Chess in the context of AI

A figurine (a diminutive form of the word figure) or statuette is a small, three-dimensional sculpture that represents a human, deity or animal, or, in practice, a pair or small group of them. Figurines have been made in many media, with clay, metal, wood, glass, and today plastic or resin the most significant. Ceramic figurines not made of porcelain are called terracottas in historical contexts.

Figures with movable parts, allowing limbs to be posed, are more likely to be called dolls, mannequins, or action figures; or robots or automata, if they can move on their own. Figurines and miniatures are sometimes used in board games, such as chess, and tabletop role playing games.

Medieval India was a long period of post-classical history in the Indian subcontinent between the ancient and modern periods. It is usually regarded as running approximately from the break-up of the Gupta Empire in the 6th century to the start of the early modern period in 1526 with the start of the Mughal Empire, although some historians regard it as both starting and finishing later than these points. The medieval period is itself subdivided into the early medieval and late medieval eras.

In the early medieval period, there were more than 40 different states on the Indian subcontinent, which hosted a variety of cultures, languages, writing systems, and religions. At the beginning of the time period, Buddhism was predominant throughout the area, with the Pala Empire on the Indo Gangetic Plain sponsoring the Buddhist faith's institutions. One such institution was the Buddhist Nalanda mahavihara in modern-day Bihar, a centre of scholarship which brought a divided South Asia onto the global intellectual stage. Another accomplishment was the invention of Chaturanga, which later was exported to Europe and became chess.In Southern India, the Tamil Hindu Cholas gained prominence with an overseas empire that controlled parts of modern-day Sri Lanka, Malaysia, and Indonesia as overseas territories, and helped spread Hinduism and Buddhism into the historic cultural area of Southeast Asia. In this time period, neighbouring regions such as Afghanistan, Tibet, and Southeast Asia were under South Asian influence.

Zero-sum game is a mathematical representation in game theory and economic theory of a situation that involves two competing entities, where the result is an advantage for one side and an equivalent loss for the other. In other words, player one's gain is equivalent to player two's loss, with the result that the net improvement in benefit of the game is zero.

If the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero. Thus, cutting a cake, where taking a more significant piece reduces the amount of cake available for others as much as it increases the amount available for that taker, is a zero-sum game if all participants value each unit of cake equally. Other examples of zero-sum games in daily life include games like poker, chess, sport and bridge where one person gains and another person loses, which results in a zero-net benefit for every player. In the markets and financial instruments, futures contracts and options are zero-sum games as well.

The first millennium of the anno Domini or Common Era was a millennium spanning the years 1 to 1000 (1st to 10th centuries; in astronomy: JD 1721425.5 – 2086667.5). The world population rose more slowly than during the preceding millennium, from about 200 million in the year 1 to about 300 million in the year 1000.

In Western Eurasia (Europe and Near East), the first millennium was a time of great transition from Classical Antiquity to the Middle Ages. The 1st century saw the peak of the Roman Empire, followed by its gradual decline during the period of Late Antiquity, the rise of Christianity and the Great Migrations. The second half of the millennium is characterized as the Early Middle Ages in Europe, and marked by the Viking expansion in the west, and the continuation of the Byzantine Empire (Eastern Roman Empire) in the east.

Through the Looking-Glass, and What Alice Found There is a novel published in December 1871 by Lewis Carroll, the pen name of Charles Lutwidge Dodgson, a mathematics lecturer at Christ Church, Oxford. It is the sequel to his Alice's Adventures in Wonderland (1865), in which many of the characters were anthropomorphic playing cards. In this second novel the theme is chess. As in the earlier book, the central figure, Alice, enters a fantastical world, this time by climbing through a large looking-glass (a mirror) into a world that she can see beyond it. There she finds that, just as in a reflection, things are reversed, including logic (for example, running helps one remain stationary, walking away from something brings one towards it, chessmen are alive and nursery-rhyme characters are real).

Among the characters Alice meets are the severe Red Queen, the gentle and flustered White Queen, the quarrelsome twins Tweedledum and Tweedledee, the rude and opinionated Humpty Dumpty, and the kindly but impractical White Knight. Eventually, as in the earlier book, after a succession of strange adventures, Alice wakes and realises she has been dreaming. As in Alice's Adventures in Wonderland, the original illustrations are by John Tenniel.

