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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] |
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] |
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] |
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] |
Adversarial Search
An adversary is generally considered to be a person, group, or force that opposes and/or attacks. Adversary may also refer to: * Satan ("adversary" in Hebrew), in Abrahamic religions Entertainment Fiction * Adversary (comics), villain from the Marvel comics universe * The mysterious antagonist who invaded the homelands in the comic book series ''Fables'' Music * Ad·ver·sary, Canadian industrial musician Law * Adversarial system, a system of law commonly used in common-law countries * Adversary proceeding, proceeding used in bankruptcy processes Science * Adversarial collaboration, a scientific experiment Computer science * Adversary (cryptography), a malicious entity in cryptography whose aim is to prevent the users of the cryptosystem from achieving their goal * Adversary model, in online algorithms, used to show competitiveness of randomized algorithms * Adversarial alignment, when an adversarial users constructs inputs that bypass AI alignment Other * Adversari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plain Negamax
In geography, a plain, commonly known as flatland, is a flat expanse of land that generally does not change much in elevation, and is primarily treeless. Plains occur as lowlands along valleys or at the base of mountains, as coastal plains, and as plateaus or uplands. Plains are one of the major landforms on earth, being present on all continents and covering more than one-third of the world's land area. Plains in many areas are important for agriculture. There are various types of plains and biomes on them. Description A plain or flatland is a flat expanse of land with a layer of grass that generally does not change much in elevation, and is primarily treeless. Plains occur as lowlands along valleys or at the base of mountains, as coastal plains, and as plateaus or uplands. Plains are one of the major landforms on earth, where they are present on all continents, and cover more than one-third of the world's land area. In a valley, a plain is enclosed on two sides, but in ot ... [...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] |
Pseudocode
In computer science, pseudocode is a description of the steps in an algorithm using a mix of conventions of programming languages (like assignment operator, conditional operator, loop) with informal, usually self-explanatory, notation of actions and conditions. Although pseudocode shares features with regular programming languages, it is intended for human reading rather than machine control. Pseudocode typically omits details that are essential for machine implementation of the algorithm, meaning that pseudocode can only be verified by hand. The programming language is augmented with natural language description details, where convenient, or with compact mathematical notation. The reasons for using pseudocode are 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two-player Game
A two-player game is a multiplayer game that is played by precisely two players. This is distinct from a solitaire game, which is played by only one player. Examples The following are some examples of two-player games. This list is not intended to be exhaustive. * Board games: ** Chess ** Checkers ** Go ** Some wargames, such as '' Hammer of the Scots'' * Card games: ** Cribbage ** Whist ** Rummy ** 66 ** Pinochle ** '' Magic: The Gathering'', a collectible card game in which players duel * Sports: ** Cue sports, a family of games that use cue sticks and billiard balls ** Many athletic games, such as tennis ( singles) * Video games: **''Pong'' ** A Way Out See also * List of types of games * Zero-sum game Zero-sum game is a Mathematical model, mathematical representation in game theory and economic theory of a situation that involves two competition, competing entities, where the result is an advantage for one side and an equivalent loss for the o ... References {{Re ... [...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 that involves two competing entities, 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, with the result that 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, sport 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 ... [...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] |
