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Minmax
Minimax (sometimes MinMax, MM or saddle point) is a decision rule used in artificial intelligence, decision theory, game theory, statistics, and philosophy for ''mini''mizing the possible loss for a worst case (''max''imum loss) scenario. When dealing with gains, it is referred to as "maximin" – to maximize the minimum gain. Originally formulated for several-player zero-sum game theory, covering both the cases where players take alternate moves and those where they make simultaneous moves, it has also been extended to more complex games and to general decision-making in the presence of uncertainty. Game theory In general games The maximin value is the highest value that the player can be sure to get without knowing the actions of the other players; equivalently, it is the lowest value the other players can force the player to receive when they know the player's action. Its formal definition is: :\underline = \max_ \min_ Where: * is the index of the player of interest. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Folk Theorem (game Theory)
In game theory, folk theorems are a class of theorems describing an abundance of Nash equilibrium payoff profiles in repeated games . The original Folk Theorem concerned the payoffs of all the Nash equilibria of an infinitely repeated game. This result was called the Folk Theorem because it was widely known among game theorists in the 1950s, even though no one had published it. Friedman's (1971) Theorem concerns the payoffs of certain subgame-perfect Nash equilibria (SPE) of an infinitely repeated game, and so strengthens the original Folk Theorem by using a stronger equilibrium concept: subgame-perfect Nash equilibria rather than Nash equilibria. The Folk Theorem suggests that if the players are patient enough and far-sighted (i.e. if the discount factor \delta \to 1 ), then repeated interaction can result in virtually any average payoff in an SPE equilibrium. "Virtually any" is here technically defined as "feasible" and "individually rational". For example, in the one-shot Pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Repeated Games
In game theory, a repeated game is an extensive form game that consists of a number of repetitions of some base game (called a stage game). The stage game is usually one of the well-studied 2-person games. Repeated games capture the idea that a player will have to take into account the impact of his or her current action on the future actions of other players; this impact is sometimes called his or her reputation. ''Single stage game'' or ''single shot game'' are names for non-repeated games. For the real-life example of a repeated game, consider two gas stations that are adjacent to one another. They compete by publicly posting pricing and have the same and constant marginal cost c (the wholesale price of gasoline). Assume that when they both charge p = 10, their joint profit is maximized, resulting in a high profit for everyone. Despite the fact that this is the best outcome for them, they are motivated to deviate. By modestly lowering the price, anyone can steal all of their c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gresham College
Gresham College is an institution of higher learning located at Barnard's Inn Hall off Holborn in Central London, England. It does not enroll students or award degrees. It was founded in 1596 under the will of Sir Thomas Gresham, and hosts over 140 free public lectures every year. Since 2001, all lectures have also been made available online. History Founding and early years Sir Thomas Gresham, founder of the Royal Exchange, left his estate jointly to the City of London Corporation and to the Mercers' Company, which today support the college through the Joint Grand Gresham Committee under the presidency of the Lord Mayor of London. Gresham's will provided for the setting up of the college – in Gresham's mansion in Bishopsgate, on the site now occupied by Tower 42, the former NatWest Tower – and endowed it with the rental income from shops sited around the Royal Exchange, which Gresham had established. The early success of the college led to the incorporation of the Royal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mixed Strategy
In game theory, a player's strategy is any of the options which they choose in a setting where the outcome depends ''not only'' on their own actions ''but'' on the actions of others. The discipline mainly concerns the action of a player in a game affecting the behavior or actions of other players. Some examples of "games" include chess, bridge, poker, monopoly, diplomacy or battleship. A player's strategy will determine the action which the player will take at any stage of the game. In studying game theory, economists enlist a more rational lens in analyzing decisions rather than the psychological or sociological perspectives taken when analyzing relationships between decisions of two or more parties in different disciplines. The strategy concept is sometimes (wrongly) confused with that of a move. A move is an action taken by a player at some point during the play of a game (e.g., in chess, moving white's Bishop a2 to b3). A strategy on the other hand is a complete algorithm for p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IBM Deep Blue
Deep Blue was a chess-playing expert system run on a unique purpose-built IBM supercomputer. It was the first computer to win a game, and the first to win a match, against a reigning world champion under regular time controls. Development began in 1985 at Carnegie Mellon University under the name ChipTest. It then moved to IBM, where it was first renamed Deep Thought, then again in 1989 to Deep Blue. It first played world champion Garry Kasparov in a six-game match in 1996, where it lost four games to two. It was upgraded in 1997 and in a six-game re-match, it defeated Kasparov by winning three games and drawing one. Deep Blue's victory is considered a milestone in the history of artificial intelligence and has been the subject of several books and films. History While a doctoral student at Carnegie Mellon University, Feng-hsiung Hsu began development of a chess-playing supercomputer under the name ChipTest. The machine won the North American Computer Chess Champ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ply (chess) , a spinning technique to make yarn