Perceptual learning is the learning of perception skills, such as differentiating two musical tones from one another or categorizations of spatial and temporal patterns relevant to real-world expertise. Examples of this may include reading, seeing relations among chess pieces, and knowing whether or not an X-ray image shows a tumor.

Sensory modalities may include visual, auditory, tactile, olfactory, and taste. Perceptual learning forms important foundations of complex cognitive processes (i.e., language) and interacts with other kinds of learning to produce perceptual expertise. Underlying perceptual learning are changes in the neural circuitry. The ability for perceptual learning is retained throughout life.

In the philosophy of mathematics, formalism is the view that holds that statements of mathematics and logic can be considered to be statements about the consequences of the manipulation of strings (alphanumeric sequences of symbols, usually as equations) using established manipulation rules. A central idea of formalism "is that mathematics is not a body of propositions representing an abstract sector of reality, but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than ludo or chess."

According to formalism, mathematical statements are not "about" numbers, sets, triangles, or any other mathematical objects in the way that physical statements are about material objects. Instead, they are purely syntactic expressions—formal strings of symbols manipulated according to explicit rules without inherent meaning. These symbolic expressions only acquire interpretation (or semantics) when we choose to assign it, similar to how chess pieces follow movement rules without representing real-world entities. This view stands in stark contrast to mathematical realism, which holds that mathematical objects genuinely exist in some abstract realm.

Artificial intelligence (AI) is the capability of computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of research in computer science that develops and studies methods and software that enable machines to perceive their environment and use learning and intelligence to take actions that maximize their chances of achieving defined goals.

High-profile applications of AI include advanced web search engines (e.g., Google Search); recommendation systems (used by YouTube, Amazon, and Netflix); virtual assistants (e.g., Google Assistant, Siri, and Alexa); autonomous vehicles (e.g., Waymo); generative and creative tools (e.g., language models and AI art); and superhuman play and analysis in strategy games (e.g., chess and Go). However, many AI applications are not perceived as AI: "A lot of cutting edge AI has filtered into general applications, often without being called AI because once something becomes useful enough and common enough it's not labeled AI anymore."

In mathematics and related fields, an abstract structure is a way of describing a set of mathematical objects and the relationships between them, focusing on the essential rules and properties rather than any specific meaning or example.

For example, in a game such as chess, the rules of how the pieces move and interact define the structure of the game, regardless of whether the pieces are made of wood or plastic. Similarly, an abstract structure defines a framework of objects, operations, and relationships. These structures are studied in their own right, revealing fundamental mathematical principles. While a real-world object or computer program might represent, instantiate, or implement an abstract structure, the structure itself exists as an abstract concept, independent of any particular representation.

In the Middle Ages, the Volga trade route connected Northern Europe and Northwestern Russia with the Caspian Sea and the Sasanian Empire, via the Volga River. The Rus used this route to trade with Muslim countries on the southern shores of the Caspian Sea, sometimes penetrating as far as Baghdad. The powerful Volga Bulgars (cousins of today's Balkan Bulgarians) formed a seminomadic confederation and traded through the Volga river with Viking people of Rus' and Scandinavia (Swedes, Danes, Norwegians) and with the southern Byzantine Empire (Eastern Roman Empire) Furthermore, Volga Bulgaria, with its two cities Bulgar and Suvar east of what is today Moscow, traded with Russians and the fur-selling Ugrians. Chess was introduced to Medieval Rus via the Caspian-Volga trade routes from Persia and Arabia.

There was a second route from the Baltic Sea to the Dnieper, which ran along the Western Dvina (Daugava) between Lovat and Dnieper in the Smolensk region and along the Kasplya River to Gnezdovo. The Volga trade route functioned concurrently with the Dnieper trade route, better known as the trade route from the Varangians to the Greeks, and lost its importance in the 11th century.

Chaturanga (Sanskrit: चतुरङ्ग, IAST: caturaṅga, pronounced [tɕɐtuˈɾɐŋɡɐ]) is an ancient Indian strategy board game. It is first known from India around the seventh century AD.

