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NegaScout
Principal variation search (sometimes equated with the practically identical NegaScout) is a negamax algorithm that can be faster than alpha–beta pruning. Like alpha–beta pruning, NegaScout is a directional search algorithm for computing the minimax value of a node in a tree. It dominates alpha–beta pruning in the sense that it will never examine a node that can be pruned by alpha–beta; however, it relies on accurate node ordering to capitalize on this advantage. NegaScout works best when there is a good move ordering. In practice, the move ordering is often determined by previous shallower searches. It produces more cutoffs than alpha–beta by assuming that the first explored node is the best. In other words, it supposes the first node is in the principal variation. Then, it can check whether that is true by searching the remaining nodes with a null window (also known as a scout window; when alpha and beta are equal), which is faster than searching with the regular al ... [...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, combinatorial game theory, statistics, and philosophy for ''minimizing'' the possible loss function, loss for a Worst-case scenario, 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_ W ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variation (game Tree)
A variation can refer to a specific sequence of successive moves in a turn-based game, often used to specify a hypothetical future state of a game that is being played. Although the term is most commonly used in the context of Chess analysis, it has been applied to other games. It also is a useful term used when describing computer tree-search algorithms (for example minimax) for playing games such as Go{{cite web , url=http://www.andromeda.com/people/ddyer/go/search.html, title=Searches, tree pruning and tree ordering in Go, date=21 December 2007 or Chess. A variation can be any number of steps as long as each step would be legal if it were to be played. It is often as far ahead as a human or computer can calculate; or however long is necessary to reach a particular position of interest. It may also lead to a terminal state in the game, in which case the term "winning variation" or "losing variation" is sometimes used. Principal variation The principal variation refers to the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Killer Heuristic
In competitive two-player games, the killer heuristic is a move-ordering method based on the observation that a strong move or small set of such moves in a particular position may be equally strong in similar positions at the same move (ply) in the game tree. Retaining such moves obviates the effort of rediscovering them in sibling nodes. This technique improves the efficiency of alpha–beta pruning, which in turn improves the efficiency of the minimax algorithm. Alpha–beta pruning works best when the best moves are considered first. This is because the best moves are the ones most likely to produce a ''cutoff'', a condition where the game-playing program knows that the position it is considering could not possibly have resulted from best play by both sides and so need not be considered further. I.e. the game-playing program will always make its best available move for each position. It only needs to consider the other player's possible responses to that best move, and can skip ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Negamax
Negamax search is a variant form of minimax search that relies on the Zero-sum (Game theory), 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 p ... [...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] |
Tree (data Structure)
In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be connected to exactly one parent, except for the ''root'' node, which has no parent (i.e., the root node as the top-most node in the tree hierarchy). These constraints mean there are no cycles or "loops" (no node can be its own ancestor), and also that each child can be treated like the root node of its own subtree, making recursion a useful technique for tree traversal. In contrast to linear data structures, many trees cannot be represented by relationships between neighboring nodes (parent and children nodes of a node under consideration, if they exist) in a single straight line (called edge or link between two adjacent nodes). Binary trees are a commonly used type, which constrain the number of children for each parent to at most two. Whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexander Reinefeld
Alexander Reinefeld (born 1957) is a German computer scientist and games researcher. He is the head of computer science at Zuse Institute Berlin. His contributions to the field include the NegaScout algorithm. Biography Alexander Reinefeld studied physics at the Technical University of Braunschweig and computer science at the University of Hamburg and during two one-year visits in Edmonton at the University of Alberta. In 1982 he concluded his ''Diplom'' (equivalent to MSc) in computer science and in 1987 he received his Ph.D at the University of Hamburg. From 1983 to 1987, he worked as a scientific employee, and from 1989 to 1992 as assistant at the University of Hamburg. During the years 1987 to 1990 he collected industrial experience as a management consultant in the areas of systems analysis, databases and compiler building. In 1992 Reinefeld collaborated with the Paderborn Center for Parallel Computing (PC²) at the University of Paderborn. Since 1998, Alexander Reinefel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SSS*
SSS* is a search algorithm, introduced by George Stockman in 1979, that conducts a state space search traversing a game tree in a best-first fashion similar to that of the A* search algorithm. SSS* is based on the notion of solution trees. Informally, a solution tree can be formed from any arbitrary game tree by pruning the number of branches at each MAX node to one. Such a tree represents a complete strategy for MAX, since it specifies exactly one MAX action for every possible sequence of moves made by the opponent. Given a game tree, SSS* searches through the space of partial solution trees, gradually analyzing larger and larger subtrees, eventually producing a single solution tree with the same root and Minimax value as the original game tree. SSS* never examines a node that alpha–beta pruning would prune, and may prune some branches that alpha–beta would not. Stockman speculated that SSS* may therefore be a better general algorithm than alpha–beta. However, Igor Roiz ... [...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] |
Judea Pearl
Judea Pearl (; born September 4, 1936) is an Israeli-American computer scientist and philosopher, best known for championing the probabilistic approach to artificial intelligence and the development of Bayesian networks (see the article on belief propagation). He is also credited for developing a theory of causal and counterfactual inference based on structural models (see article on causality). In 2011, the Association for Computing Machinery (ACM) awarded Pearl with the Turing Award, the highest distinction in computer science, "for fundamental contributions to artificial intelligence through the development of a calculus for probabilistic and causal reasoning". He is the author of several books, including the technical '' Causality: Models, Reasoning and Inference'', and '' The Book of Why'', a book on causality aimed at the general public. Judea Pearl is the father of journalist Daniel Pearl, who was kidnapped and murdered by terrorists in Pakistan connected with Al-Qaeda a ... [...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] |
Articles With Example Pseudocode
Article often refers to: * Article (grammar), a grammatical element used to indicate definiteness or indefiniteness * Article (publishing) An article or piece is a written work published in a Publishing, print or electronic media, electronic medium, for the propagation of news, research results, academic analysis or debate. News A news article discusses current or recent news of e ..., a piece of nonfictional prose that is an independent part of a publication Article(s) may also refer to: Government and law * Elements of treaties of the European Union * Articles of association, the regulations governing a company, used in India, the UK and other countries; called articles of incorporation in the US * Articles of clerkship, the contract accepted to become an articled clerk * Articles of Confederation, the predecessor to the current United States Constitution * Article of impeachment, a formal document and charge used for impeachment in the United States * Article of ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