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Ply, Pli, Plies or Plying may refer to: Common uses * Ply (layer), typically of paper or wood ** Plywood, made of layers of wood ** Tire ply, a layer of cords embedded in the rubber of a tire Places * Plymouth railway station, England, station code PLY *Plymouth Municipal Airport (Indiana), IATA airport code PLY People * Plies (rapper), American rapper Arts, entertainment, and media * Ply (game theory), a turn in game play * PLY (postnominal), a postnominal for athletes that participate in the Paralympic Games Computing and technology * PLY (file format) or Polygon File Format * PLY (Python Lex-Yacc), a parsing tool for Python * Plying In the textile arts, plying (from the French verb ''plier'', "to fold", from the Latin verb ''plico'', from the ancient Greek verb .) is a process of twisting one or more strings (called strands) of yarn together to create a stronger yarn. Strands ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heuristic
A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate, short-term goal or approximation. Where finding an optimal solution is impossible or impractical, heuristic methods can be used to speed up the process of finding a satisfactory solution. Heuristics can be mental shortcuts that ease the cognitive load of making a decision. Examples that employ heuristics include using trial and error, a rule of thumb or an educated guess. Heuristics are the strategies derived from previous experiences with similar problems. These strategies depend on using readily accessible, though loosely applicable, information to control problem solving in human beings, machines and abstract issues. When an individual applies a heuristic in practice, it generally performs as expected. However it can alternatively cre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Go (board Game)
Go is an abstract strategy board game for two players in which the aim is to surround 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 playing pieces are called stones. One player uses the white stones and the other, black. The players take turns placing the stones on the vacant intersections (''points'') of a board. Once placed on the board, stones may not be moved, but stones are removed from the board if the stone (or group of stones) is surrounded by opposing stones on all orthogonally adjacent points, in which case the stone or group is ''captured''. The game proceeds until neither player wishes to make another move. When ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chess
Chess is a board game for two players, called White and Black, each controlling an army of chess pieces in their color, with the objective to checkmate the opponent's king. It is sometimes called international chess or Western chess to distinguish it from related games, such as xiangqi (Chinese chess) and shogi (Japanese chess). The recorded history of chess goes back at least to the emergence of a similar game, chaturanga, in seventh-century India. The rules of chess as we know them today emerged in Europe at the end of the 15th century, with standardization and universal acceptance by the end of the 19th century. Today, chess is one of the world's most popular games, played by millions of people worldwide. Chess is an abstract strategy game that involves no hidden information and no use of dice or cards. It is played on a chessboard with 64 squares arranged in an eight-by-eight grid. At the start, each player controls sixteen pieces: one king, one queen, two rooks, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Horton Conway
John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branches of recreational mathematics, most notably the invention of the cellular automaton called the Game of Life. Born and raised in Liverpool, Conway spent the first half of his career at the University of Cambridge before moving to the United States, where he held the John von Neumann Professorship at Princeton University for the rest of his career. On 11 April 2020, at age 82, he died of complications from COVID-19. Early life and education Conway was born on 26 December 1937 in Liverpool, the son of Cyril Horton Conway and Agnes Boyce. He became interested in mathematics at a very early age. By the time he was 11, his ambition was to become a mathematician. After leaving sixth form, he studied mathematics at Gonville and Caius College, Camb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evaluation Function
An evaluation function, also known as a heuristic evaluation function or static evaluation function, is a function used by game-playing computer programs to estimate the value or goodness of a position (usually at a leaf or terminal node) in a game tree. Most of the time, the value is either a real number or a quantized integer, often in ''n''ths of the value of a playing piece such as a stone in go or a pawn in chess, where ''n'' may be tenths, hundredths or other convenient fraction, but sometimes, the value is an array of three values in the unit interval, representing the win, draw, and loss percentages of the position. There do not exist analytical or theoretical models for evaluation functions for unsolved games, nor are such functions entirely ad-hoc. The composition of evaluation functions is determined empirically by inserting a candidate function into an automaton and evaluating its subsequent performance. A significant body of evidence now exists for several games l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a Heuristic (computer science), heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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