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Null-move Heuristic
In computer chess programs, the null-move heuristic is a heuristic technique used to enhance the speed of the alpha–beta pruning algorithm. Rationale Alpha–beta pruning speeds the minimax algorithm by identifying ''cutoffs'', points in the game tree where the current position is so good for the side to move that best play by the other side would have avoided it. Since such positions could not have resulted from best play, they and all branches of the game tree stemming from them can be ignored. The faster the program produces cutoffs, the faster the search runs. The null-move heuristic is designed to guess cutoffs with less effort than would otherwise be required, whilst retaining a reasonable level of accuracy. The null-move heuristic is based on the fact that most reasonable chess moves improve the position for the side that played them. So, if the player whose turn it is to move can forfeit the right to move (or make a null move – an illegal action in chess) and stil ... [...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] |
Heuristic (computer Science)
A heuristic or heuristic technique (''problem solving'', ''Heuristic (psychology), mental shortcut'', ''rule of thumb'') is any approach to problem solving that employs a Pragmatism, pragmatic method that is not fully Mathematical optimisation, optimized, perfected, or Rationality, rationalized, but is nevertheless "good enough" as an approximation or attribute substitution. Where finding an optimal solution is impossible or impractical, heuristic methods can be used to speed up the process of finding a satisfactory solution. Heuristics can be mental shortcuts that ease the cognitive load of Decision-making, making a decision. Context Gigerenzer & Gaissmaier (2011) state that Set (mathematics), sub-sets of ''strategy'' include heuristics, regression analysis, and Bayesian inference. Heuristics are strategies based on rules to generate optimal decisions, like the anchoring effect and utility maximization problem. These strategies depend on using readily accessible, thoug ... [...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] |
Search Algorithm
In computer science, a search algorithm is an algorithm designed to solve a search problem. Search algorithms work to retrieve information stored within particular data structure, or calculated in the Feasible region, search space of a problem domain, with Continuous or discrete variable, either discrete or continuous values. Although Search engine (computing), search engines use search algorithms, they belong to the study of information retrieval, not algorithmics. The appropriate search algorithm to use often depends on the data structure being searched, and may also include prior knowledge about the data. Search algorithms can be made faster or more efficient by specially constructed database structures, such as search trees, hash maps, and database indexes. Search algorithms can be classified based on their mechanism of searching into three types of algorithms: linear, binary, and hashing. Linear search algorithms check every record for the one associated with a target key i ... [...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] |
Minimax Algorithm
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] |
Game Tree
In the context of combinatorial game theory, a game tree is a graph representing all possible game states within a sequential game that has perfect information. Such games include chess, checkers, Go, and tic-tac-toe. A game tree can be used to measure the complexity of a game, as it represents all the possible ways that the game can pan out. Due to the large game trees of complex games such as chess, algorithms that are designed to play this class of games will use partial game trees, which makes computation feasible on modern computers. Various methods exist to solve game trees. If a complete game tree can be generated, a deterministic algorithm, such as backward induction or retrograde analysis can be used. Randomized algorithms and minmax algorithms such as MCTS can be used in cases where a complete game tree is not feasible. Understanding the game tree To better understand the game tree, it can be thought of as a technique for analyzing adversarial games, whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Null Move
In game theory, a null move or pass is a decision by a player to not make a move when it is that player's turn to move. Even though null moves are against the rules of many games, they are often useful to consider when analyzing these games. Examples of this include the analysis of zugzwang (a situation in chess or other games in which a null move, if it were allowed, would be better than any other move), and the null-move heuristic in game tree In the context of combinatorial game theory, a game tree is a graph representing all possible game states within a sequential game that has perfect information. Such games include chess, checkers, Go, and tic-tac-toe. A game tree can be us ... analysis (a method of pruning game trees involving making a null move and then searching to a lower depth).. The reason a reduced-depth null move is effective in game tree alpha-beta search reduction is that tactical threats tend to show up very quickly, in just one or two moves. If the oppon ... [...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] |
Ply (game Theory)
In two-or-more-player sequential games, a ply is one turn taken by one of the players. The word is used to clarify what is meant when one might otherwise say "turn". The word "turn" can be a problem since it means different things in different traditions. For example, in standard chess terminology, one ''move'' consists of a turn by each player; therefore a ply in chess is a ''half-move''. Thus, after 20 moves in a chess game, 40 plies have been completed—20 by white and 20 by black. In the game of Go (game), Go, by contrast, a ply is the normal unit of counting moves; so for example to say that a game is ''250 moves long'' is to imply 250 plies. In poker with ''n'' players the word "street" is used for a full betting round consisting of ''n'' plies; each dealt card may sometimes also be called a "street". For instance, in heads up Texas hold'em, a street consists of 2 plies, with possible plays being check/raise/call/fold: the first by the player at the big blind, and the sec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zugzwang
Zugzwang (; ) is a situation found in chess and other turn-based games wherein one player is put at a disadvantage because of their obligation to make a move; a player is said to be "in zugzwang" when any legal move will worsen their position. Although the term is used less precisely in games such as chess, it is used specifically in combinatorial game theory to denote a move that directly changes the outcome of the game from a win to a loss. Putting the opponent in zugzwang is a common way to help the superior side win a game, and in some cases it is necessary in order to make the win possible. More generally, the term can also be used to describe a situation where none of the available options lead to a good outcome. The term ''zugzwang'' was used in German chess literature in 1858 or earlier, and the first known use of the term in English was by World Champion Emanuel Lasker in 1905. The concept of zugzwang was known to chess players many centuries before the term was coine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nathan Netanyahu
Nathan S. Netanyahu (; born 28 November 1951) is an Israeli computer scientist and a professor of computer science at Bar-Ilan University. Netanyahu is the son of mathematician Elisha Netanyahu and Supreme Court of Israel justice Shoshana Netanyahu, the nephew of historian Benzion Netanyahu, and the cousin of current Prime Minister of Israel Benjamin Netanyahu. He did his graduate studies at the University of Maryland, College Park, earning a Ph.D. in 1992 under the supervision of David Mount and Azriel Rosenfeld. Netanyahu has co-authored highly cited research papers on nearest neighbor search and k-means clustering.. He has published many papers on computer chess, was the local organizer of the 12th World Computer Chess Championship in 2004, and was program co-chair for the 4th International Conference on Computers and Games, colocated with the WCCC. Another frequent topic in his research is image registration Image registration is the process of transforming different ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