While there is some uncertainty, the prevailing view among chess historians is that chaturanga is the common ancestor of the board games chess, xiangqi (Chinese), janggi (Korean), shogi (Japanese), sittuyin (Burmese), makruk (Thai), ouk chatrang (Cambodian) and modern Indian chess. It was adopted as chatrang (shatranj) in Sassanid Persia, which in turn was the form of chess brought to late-medieval Europe.

Predispositioning theory, in the field of decision theory and systems theory, is a theory focusing on the stages between a complete order and a complete disorder.

Predispositioning theory was founded by Aron Katsenelinboigen (1927–2005), a professor in the Wharton School who dealt with indeterministic systems such as chess, business, economics, and other fields of knowledge and also made an essential step forward in elaboration of styles and methods of decision-making.

In planning and policy, a wicked problem is a problem that is difficult or impossible to solve because of incomplete, contradictory, and changing requirements that are often difficult to recognize. It refers to an idea or problem that cannot be fixed, where there is no single solution to the problem; "wicked" does not indicate evil, but rather resistance to resolution. Another definition is "a problem whose social complexity means that it has no determinable stopping point". Because of complex interdependencies, the effort to solve one aspect of a wicked problem may reveal or create other problems. Due to their complexity, wicked problems are often characterized by organized irresponsibility.

The phrase was originally used in social planning. Its modern sense was introduced in 1967 by C. West Churchman in a guest editorial he wrote in the journal Management Science. He explains that "The adjective 'wicked' is supposed to describe the mischievous and even evil quality of these problems, where proposed 'solutions' often turn out to be worse than the symptoms". In the editorial, he credits Horst Rittel with first describing wicked problems, though it may have been Churchman who coined the term. Churchman discussed the moral responsibility of operations research "to inform the manager in what respect our 'solutions' have failed to tame his wicked problems." Rittel and Melvin M. Webber formally described the concept of wicked problems in a 1973 treatise, contrasting "wicked" problems with relatively "tame", solvable problems in mathematics, chess, or puzzle solving.

Tabletop games or tabletops are games that are normally played on a table or other flat surface, such as board games, card games, dice games, miniature wargames, tabletop role-playing games, or tile-based games.

This glossary of board games explains commonly used terms in board games, in alphabetical order. For a list of board games, see List of board games; for terms specific to chess, see Glossary of chess; for terms specific to chess problems, see Glossary of chess problems.

An abstract strategy game is a type of strategy game that has minimal or no narrative theme, an outcome determined only by player choice (with minimal or no randomness), and in which each player has perfect information about the game. For example, Go is a pure abstract strategy game since it fulfills all three criteria; chess and related games are nearly so but feature a recognizable theme of ancient warfare; and Stratego is borderline since it is deterministic, loosely based on 19th-century Napoleonic warfare, and features concealed information.

A chessboard is a game board used to play chess. It consists of 64 squares, 8 rows by 8 columns, on which the chess pieces are placed. It is square in shape and uses two colors of squares, one light and one dark, in a checkered pattern. During play, the board is oriented such that each player's near-right corner square is a light square.

The columns of a chessboard are known as files, the rows are known as ranks, and the lines of adjoining same-colored squares (each running from one edge of the board to an adjacent edge) are known as diagonals. Each square of the board is named using algebraic, descriptive, or numeric chess notation; algebraic notation is the FIDE standard. In algebraic notation, using White's perspective, files are labeled a through h from left to right, and ranks are labeled 1 through 8 from bottom to top; each square is identified by the file and rank that it occupies. The a- through d-files constitute the queenside, and the e- through h-files constitute the kingside; the 1st through 4th ranks constitute White's side, and the 5th through 8th ranks constitute Black's side.

In chess, the player who moves first is called White, and the player who moves second is called Black. Their pieces are the white pieces and the black pieces. The pieces are often not literally white and black, but usually contrasting light and dark colors. The 64 squares of the chessboard, which is colored in a checkered pattern, are likewise the "white squares" or "light squares", and "black squares" or "dark squares"; they are usually of contrasting light and dark color rather than literally white and black. For example, the squares on vinyl boards may be off-white ("buff") and green, while those on wood boards are often light brown and dark brown.

An entry in the Glossary of terms in the Laws of Chess at the end of the current FIDE laws also appears for Black.