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Zobrist Hashing
Zobrist hashing (also referred to as Zobrist keys or Zobrist signatures Bruce Moreland/ref>) is a hash function construction used in computer programs that play abstract board games, such as chess and Go, to implement transposition tables, a special kind of hash table that is indexed by a board position and used to avoid analyzing the same position more than once. Zobrist hashing is named for its inventor, Albert Lindsey Zobrist.Albert Lindsey Zobrist''A New Hashing Method with Application for Game Playing'' Tech. Rep. 88, Computer Sciences Department, University of Wisconsin, Madison, Wisconsin, (1969). It has also been applied as a method for recognizing substitutional alloy configurations in simulations of crystalline materials. Zobrist hashing is the first known instance of the generally useful underlying technique called tabulation hashing. Calculation of the hash value Zobrist hashing starts by randomly generating bitstrings for each possible element of a board game, i.e. f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hash Function
A hash function is any function that can be used to map data of arbitrary size to fixed-size values. The values returned by a hash function are called ''hash values'', ''hash codes'', ''digests'', or simply ''hashes''. The values are usually used to index a fixed-size table called a ''hash table''. Use of a hash function to index a hash table is called ''hashing'' or ''scatter storage addressing''. Hash functions and their associated hash tables are used in data storage and retrieval applications to access data in a small and nearly constant time per retrieval. They require an amount of storage space only fractionally greater than the total space required for the data or records themselves. Hashing is a computationally and storage space-efficient form of data access that avoids the non-constant access time of ordered and unordered lists and structured trees, and the often exponential storage requirements of direct access of state spaces of large or variable-length keys. Use of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rook (chess)
The rook (; ♖, ♜) is a piece in the game of chess. It may move any number of squares horizontally or vertically without jumping, and it may an enemy piece on its path; additionally, it may participate in castling. Each player starts the game with two rooks, one in each corner on their own side of the board. Formerly, the rook (from Persian رخ ''rokh''/''rukh'', meaning "chariot") was alternatively called the tower, marquess, rector, and comes (count or earl). The term "castle" is considered to be informal, incorrect, or old-fashioned. Placement and movement The white rooks start on squares a1 and h1, while the black rooks start on a8 and h8. The rook moves horizontally or vertically, through any number of unoccupied squares (see diagram). The rook cannot jump over pieces. The rook may capture an enemy piece by moving to the square on which the enemy piece stands, removing it from play. The rook also participates with the king in a special move called castling, wherein i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Artificial Intelligence
In video games, artificial intelligence (AI) is used to generate responsive, adaptive or intelligent behaviors primarily in non-player characters (NPCs) similar to human-like intelligence. Artificial intelligence has been an integral part of video games since their inception in the 1950s. AI in video games is a distinct subfield and differs from academic AI. It serves to improve the game-player experience rather than machine learning or decision making. During the golden age of arcade video games the idea of AI opponents was largely popularized in the form of graduated difficulty levels, distinct movement patterns, and in-game events dependent on the player's input. Modern games often implement existing techniques such as pathfinding and decision trees to guide the actions of NPCs. AI is often used in mechanisms which are not immediately visible to the user, such as data mining and procedural-content generation. In general, game AI does not, as might be thought and sometimes i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Go
Computer Go is the field of artificial intelligence (AI) dedicated to creating a computer program that plays the traditional board game Go. The field is sharply divided into two eras. Before 2015, the programs of the era were weak. The best efforts of the 1980s and 1990s produced only AIs that could be defeated by beginners, and AIs of the early 2000s were intermediate level at best. Professionals could defeat these programs even given handicaps of 10+ stones in favor of the AI. Many of the algorithms such as alpha-beta minimax that performed well as AIs for checkers and chess fell apart on Go's 19x19 board, as there were too many branching possibilities to consider. Creation of a human professional quality program with the techniques and hardware of the time was out of reach. Some AI researchers speculated that the problem was unsolvable without creation of human-like AI. The application of Monte Carlo tree search to Go algorithms provided a notable improvement in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Chess
Computer chess includes both hardware (dedicated computers) and software capable of playing chess. Computer chess provides opportunities for players to practice even in the absence of human opponents, and also provides opportunities for analysis, entertainment and training. Computer chess applications that play at the level of a chess master or higher are available on hardware from supercomputers to smart phones. Standalone chess-playing machines are also available. Stockfish, GNU Chess, Fruit, and other free open source applications are available for various platforms. Computer chess applications, whether implemented in hardware or software, utilize different strategies than humans to choose their moves: they use heuristic methods to build, search and evaluate trees representing sequences of moves from the current position and attempt to execute the best such sequence during play. Such trees are typically quite large, thousands to millions of nodes. The computational speed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alpha-beta Pruning
