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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. 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. for each combination of a piece and a position (in the game of chess, that's 6 pieces × 2 colors × 64 board positions, with a constant number of additional bitstrings for ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hash Function
A hash function is any Function (mathematics), function that can be used to map data (computing), data of arbitrary size to fixed-size values, though there are some hash functions that support variable-length output. The values returned by a hash function are called ''hash values'', ''hash codes'', (''hash/message'') ''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 s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...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-playable characters (NPCs) similar to human-like intelligence. Artificial intelligence has been an integral part of video games since their inception in 1948, first seen in the game ''Nim''. 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. One of the most infamous examples ... [...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 title, chess grandmaster or higher are available on hardware from supercomputers to Smartphone, smart phones. Standalone chess-playing machines are also available. Stockfish (chess), Stockfish, Leela Chess Zero, GNU Chess, Fruit (software), Fruit, and other free open source applications are available for various platforms. Computer chess applications, whether implemented in hardware or software, use different strategies than humans to choose their moves: they use Heuristic (computer science), heuristic methods to build, search and evaluate Tree (data structure), trees representing sequences of moves from the current position and attempt to execute ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alpha–beta Pruning
Alpha–beta pruning is a search algorithm that seeks to decrease the number of nodes that are evaluated by the Minimax#Minimax algorithm with alternate moves, minimax algorithm in its game tree, search tree. It is an adversarial search algorithm used commonly for machine playing of two-player Combinatorial game theory, combinatorial games (Tic-tac-toe, Chess, Connect 4, etc.). It stops evaluating a move when at least one possibility has been found that proves the move to be worse than a previously examined move. Such moves need not be evaluated further. When applied to a standard minimax tree, it returns the same move as minimax would, but prunes away branches that cannot possibly influence the final decision. History John McCarthy during the Dartmouth workshop, Dartmouth Workshop met Alex Bernstein of IBM, who was writing a chess program. McCarthy invented alpha–beta search and recommended it to him, but Bernstein was "unconvinced". Allen Newell and Herbert A. Simon who us ... [...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. The name comes from the Monte Carlo Casino in Monaco, where the primary developer of the method, mathematician Stanisław Ulam, was inspired by his uncle's gambling habits. Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration, and generating draws from a probability distribution. They can also be used to model phenomena with significant uncertainty in inputs, such as calculating the risk of a nuclear power plant failure. Monte Carlo methods are often implemented using computer simulations, and they can provide approximate solutions to problems that are otherwise intractable or too complex to analyze mathematically. Monte Carlo methods are widely used in various ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Substitutional Alloy
An alloy is a mixture of chemical elements of which in most cases at least one is a metallic element, although it is also sometimes used for mixtures of elements; herein only metallic alloys are described. Metallic alloys often have properties that differ from those of the pure elements from which they are made. The vast majority of metals used for commercial purposes are alloyed to improve their properties or behavior, such as increased strength, hardness or corrosion resistance. Metals may also be alloyed to reduce their overall cost, for instance alloys of gold and copper. A typical example of an alloy is 304 grade stainless steel which is commonly used for kitchen utensils, pans, knives and forks. Sometime also known as 18/8, it as an alloy consisting broadly of 74% iron, 18% chromium and 8% nickel. The chromium and nickel alloying elements add strength and hardness to the majority iron element, but their main function is to make it resistant to rust/corrosion. In an al ... [...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 is generated that cannot be reasonably predicted better than by random chance. This means that the particular outcome sequence will contain some patterns detectable in hindsight but impossible to foresee. True random number generators can be '' hardware random-number generators'' (HRNGs), 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), which generate numbers that only look random but are in fact predetermined—these generations can be reproduced simply by knowing the state of the PRNG. Various applications of randomness have led to the development of different methods for generating random data. Some of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tuple
In mathematics, a tuple is a finite sequence or ''ordered list'' of numbers or, more generally, mathematical objects, which are called the ''elements'' of the tuple. An -tuple is a tuple of elements, where is a non-negative integer. There is only one 0-tuple, called the ''empty tuple''. A 1-tuple and a 2-tuple are commonly called a singleton and an ordered pair, respectively. The term ''"infinite tuple"'' is occasionally used for ''"infinite sequences"''. Tuples are usually written by listing the elements within parentheses "" and separated by commas; for example, denotes a 5-tuple. Other types of brackets are sometimes used, although they may have a different meaning. An -tuple can be formally defined as the image of a function that has the set of the first natural numbers as its domain. Tuples may be also defined from ordered pairs by a recurrence starting from an ordered pair; indeed, an -tuple can be identified with the ordered pair of its first elements and its t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set (mathematics)
In mathematics, a set is a collection of different things; the things are '' elements'' or ''members'' of the set and are typically mathematical objects: numbers, symbols, points in space, lines, other geometric shapes, variables, or other sets. A set may be finite or infinite. There is a unique set with no elements, called the empty set; a set with a single element is a singleton. 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. Context Before the end of the 19th century, sets were not studied specifically, and were not clearly distinguished from sequences. Most mathematicians considered infinity as potentialmeaning that it is the result of an endless processand were reluctant to consider infinite sets, that is sets whose number of members is not a natural number. Specific ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rules Of Go
The rules of Go govern the play of the game of Go, a two-player board game. The rules 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
