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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.
Algebraic notation is the standard method for recording and describing the moves in a game of chess. It is based on a system of coordinates to uniquely identify each square on the board. [ 1 ] It is now almost universally used by books, magazines, newspapers and software, and is the only form of notation recognized by FIDE , [ 2 ] the ...
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.
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.
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.
Chess opening theory books that provide these tables are usually quite large and difficult for beginners to use. Because the table entries typically do not include the themes or goals involved in a given line, beginners will either try to memorize the tables or simply drown in the detail.
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 ...