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Negamax AlphaBeta
Negamax search is a variant form of minimax search that relies on the zero-sum property of a two-player game. This algorithm relies on the fact that to simplify the implementation of the minimax algorithm. More precisely, the value of a position to player A in such a game is the negation of the value to player B. Thus, the player on move looks for a move that maximizes the negation of the value resulting from the move: this successor position must by definition have been valued by the opponent. The reasoning of the previous sentence works regardless of whether A or B is on move. This means that a single procedure can be used to value both positions. This is a coding simplification over minimax, which requires that A selects the move with the maximum-valued successor while B selects the move with the minimum-valued successor. It should not be confused with negascout, an algorithm to compute the minimax or negamax value quickly by clever use of alpha-beta pruning discovered in the 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimax
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] |
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] |
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] |
UMI Research Press
The University of Michigan Press is part of Michigan Publishing at the University of Michigan Library. It publishes 170 new titles each year in the humanities and social sciences. Titles from the press have earned numerous awards, including Lambda Literary Awards, the PEN/Faulkner Award, the Joe A. Callaway Award, and the Nautilus Book Award. The press has published works by authors who have been awarded the Pulitzer Prize, the National Humanities Medal and the Nobel Prize in Economics. History From 1858 to 1930, the University of Michigan had no organized entity for its scholarly publications, which were generally conference proceedings or department-specific research. The University Press was established in 1930 under the university's Graduate School, and in 1935, Frank E. Robbins, assistant to university president Alexander G. Ruthven, was appointed as the managing editor of the University Press. He would hold this position until 1954, when Fred D. Wieck was appointed as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oreilly Media
O'Reilly Media (formerly O'Reilly & Associates) is an American learning company established by Tim O'Reilly that Publishing, publishes books, produces tech conferences, and provides an Educational technology, online learning platform. Its distinctive brand features a woodcut of an animal on many of its book covers. Company Early days The company began in 1978 as a private consulting firm doing technical writing, based in the Cambridge, Massachusetts, Cambridge, Massachusetts area. In 1984, it began to retain publishing rights on manuals created for Unix vendors. A few 70-page "Nutshell Handbooks" were well-received, but the focus remained on the consulting business until 1988. After a conference displaying O'Reilly's preliminary Xlib manuals attracted significant attention, the company began increasing production of manuals and books. The original cover art consisted of animal designs developed by Edie Freedman because she thought that Unix program names sounded like "weird an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Memoization
In computing, memoization or memoisation is an optimization technique used primarily to speed up computer programs by storing the results of expensive function calls and returning the cached result when the same inputs occur again. Memoization has also been used in other contexts (and for purposes other than speed gains), such as in simple mutually recursive descent parsing. Although related to caching, memoization refers to a specific case of this optimization, distinguishing it from forms of caching such as buffering or page replacement. In the context of some logic programming languages, memoization is also known as tabling. Etymology The term "memoization" was coined by Donald Michie in 1968 and is derived from the Latin word "memorandum" ("to be remembered"), usually truncated as "memo" in American English, and thus carries the meaning of "turning he results ofa function into something to be remembered". While "memoization" might be confused with "memorization" (becaus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transposition Table
{{no footnotes, date=November 2017 A transposition table is a cache of previously seen positions, and associated evaluations, in a game tree generated by a computer game playing program. If a position recurs via a different sequence of moves, the value of the position is retrieved from the table, avoiding re-searching the game tree below that position. Transposition tables are primarily useful in perfect-information games (where the entire state of the game is known to all players at all times). The usage of transposition tables is essentially memoization applied to the tree search and is a form of dynamic programming. Transposition tables are typically implemented as hash tables encoding the current board position as the hash index. The number of possible positions that may occur in a game tree is an exponential function of depth of search, and can be thousands to millions or even much greater. Transposition tables may therefore consume most of available system memory and ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Foreach Loop
In computer programming, foreach loop (or for each loop) is a control flow statement for traversing items in a collection. is usually used in place of a standard loop statement. Unlike other loop constructs, however, loops usually maintain no explicit counter: they essentially say "do this to everything in this set", rather than "do this times". This avoids potential off-by-one errors and makes code simpler to read. In object-oriented languages, an iterator, even if implicit, is often used as the means of traversal. The statement in some languages has some defined order, processing each item in the collection from the first to the last. The statement in many other languages, especially array programming languages, does not have any particular order. This simplifies loop optimization in general and in particular allows vector processing of items in the collection concurrently. Syntax Syntax varies among languages. Most use the simple word for, roughly as follows: for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MTD(f)
MTD(f) is an alpha-beta game tree search algorithm modified to use ‘zero-window’ initial search bounds, and memory (usually a transposition table) to reuse intermediate search results. MTD(f) is a shortened form of MTD(n,f) which stands for Memory-enhanced Test Driver with node ‘n’ and value ‘f’. The efficacy of this paradigm depends on a good initial guess, and the supposition that the final minimax value lies in a narrow window around the guess (which becomes an upper/lower bound for the search from root). The memory structure is used to save an initial guess determined elsewhere. MTD(f) was introduced in 1994 and largely supplanted NegaScout (PVS), the previously dominant search paradigm for chess, checkers, othello and other game automatons. Origin MTD(f) was first described in a University of Alberta Technical Report authored by Aske Plaat, Jonathan Schaeffer, Wim Pijls, and Arie de Bruin, which would later receive the ICCA Novag Best Computer Chess Publication ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Negamax AlphaBeta
Negamax search is a variant form of minimax search that relies on the zero-sum property of a two-player game. This algorithm relies on the fact that to simplify the implementation of the minimax algorithm. More precisely, the value of a position to player A in such a game is the negation of the value to player B. Thus, the player on move looks for a move that maximizes the negation of the value resulting from the move: this successor position must by definition have been valued by the opponent. The reasoning of the previous sentence works regardless of whether A or B is on move. This means that a single procedure can be used to value both positions. This is a coding simplification over minimax, which requires that A selects the move with the maximum-valued successor while B selects the move with the minimum-valued successor. It should not be confused with negascout, an algorithm to compute the minimax or negamax value quickly by clever use of alpha-beta pruning discovered in the 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zero-sum (Game Theory)
Zero-sum game is a mathematical representation in game theory and economic theory of a situation which involves two sides, 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, therefore 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, 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. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudocode
In computer science, pseudocode is a plain language description of the steps in an algorithm or another system. Pseudocode often uses structural conventions of a normal programming language, but is intended for human reading rather than machine reading. It typically omits details that are essential for machine understanding of the algorithm, such as variable declarations and language-specific code. The programming language is augmented with natural language description details, where convenient, or with compact mathematical notation. The purpose of using pseudocode is that it is easier for people to understand than conventional programming language code, and that it is an efficient and environment-independent description of the key principles of an algorithm. It is commonly used in textbooks and scientific publications to document algorithms and in planning of software and other algorithms. No broad standard for pseudocode syntax exists, as a program in pseudocode is not an executa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
