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Go (game)
# Go is an abstract strategy game, abstract strategy board game for two players in which the aim is to fence off more territory than the opponent. The game was invented in China more than 2,500 years ago and is believed to be the oldest board game continuously played to the present day. A 2016 survey by the International Go Federation's 75 member nations found that there are over 46 million people worldwide who know how to play Go, and over 20 million current players, the majority of whom live in East Asia. The Game piece (board game), playing pieces are called ''Go equipment#Stones, stones''. One player uses the white stones and the other black stones. The players take turns placing their stones on the vacant intersections (''points'') on the #Boards, board. Once placed, stones may not be moved, but ''captured stones'' are immediately removed from the board. A single stone (or connected group of stones) is ''captured'' when surrounded by the opponent's stones on all Orthogona ...
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Board Game
A board game is a type of tabletop game that involves small objects () that are placed and moved in particular ways on a specially designed patterned game board, potentially including other components, e.g. dice. The earliest known uses of the term "board game" are between the 1840s and 1850s. While game boards are a necessary and sufficient condition of this genre, card games that do not use a standard deck of cards, as well as games that use neither cards nor a game board, are often colloquially included, with some referring to this genre generally as "table and board games" or simply "tabletop games". Eras Ancient era Board games have been played, traveled, and evolved in most cultures and societies throughout history Board games have been discovered in a number of archaeological sites. The oldest discovered gaming pieces were discovered in southwest Turkey, a set of elaborate sculptured stones in sets of four designed for a chess-like game, which were created during the ...
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Grid Graph
In graph theory, a lattice graph, mesh graph, or grid graph is a Graph (discrete mathematics), graph whose graph drawing, drawing, Embedding, embedded in some Euclidean space , forms a regular tiling. This implies that the group (mathematics), group of Bijection, bijective transformations that send the graph to itself is a lattice (group), lattice in the group-theoretical sense. Typically, no clear distinction is made between such a graph in the more abstract sense of graph theory, and its drawing in space (often the plane or 3D space). This type of graph may more shortly be called just a lattice, mesh, or grid. Moreover, these terms are also commonly used for a finite section of the infinite graph, as in "an 8 × 8 square grid". The term lattice graph has also been given in the literature to various other kinds of graphs with some regular structure, such as the Cartesian product of graphs, Cartesian product of a number of complete graphs. Square grid graph A comm ...
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Houghton Mifflin Harcourt
Houghton Mifflin Harcourt Company ( ; HMH) is an American publisher of textbooks, instructional technology materials, assessments, and reference works. The company is based in the Financial District, Boston, Boston Financial District. It was formerly known as the Houghton Mifflin Company, but it changed its name following the 2007 acquisition of Harcourt (publisher), Harcourt Publishing. Prior to March 2010, it was a subsidiary of EMPG, Education Media and Publishing Group Limited, an Irish-owned holding company registered in the Cayman Islands and formerly known as Riverdeep. In 2022, it was acquired by Veritas Capital, a New York-based private-equity firm. Company history In 1832, William Ticknor and John Allen purchased a bookselling business in Boston and began to involve themselves in publishing; James T. Fields joined as a partner in 1843. Fields and Ticknor gradually gathered an impressive list of writers, including Ralph Waldo Emerson, Nathaniel Hawthorne, and Henry Dav ...
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Observable Universe
The observable universe is a Ball (mathematics), spherical region of the universe consisting of all matter that can be observation, observed from Earth; the electromagnetic radiation from these astronomical object, objects has had time to reach the Solar System and Earth since the beginning of the metric expansion of space, cosmological expansion. Assuming the universe is isotropy, isotropic, the distance to the edge of the observable universe is equidistant, the same in every direction. That is, the observable universe is a sphere, spherical region centered on the observer. Every location in the universe has its own observable universe, which may or may not overlap with the one centered on Earth. The word ''observable'' in this sense does not refer to the capability of modern technology to detect light or other information from an object, or whether there is anything to be detected. It refers to the physical limit created by the speed of light itself. No signal can travel faster ...
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Ply (game Theory)
In two-or-more-player sequential games, a ply is one turn taken by one of the players. The word is used to clarify what is meant when one might otherwise say "turn". The word "turn" can be a problem since it means different things in different traditions. For example, in standard chess terminology, one ''move'' consists of a turn by each player; therefore a ply in chess is a ''half-move''. Thus, after 20 moves in a chess game, 40 plies have been completed—20 by white and 20 by black. In the game of Go (game), Go, by contrast, a ply is the normal unit of counting moves; so for example to say that a game is ''250 moves long'' is to imply 250 plies. In poker with ''n'' players the word "street" is used for a full betting round consisting of ''n'' plies; each dealt card may sometimes also be called a "street". For instance, in heads up Texas hold'em, a street consists of 2 plies, with possible plays being check/raise/call/fold: the first by the player at the big blind, and the sec ...
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Game-tree Complexity
Combinatorial game theory measures game complexity in several ways: #State-space complexity (the number of legal game positions from the initial position) #Game tree size (total number of possible games) #Decision complexity (number of leaf nodes in the smallest decision tree for initial position) #Game-tree complexity (number of leaf nodes in the smallest full-width decision tree for initial position) #Computational complexity (asymptotic difficulty of a game as it grows arbitrarily large) These measures involve understanding the game positions, possible outcomes, and computational complexity of various game scenarios. Measures of game complexity State-space complexity The ''state-space complexity'' of a game is the number of legal game positions reachable from the initial position of the game. When this is too hard to calculate, an upper bound can often be computed by also counting (some) illegal positions (positions that can never arise in the course of a game). Game t ...