Alphabeta is an Israeli musical group. Alphabeta or Alpha Beta may also refer to: *The Greek alphabet, from ''Alpha'' (Αα) and ''Beta'' (Ββ), the first two letters *Alpha Beta, a former chain of Californian supermarkets *Alpha and beta anomers (chemistry) *Alpha–beta pruning, a type of search algorithm *Alpha-beta transformation, a mathematical transformation in electrical engineering *Alpha-beta unsaturated carbonyl compounds, a class of organic compounds *Alpha beta filter, a predictive filter *Alpha (finance) and Beta (finance), two measures characterizing the return of an investment portfolio *The Alpha Betas, a fraternity in the ''Revenge of the Nerds'' film series *''Alpha Betas,'' an animated webseries created by Chris Bruno and David Howard Lee starring Evan Fong Evan Fong (born 31 May 1992), known online as VanossGaming (or simply Vanoss), is a Canadian internet personality, video game commentator, music producer, and DJ. He posts montage-style videos on YouTube ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Simulations
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution. In physics-related problems, Monte Carlo methods are useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model, interacting particle systems, McKean–Vlasov processes, kinetic models of gases). Other examples include modeling phenomena with significant uncertainty in inputs such as the calculation of risk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Substitutional Alloy
An alloy is a mixture of chemical elements of which at least one is a metal. Unlike chemical compounds with metallic bases, an alloy will retain all the properties of a metal in the resulting material, such as electrical conductivity, ductility, opacity, and luster, but may have properties that differ from those of the pure metals, such as increased strength or hardness. In some cases, an alloy may reduce the overall cost of the material while preserving important properties. In other cases, the mixture imparts synergistic properties to the constituent metal elements such as corrosion resistance or mechanical strength. Alloys are defined by a metallic bonding character. The alloy constituents are usually measured by mass percentage for practical applications, and in atomic fraction for basic science studies. Alloys are usually classified as substitutional or interstitial alloys, depending on the atomic arrangement that forms the alloy. They can be further classified as homogene ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Number Generator
Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols that cannot be reasonably predicted better than by random chance is generated. This means that the particular outcome sequence will contain some patterns detectable in hindsight but unpredictable to foresight. True random number generators can be '' hardware random-number generators'' (HRNGS) that generate random numbers, wherein each generation is a function of the current value of a physical environment's attribute that is constantly changing in a manner that is practically impossible to model. This would be in contrast to so-called "random number generations" done by ''pseudorandom number generators'' (PRNGs) that generate numbers that only look random but are in fact pre-determined—these generations can be reproduced simply by knowing the state of the PRNG. Various applications of randomness have led to the development of several different meth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tuple
In mathematics, a tuple is a finite ordered list (sequence) of elements. An -tuple is a sequence (or ordered list) of elements, where is a non-negative integer. There is only one 0-tuple, referred to as ''the empty tuple''. An -tuple is defined inductively using the construction of an ordered pair. Mathematicians usually write tuples by listing the elements within parentheses "" and separated by a comma and a space; for example, denotes a 5-tuple. Sometimes other symbols are used to surround the elements, such as square brackets "nbsp; or angle brackets "⟨ ⟩". Braces "" are used to specify arrays in some programming languages but not in mathematical expressions, as they are the standard notation for sets. The term ''tuple'' can often occur when discussing other mathematical objects, such as vectors. In computer science, tuples come in many forms. Most typed functional programming languages implement tuples directly as product types, tightly associated with algebr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set (mathematics)
A set is the mathematical model for a collection of different things; a set contains '' elements'' or ''members'', which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if they have precisely the same elements. Sets are ubiquitous in modern mathematics. Indeed, set theory, more specifically Zermelo–Fraenkel set theory, has been the standard way to provide rigorous foundations for all branches of mathematics since the first half of the 20th century. History The concept of a set emerged in mathematics at the end of the 19th century. The German word for set, ''Menge'', was coined by Bernard Bolzano in his work ''Paradoxes of the Infinite''. Georg Cantor, one of the founders of set theory, gave the following defin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rules Of Go
The rules of Go have seen some variation over time and from place to place. This article discusses those sets of rules broadly similar to the ones currently in use in East Asia. Even among these, there is a degree of variation. Notably, Chinese and Japanese rules differ in a number of aspects. The most significant of these are the scoring method, together with attendant differences in the manner of ending the game. While differences between sets of rules may have moderate strategic consequences on occasion, they do not change the character of the game. The different sets of rules usually lead to the same game result, so long as the players make minor adjustments near the end of the game. Differences in the rules are said to cause problems in perhaps one in every 10,000 games in competition. This article first presents a simple set of rules which are, except for wording, identical to those usually referred to as the Tromp–Taylor Rules, themselves close in most essential respect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
