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In game theory, Zermelo's theorem is a theorem about finite two-person games of perfect information in which the players move alternately and in which chance does not affect the decision making process. It says that if the game cannot end in a draw, then one of the two players must have a winning strategy (i.e. can force a win).
Chess initial position. The game of chess is commonly divided into three phases: the opening, middlegame, and endgame. [1] There is a large body of theory regarding how the game should be played in each of these phases, especially the opening and endgame.
A variant first described by Claude Shannon provides an argument about the game-theoretic value of chess: he proposes allowing the move of “pass”. In this variant, it is provable with a strategy stealing argument that the first player has at least a draw thus: if the first player has a winning move in the initial position, let him play it, else pass.
Chess is an example of a game of perfect information. In economics , perfect information (sometimes referred to as "no hidden information") is a feature of perfect competition . With perfect information in a market, all consumers and producers have complete and instantaneous knowledge of all market prices, their own utility, and own cost functions.
Analysis of "pure" abstract strategy games is the subject of combinatorial game theory. Abstract strategy games with hidden information, bluffing, or simultaneous move elements are better served by Von Neumann–Morgenstern game theory, while those with a component of luck may require probability theory incorporated into either of the above.
A chess opening theory table or ECO table (Encyclopaedia of Chess Openings) presents lines of moves, typically (but not always) from the starting position. Notated chess moves are presented in the table from left to right. Variations on a given line are given horizontally below the parent line.
To better understand the game tree, it can be thought of as a technique for analyzing adversarial games, which determine the actions that player takes to win the game. In game theory, a game tree is a directed graph whose nodes are positions in a game (e.g., the arrangement of the pieces in a board game) and whose edges are moves (e.g., to move ...
There are other symbols used by various chess engines and publications, such as Chess Informant and Encyclopaedia of Chess Openings, when annotating moves or describing positions. [8] Many of the symbols now have Unicode encodings, but quite a few still require a special chess font with appropriated characters.