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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] |
Alpha–beta Pruning
Alpha–beta pruning is a search algorithm that seeks to decrease the number of nodes that are evaluated by the minimax algorithm in its search tree. It is an adversarial search algorithm used commonly for machine playing of two-player 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 Allen Newell and Herbert A. Simon who used what John McCarthy calls an "approximation" in 1958 wrote that alpha–beta "appears to have been reinvented a number of times". Arthur Samuel had an early version for a checkers simulation. Richards, Timothy Hart, Michael Levin and/or Daniel Edwards also invented alpha–beta independently in the United States. McC ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 alpha-beta wi ... [...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 Roizen and ... [...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] |
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] |
Checkers
Checkers (American English), also known as draughts (; British English), is a group of strategy board games for two players which involve diagonal moves of uniform game pieces and mandatory captures by jumping over opponent pieces. Checkers is developed from alquerque. The term "checkers" derives from the checkered board which the game is played on, whereas "draughts" derives from the verb "to draw" or "to move". The most popular forms of checkers in Anglophone countries are American checkers (also called English draughts), which is played on an 8×8 checkerboard; Russian draughts, Turkish draughts both on an 8x8 board, and International draughts, played on a 10×10 board – the latter is widely played in many countries worldwide. There are many other variants played on 8×8 boards. Canadian checkers and Singaporean/Malaysian checkers (also locally known as ''dum'') are played on a 12×12 board. American checkers was weakly solved in 2007 by a team of Canadian computer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reversi
Reversi is a strategy board game for two players, played on an 8×8 uncheckered board. It was invented in 1883. Othello, a variant with a fixed initial setup of the board, was patented in 1971. Basics There are sixty-four identical game pieces called ''disks'', which are light on one side and dark on the other. Players take turns placing disks on the board with their assigned color facing up. During a play, any disks of the opponent's color that are in a straight line and bounded by the disk just placed and another disk of the current player's color are turned over to the current player's color. The objective of the game is to have the majority of disks turned to display one's color when the last playable empty square is filled. History Original version Englishmen Lewis Waterman and John W. Mollett both claim to have invented the game of Reversi in 1883, each denouncing the other as a fraud. The game gained considerable popularity in England at the end of the 19th century ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Stockman (computer Scientist)
George Henry Stockman (3 July 1833 - 30 June 1912) was a first lieutenant in the United States Army who was awarded the Medal of Honor for gallantry during the American Civil War. He was awarded the medal on 9 July 1894 for actions performed at the Siege of Vicksburg on 22 May 1863. Personal life Stockman was born in Muenden, Germany on 3 July 1833. He died on 30 June 1912 and was buried in West Laurel Hill Cemetery in Bala-Cynwyd, Pennsylvania. Military service Stockman enlisted in the Army as a first lieutenant on 1 June 1861 in Chicago, Illinois and was assigned to G Company of the 6th Missouri Infantry. During the course of his enlistment, he was transferred to Company C of the same unit. On 22 May 1863, at the Siege of Vicksburg in Mississippi, Stockman volunteered to participate in an extremely dangerous charge on Confederate positions to the south of Vicksburg Vicksburg most commonly refers to: * Vicksburg, Mississippi, a city in western Mississippi, United States ... [...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 and the Inte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iterative Deepening Depth-first Search
In computer science, iterative deepening search or more specifically iterative deepening depth-first search (IDS or IDDFS) is a state space/graph search strategy in which a depth-limited version of depth-first search is run repeatedly with increasing depth limits until the goal is found. IDDFS is optimal like breadth-first search, but uses much less memory; at each iteration, it visits the nodes in the search tree in the same order as depth-first search, but the cumulative order in which nodes are first visited is effectively breadth-first. Algorithm for directed graphs The following pseudocode shows IDDFS implemented in terms of a recursive depth-limited DFS (called DLS) for directed graphs. This implementation of IDDFS does not account for already-visited nodes and therefore does not work for undirected graphs. function IDDFS(root) is for depth from 0 to ∞ do found, remaining ← DLS(root, depth) if found ≠ null then return found ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chess Engine
In computer chess, a chess engine is a computer program that analyzes chess or chess variant positions, and generates a move or list of moves that it regards as strongest. A chess engine is usually a back end with a command-line interface with no graphics or windowing. Engines are usually used with a front end, a windowed graphical user interface such as Chessbase or WinBoard that the user can interact with via a keyboard, mouse or touchscreen. This allows the user to play against multiple engines without learning a new user interface for each, and allows different engines to play against each other. Many chess engines are now available for mobile phones and tablets, making them even more accessible. History The meaning of the term "chess engine" has evolved over time. In 1986, Linda and Tony Scherzer entered their program Bebe into the 4th World Computer Chess Championship, running it on "Chess Engine," their brand name for the chess computer hardware made, and markete ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chinook (draughts Player)
Chinook is a computer program that plays checkers (also known as draughts). It was developed between the years 1989 to 2007 at the University of Alberta, by a team led by Jonathan Schaeffer and consisting of Rob Lake, Paul Lu, Martin Bryant, and Norman Treloar. The program's algorithms include an opening book which is a library of opening moves from games played by checkers grandmasters; a deep search algorithm; a good move evaluation function; and an end-game database for all positions with eight pieces or fewer. All of Chinook's knowledge was programmed by its creators, rather than learned using an artificial intelligence system. Man vs. Machine World Champion Chinook is the first computer program to win the world champion title in a competition against humans. In 1990 it won the right to play in the human World Championship by being second to Marion Tinsley in the US Nationals. At first, the American Checkers Federation and English Draughts Association were against the partic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
