The game structure and nature of chess is related to several branches of mathematics. Many combinatorical and topological problems connected to chess were known of for hundreds of years. In 1913, Ernst Zermelo used chess as a basis for his theory of game strategies, which is considered as one of the predecessors of game theory.[86]
The number of legal positions in chess is estimated to be between 1043 and 1047 (a provable upper bound[87][88]), with a game-tree complexity of approximately 10123. The game-tree complexity of chess was first calculated by Claude Shannon as 10120, a number known as the Shannon number.[89] Typically an average position has thirty to forty possible moves, but there may be as few as zero (in the case of checkmate or stalemate) or as many as 218.[90]
One of the most important mathematical challenge of chess is the development of algorithms that can play chess. The idea of creating a chess-playing machine dates to the 18th century; around 1769, the chess-playing automaton called The Turk became famous before being exposed as a hoax.[91] Serious trials based on automatons, such as El Ajedrecista, were too complex and limited to be useful.
Since the advent of the digital computer in the 1950s, chess enthusiasts, computer engineers and computer scientists have built, with increasing degrees of seriousness and success, chess-playing machines and computer programs.[92] The groundbreaking paper on computer chess, "Programming a Computer for Playing Chess", was published in 1950 by Shannon.[note 7] He wrote:
The chess machine is an ideal one to start with, since: (1) the problem is sharply defined both in allowed operations (the moves) and in the ultimate goal (checkmate); (2) it is neither so simple as to be trivial nor too difficult for satisfactory solution; (3) chess is generally considered to require "thinking" for skillful play; a solution of this problem will force us either to admit the possibility of a mechanized thinking or to further restrict our concept of "thinking"; (4) the discrete structure of chess fits well into the digital nature of modern computers.
The number of legal positions in chess is estimated to be between 1043 and 1047 (a provable upper bound[87][88]), with a game-tree complexity of approximately 10123. The game-tree complexity of chess was first calculated by Claude Shannon as 10120, a number known as the Shannon number.[89] Typically an average position has thirty to forty possible moves, but there may be as few as zero (in the case of checkmate or stalemate) or as many as 218.[90]
One of the most important mathematical challenge of chess is the development of algorithms that can play chess. The idea of creating a chess-playing machine dates to the 18th century; around 1769, the chess-playing automaton called The Turk became famous before being exposed as a hoax.[91] Serious trials based on automatons, such as El Ajedrecista, were too complex and limited to be useful.
Since the advent of the digital computer in the 1950s, chess enthusiasts, computer engineers and computer scientists have built, with increasing degrees of seriousness and success, chess-playing machines and computer programs.[92] The groundbreaking paper on computer chess, "Programming a Computer for Playing Chess", was published in 1950 by Shannon.[note 7] He wrote:
The chess machine is an ideal one to start with, since: (1) the problem is sharply defined both in allowed operations (the moves) and in the ultimate goal (checkmate); (2) it is neither so simple as to be trivial nor too difficult for satisfactory solution; (3) chess is generally considered to require "thinking" for skillful play; a solution of this problem will force us either to admit the possibility of a mechanized thinking or to further restrict our concept of "thinking"; (4) the discrete structure of chess fits well into the digital nature of modern computers.
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