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State-space Complexity
In computer science, a state space is a discrete space representing the set of all possible configurations of a system. It is a useful abstraction for reasoning about the behavior of a given system and is widely used in the fields of artificial intelligence and game theory. For instance, the toy problem Vacuum World has a discrete finite state space in which there are a limited set of configurations that the vacuum and dirt can be in. A "counter" system, where states are the natural numbers starting at 1 and are incremented over time has an infinite discrete state space. The angular position of an undamped pendulum is a continuous (and therefore infinite) state space. Definition State spaces are useful in computer science as a simple model of machines. Formally, a state space can be defined as a tuple 'N'', ''A'', ''S'', ''G''where: * ''N'' is a set of states * ''A'' is a set of arcs connecting the states * ''S'' is a nonempty subset of ''N'' that contains star ...
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Chess
Chess is a board game for two players. It is an abstract strategy game that involves Perfect information, no hidden information and no elements of game of chance, chance. It is played on a square chessboard, board consisting of 64 squares arranged in an 8×8 grid. The players, referred to as White and Black in chess, "White" and "Black", each control sixteen Chess piece, pieces: one king (chess), king, one queen (chess), queen, two rook (chess), rooks, two bishop (chess), bishops, two knight (chess), knights, and eight pawn (chess), pawns, with each type of piece having a different pattern of movement. An enemy piece may be captured (removed from the board) by moving one's own piece onto the square it occupies. The object of the game is to "checkmate" (threaten with inescapable capture) the enemy king. There are also several ways a game can end in a draw (chess), draw. The recorded history of chess goes back to at least the emergence of chaturanga—also thought to be an ancesto ...
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Rules
Rule or ruling may refer to: Human activity * The exercise of political or personal control by someone with authority or power * Business rule, a rule pertaining to the structure or behavior internal to a business * School rule, a rule that is part of school discipline * Sport rule, a rule that defines how a sport is played * Game rule, a rule that defines how a game is played * Morality, a rule or element of a moral code for guiding choices in human behavior * Norm (philosophy), a kind of sentence or a reason to act, feel or believe * Social norm, explicit or implicit rules used within society or by a group * Rule of thumb, a principle with broad application that is not intended to be strictly accurate or reliable for every situation * Unspoken rule, an assumed rule of human behavior that is not voiced or written down Science * Ruler or "rule"; a distance measuring device * Slide rule, a mechanical analog computer * Rule of inference or transformation rule, a term in log ...
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Zuo Zhuan
The ''Zuo Zhuan'' ( zh, t=左傳, w=Tso Chuan; ), often translated as ''The Zuo Tradition'' or as ''The Commentary of Zuo'', is an ancient Chinese narrative history traditionally regarded as a commentary on the ancient Chinese chronicle the '' Spring and Autumn Annals''. It comprises 30 chapters covering the period from 722 to 468BC, and focuses mainly on political, diplomatic, and military affairs from that era. For many centuries, the ''Zuo Zhuan'' was the primary text through which educated Chinese learned their ancient history. The ''Zuo Zhuan'' does not simply explain the wording of the ''Spring and Autumn Annals'', but rather expounds upon its historical background with rich and lively accounts of the history and culture of the Spring and Autumn period (771476 BC). The ''Zuo Zhuan'' is the source of more Chinese sayings and idioms than any other classical work, and its concise, flowing style served as a paragon of elegant Classical Chinese. Its tendency toward thi ...
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Aristocratic
Aristocracy (; ) is a form of government that places power in the hands of a small, privileged ruling class, the aristocrats. Across Europe, the aristocracy exercised immense economic, political, and social influence. In Western Christian countries, the aristocracy was mostly equal with magnates, also known as the titled or higher nobility, however the members of the more numerous social class, the untitled lower nobility ( petty nobility or gentry) were not part of the aristocracy. Classical aristocracy In ancient Greece, the Greeks conceived aristocracy as rule by the best-qualified citizens—and often contrasted it favorably with monarchy, rule by an individual. The term was first used by such ancient Greeks as Aristotle and Plato, who used it to describe a system where only the best of the citizens, chosen through a careful process of selection, would become rulers, and hereditary rule would actually have been forbidden, unless the rulers' children performed best and ...
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Four Arts
The four arts (), or the four arts of the Chinese scholar, were the four main academic and artistic talents required of the aristocratic ancient Chinese scholar-gentleman. They were the mastery of the ''qin'' (the guqin, a stringed instrument, 琴), ''qi'' (the strategy game of Go, 棋), ''shu'' (Chinese calligraphy, 書) and ''hua'' ( Chinese painting, 畫), and are also referred to by listing all four: zh, t=琴棋書畫, p=qínqíshūhuà, labels=no. Origin of the concept Although the individual elements of the concept have very long histories as activities befitting a learned person in ancient Chinese history, the earliest written source putting the four together is Zhang Yanyuan's 9th century ''Fashu Yaolu'' (Compendium of Calligraphy) from the Tang dynasty. File:The Eighteen Scholars by an anonymous Ming artist 1.jpg, ''Qin'' File:The Eighteen Scholars by an anonymous Ming artist 2.jpg, ''Weiqi (Go)'' File:The Eighteen Scholars by an anonymous Ming artist 3.jpg, '' ...
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