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Infinite Chess
Infinite chess is any variation of the game of chess played on an unbounded chessboard. Versions of infinite chess have been introduced independently by multiple players, chess theorists, and mathematicians, both as a playable game and as a model for theoretical study. It has been found that even though the board is unbounded, there are ways in which a player can win the game in a finite number of moves. Background Classical (FIDE) chess is played on an 8×8 board (64 squares). However, the history of chess includes variants of the game played on boards of various sizes. A predecessor game called courier chess was played on a slightly larger 12×8 board (96 squares) in the 12th century, and continued to be played for at least six hundred years. Japanese chess (shogi) has been played historically on boards of various sizes; the largest is taikyoku shōgi ("ultimate chess"). This chess-like game, which dates to the mid 16th century, was played on a 36×36 board (1296 squares) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinite Chess
Infinite chess is any variation of the game of chess played on an unbounded chessboard. Versions of infinite chess have been introduced independently by multiple players, chess theorists, and mathematicians, both as a playable game and as a model for theoretical study. It has been found that even though the board is unbounded, there are ways in which a player can win the game in a finite number of moves. Background Classical (FIDE) chess is played on an 8×8 board (64 squares). However, the history of chess includes variants of the game played on boards of various sizes. A predecessor game called courier chess was played on a slightly larger 12×8 board (96 squares) in the 12th century, and continued to be played for at least six hundred years. Japanese chess (shogi) has been played historically on boards of various sizes; the largest is taikyoku shōgi ("ultimate chess"). This chess-like game, which dates to the mid 16th century, was played on a 36×36 board (1296 squares) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nightrider (chess)
The nightrider, alternatively spelled knightrider and also known as the knightmare or unicorn (though the latter term sometimes refers to the Bishop (chess), bishop+nightrider compound), is a fairy chess piece that can move any number of steps as a knight (chess), knight in the same direction. The nightrider is often represented by an altered version of the knight's icon. at ''The Chess Variant Pages'' In this article, the nightrider is represented by an inverted knight and Algebraic notation (chess), notated as ''N''; the knight is abbreviated as ''S'' for the German name ''Springer''. The nightrider was invented by Thomas Rayner Dawson in 1925. It is often used in chess problems. Movement The nightrider moves and captures any number of steps as a knight (2 vertically and ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chess Variants
A chess variant is a game related to, derived from, or inspired by chess. Such variants can differ from chess in many different ways. "International" or "Western" chess itself is one of a family of games which have related origins and could be considered variants of each other. Chess developed from '' chaturanga'', from which other members of this family, such as ''shatranj'', Tamerlane chess, '' shogi'', and ''xiangqi'' also evolved. Many chess variants are designed to be played with the equipment of regular chess. Most variants have a similar public-domain status as their parent game, but some have been made into commercial proprietary games. Just as in traditional chess, chess variants can be played over the board, by correspondence, or by computer. Some internet chess servers facilitate the play of some variants in addition to orthodox chess. In the context of chess problems, chess variants are called heterodox chess or fairy chess. Fairy chess variants tend to be created ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fairy Chess Piece
A fairy chess piece, variant chess piece, unorthodox chess piece, or heterodox chess piece is a chess piece not used in conventional chess but incorporated into certain chess variants and some chess problems. Compared to conventional pieces, fairy pieces vary mostly in the way they move, but they may also follow special rules for capturing, promotions, etc. Because of the distributed and uncoordinated nature of unorthodox chess development, the same piece can have different names, and different pieces can have the same name in various contexts. Most are symbolised as inverted or rotated icons of the standard pieces in diagrams, and the meanings of these "wildcards" must be defined in each context separately. Pieces invented for use in chess variants rather than problems sometimes instead have special icons designed for them, but with some exceptions (the princess, empress, and occasionally amazon), many of these are not used beyond the individual games for which they were invented ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Chess Variants
This is a list of chess variants. Many thousands of variants exist. The 2007 catalogue ''The Encyclopedia of Chess Variants'' estimates that there are well over 2,000, and many more were considered too trivial for inclusion in the catalogue. Chess-derived games These chess variants are derived from chess by changing the board, board setup, pieces, or rules. Standard rules and standard piece types Many variants employ standard chess rules and mechanics, but vary the starting position of the pieces or number of pieces. Standard rules, standard piece types, variant board In these variants, the same pieces and rules as in chess are used, but the board is different; It can be smaller or larger, the shape of either the board or individual spaces can be non-square or modular, or it can even be extra-dimensional or unbounded. The movement of pieces in some variants is modified in concurrence with the geometry of the gameboard. * Active Chess: Played on a 9×8 board, adding a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Presburger Arithmetic
