1941 – Predating comparable work by at least a decade, develops computer chess algorithms in his programming formalism. Because of the circumstances of the Second World War, however, they were not published, and did not come to light, until the 1970s. 1948 – 's book Cybernetics describes how a chess program could be developed using a depth-limited minimax search with an. 1950 – publishes 'Programming a Computer for Playing Chess', one of the first papers on the problem of computer chess. 1951 – is first to publish a program, developed on paper, that was capable of playing a full game of chess. 1952 – develops a program that solves chess problems.

Main article: 'Chess engine' normally refers to the algorithmic part of a chess program or machine. The user interface part is often a separate program, which the chess engine plugs into as a substitutable or replaceable module. Chess engines may consist of a software chess program running on a conventional digital computer, or a software program running on a conventional computer with dedicated chess-specific microprogramming or hardware to speed esp. Tree searching and position evaluation, or a hardware/software/firmware machine dedicated exclusively to playing chess.

Distributed computing programs that play chess utilizing multiple processors or multiple networked machines have also been developed. Most generally available commercial chess programs are software that runs on PC-type hardware.

Such programs running on even very modest hardware (as small as cellphones) are vastly stronger than most human chess players. See also.