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Information sets are used in extensive form games and are often depicted in game trees. Game trees show the path from the start of a game and the subsequent paths that can be made depending on each player's next move. For non-perfect information game problems, there is hidden information.
In the context of combinatorial game theory, which typically studies sequential games with perfect information, a game tree is a graph representing all possible game states within such a game. Such games include well-known ones such as chess , checkers , Go , and tic-tac-toe .
Essentially, combinatorial game theory has contributed new methods for analyzing game trees, for example using surreal numbers, which are a subclass of all two-player perfect-information games. [3] The type of games studied by combinatorial game theory is also of interest in artificial intelligence , particularly for automated planning and ...
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An imperfect information game is played when the players do not know all moves already made by the opponent such as a simultaneous move game. [22] Examples of perfect-information games include tic-tac-toe, checkers, chess, and Go. [23] [24] [25] Many card games are games of imperfect information, such as poker and bridge. [26]
In game theory, an extensive-form game is a specification of a game allowing (as the name suggests) for the explicit representation of a number of key aspects, like the sequencing of players' possible moves, their choices at every decision point, the (possibly imperfect) information each player has about the other player's moves when they make a decision, and their payoffs for all possible ...
It is also related to more generally solving chess-like games (i.e. combinatorial games of perfect information) such as Capablanca chess and infinite chess. In a weaker sense, solving chess may refer to proving which one of the three possible outcomes (White wins; Black wins; draw) is the result of two perfect players, without necessarily ...
A solved game is a game whose outcome (win, lose or draw) can be correctly predicted from any position, assuming that both players play perfectly.This concept is usually applied to abstract strategy games, and especially to games with full information and no element of chance; solving such a game may use combinatorial game theory and/or computer assistance.