Presburger arithmetic is the first-order theory of the natural numbers with addition, named in honor of Mojżesz Presburger, who introduced it in 1929. The signature of Presburger arithmetic contains only the addition operation and equality, omitting the multiplication operation entirely. The axioms include a schema of induction. Presburger arithmetic is much weaker than Peano arithmetic, which includes both addition and multiplication operations. Unlike Peano arithmetic, Presburger arithmetic is a decidable theory. This means it is possible to algorithmically determine, for any sentence in the language of Presburger arithmetic, whether that sentence is provable from the axioms of Presburger arithmetic. The asymptotic running-time computational complexity of this algorithm is at least doubly exponential, however, as shown by . Overview The language of Presburger arithmetic contains constants 0 and 1 and a binary function +, interpreted as addition. In this language, the axioms ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sentence (mathematical Logic)
:''This article is a technical mathematical article in the area of predicate logic. For the ordinary English language meaning see Sentence (linguistics), for a less technical introductory article see Statement (logic).'' In mathematical logic, a sentence (or closed formula)Edgar Morscher, "Logical Truth and Logical Form", ''Grazer Philosophische Studien'' 82(1), pp. 77–90. of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence can be viewed as expressing a proposition, something that ''must'' be true or false. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed truth values: As the free variables of a (general) formula can range over several values, the truth value of such a formula may vary. Sentences without any logical connectives or quantifiers in them are known as atomic sentences; by analogy to atomic formula. Sentences are then built up out of atomic formulas by applying con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Checkmate
Checkmate (often shortened to mate) is any game position in chess and other chess-like games in which a player's king is in check (threatened with ) and there is no possible escape. Checkmating the opponent wins the game. In chess, the king is never actually captured—the player loses as soon as the player's king is checkmated. In formal games, it is usually considered good etiquette to resign an inevitably lost game before being checkmated. If a player is not in check but has no legal move, then it is '' stalemate'', and the game immediately ends in a draw. A checkmating move is recorded in algebraic notation using the hash symbol "#", for example: 34.Qg3#. Examples A checkmate may occur in as few as two moves on one side with all of the pieces still on the board (as in Fool's mate, in the opening phase of the game), in a middlegame position (as in the 1956 game called the Game of the Century between Donald Byrne and Bobby Fischer), or after many moves with as few as t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory
Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has applications in all fields of social science, as well as in logic, systems science and computer science. Originally, it addressed two-person zero-sum games, in which each participant's gains or losses are exactly balanced by those of other participants. In the 21st century, game theory applies to a wide range of behavioral relations; it is now an umbrella term for the science of logical decision making in humans, animals, as well as computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum game and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Chess Variant Pages
''The Chess Variant Pages'' is a non-commercial website devoted to chess variants. It was created by Hans Bodlaender in 1995. The site is "run by hobbyists for hobbyists" and is "the most wide-ranging and authoritative web site on chess variants". The site contains a large compilation of games with published rules. The aims of the site are to educate readers about chess variants, encourage gameplay, and provide a place for free discussion. The site has featured game competitions as well as variant design competitions, and provides facilities for publishing documents. Numerous files are available for playing variants using the Zillions of Games proprietary software engine. The site also features The Game Courier software developed by Fergus Duniho which can be used to play almost any variant. There is also an extensive encyclopedia of fairy chess piece A fairy chess piece, variant chess piece, unorthodox chess piece, or heterodox chess piece is a chess piece not used in conventio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chess Piece
A chess piece, or chessman, is a game piece that is placed on a chessboard to play the game of chess. It can be either White and Black in chess, white or black, and it can be one of six types: King (chess), king, Queen (chess), queen, Rook (chess), rook, Bishop (chess), bishop, Knight (chess), knight, or Pawn (chess), pawn. Chess sets generally come with sixteen pieces of each color. Additional pieces, usually an extra queen per color, may be provided for use in Promotion (chess), promotion. Number of pieces Each player begins with sixteen pieces (but see the #Usage of the term piece, subsection below for other usage of the term ''piece''). The pieces that belong to each player are distinguished by color: the lighter colored pieces are referred to as "white" and the player that owns them as "White", whereas the darker colored pieces are referred to as "black" and the player that owns them as "Black". In a standard game, each of the two players begins with the following sixteen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chess Variant
A chess variant is a game related to, derived from, or inspired by chess. Such variants can differ from chess in many different ways. "International" or "Western" chess itself is one of a family of games which have related origins and could be considered variants of each other. Chess developed from '' chaturanga'', from which other members of this family, such as ''shatranj'', Tamerlane chess, '' shogi'', and ''xiangqi'' also evolved. Many chess variants are designed to be played with the equipment of regular chess. Most variants have a similar public-domain status as their parent game, but some have been made into commercial proprietary games. Just as in traditional chess, chess variants can be played over the board, by correspondence, or by computer. Some internet chess servers facilitate the play of some variants in addition to orthodox chess. In the context of chess problems, chess variants are called heterodox chess or fairy chess. Fairy chess variants tend to be created ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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