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Solving Chess
Solving chess consists of finding an optimal strategy for the game of chess; that is, one by which one of the players ( White or Black) can always force either a victory or a draw (see solved game). 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 revealing the optimal strategy itself (see indirect proof). No complete solution for chess in either of the two senses is known, nor is it expected that chess will be solved in the near future (if ever). Progress to date is extremely limited; there are tablebases of perfect endgame play with a small number of pieces (up to seven), and some chess variants have been solved at least weakly. Calculated estimates of game-tree complexity and st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chess
Chess is a board game for two players. It is an abstract strategy game that involves Perfect information, no hidden information and no elements of game of chance, chance. It is played on a square chessboard, board consisting of 64 squares arranged in an 8×8 grid. The players, referred to as White and Black in chess, "White" and "Black", each control sixteen Chess piece, pieces: one king (chess), king, one queen (chess), queen, two rook (chess), rooks, two bishop (chess), bishops, two knight (chess), knights, and eight pawn (chess), pawns, with each type of piece having a different pattern of movement. An enemy piece may be captured (removed from the board) by moving one's own piece onto the square it occupies. The object of the game is to "checkmate" (threaten with inescapable capture) the enemy king. There are also several ways a game can end in a draw (chess), draw. The recorded history of chess goes back to at least the emergence of chaturanga—also thought to be an ancesto ... [...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 ''makruk, ouk chatrang'', ''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, Correspondence chess, by correspondence, or computer chess, 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 che ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of California At Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a public land-grant research university in Berkeley, California, United States. Founded in 1868 and named after the Anglo-Irish philosopher George Berkeley, it is the state's first land-grant university and is the founding campus of the University of California system. Berkeley has an enrollment of more than 45,000 students. The university is organized around fifteen schools of study on the same campus, including the College of Chemistry, the College of Engineering, College of Letters and Science, and the Haas School of Business. It is classified among "R1: Doctoral Universities – Very high research activity". Lawrence Berkeley National Laboratory was originally founded as part of the university. Berkeley was a founding member of the Association of American Universities and was one of the original eight " Public Ivy" schools. In 2021, the federal funding for campus research and devel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biophysics
Biophysics is an interdisciplinary science that applies approaches and methods traditionally used in physics to study biological phenomena. Biophysics covers all scales of biological organization, from molecular to organismic and populations. Biophysical research shares significant overlap with biochemistry, molecular biology, physical chemistry, physiology, nanotechnology, bioengineering, computational biology, biomechanics, developmental biology and systems biology. The term ''biophysics'' was originally introduced by Karl Pearson in 1892. Roland Glaser. Biophysics: An Introduction'. Springer; 23 April 2012. . The term ''biophysics'' is also regularly used in academia to indicate the study of the physical quantities (e.g. electric current, temperature, stress, entropy) in biological systems. Other biological sciences also perform research on the biophysical properties of living organisms including molecular biology, cell biology, chemical biology, and bioche ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hans-Joachim Bremermann
Hans-Joachim Bremermann (1926 – 1996) was a German-American mathematician and biophysicist. He worked on computer science and evolution, introducing ideas of how mating generates new gene combinations. Bremermann's limit, named after him, is the maximum computational speed of a self-contained system in the material universe. Early life Bremermann was born in 1926, in Bremen, Germany, to Bernard Bremermann and Berta Wicke. Bremermann undertook doctoral studies at the University of Münster, completing his Staatsexamen in mathematics and physics in 1951. In the same year, his doctoral dissertation ''Die Charakterisierung von Regularitätsgebieten durch pseudokonvexe Funktionen'' was published, in which he solved a special case of the Levi problem. He was to become a specialist in complex analysis. Career Bremermann came to the United States in 1952 and held a research associate position at Stanford University. In 1953, he was appointed a research fellow at Harvard Universi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Tree
In the context of combinatorial game theory, a game tree is a graph representing all possible game states within a sequential game that has perfect information. Such games include chess, checkers, Go, and tic-tac-toe. A game tree can be used to measure the complexity of a game, as it represents all the possible ways that the game can pan out. Due to the large game trees of complex games such as chess, algorithms that are designed to play this class of games will use partial game trees, which makes computation feasible on modern computers. Various methods exist to solve game trees. If a complete game tree can be generated, a deterministic algorithm, such as backward induction or retrograde analysis can be used. Randomized algorithms and minmax algorithms such as MCTS can be used in cases where a complete game tree is not feasible. Understanding the game tree To better understand the game tree, it can be thought of as a technique for analyzing adversarial games, whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GitHub
GitHub () is a Proprietary software, proprietary developer platform that allows developers to create, store, manage, and share their code. It uses Git to provide distributed version control and GitHub itself provides access control, bug tracking system, bug tracking, software feature requests, task management, continuous integration, and wikis for every project. Headquartered in California, GitHub, Inc. has been a subsidiary of Microsoft since 2018. It is commonly used to host open source software development projects. GitHub reported having over 100 million developers and more than 420 million Repository (version control), repositories, including at least 28 million public repositories. It is the world's largest source code host Over five billion developer contributions were made to more than 500 million open source projects in 2024. About Founding The development of the GitHub platform began on October 19, 2005. The site was launched in April 2008 by Tom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophical Magazine
The ''Philosophical Magazine'' is one of the oldest scientific journals published in English. It was established by Alexander Tilloch in 1798;John Burnett"Tilloch, Alexander (1759–1825)" Dictionary of National Biography#Oxford Dictionary of National Biography, Oxford Dictionary of National Biography, Oxford University Press, Sept 2004; online edn, May 2006, accessed 17 Feb 2010 in 1822 Richard Taylor (editor), Richard Taylor became joint editor and it has been published continuously by Taylor & Francis ever since. Early history The name of the journal dates from a period when "natural philosophy" embraced all aspects of science. The very first paper published in the journal carried the title "Account of Mr Cartwright's Patent Steam Engine". Other articles in the first volume include "Methods of discovering whether Wine has been adulterated with any Metals prejudicial to Health" and "Description of the Apparatus used by Lavoisier to produce Water from its component Parts, Oxyg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fifty-move Rule
The fifty-move rule in chess states that a player can claim a draw if no has been made and no pawn has been moved in the last fifty moves (where a "move" consists of a player completing a turn followed by the opponent completing a turn). The purpose of this rule is to prevent a player with no chance of winning from obstinately continuing to play indefinitely or seeking to win by tiring the opponent. Chess positions with only a few pieces can be " solved", that is, the outcome of best play for both sides can be determined by exhaustive analysis; if the outcome is a win for one side or the other (rather than a draw), it is of interest to know whether the defending side can hold out long enough to invoke the fifty-move rule. The simplest common endings, called the basic checkmates, such as king and queen versus king, can all be won in well under 50 moves. However, in the 20th century it was discovered that certain endgame positions are winnable but require more than 50 moves (wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information Theory
Information theory is the mathematical study of the quantification (science), quantification, Data storage, storage, and telecommunications, communication of information. The field was established and formalized by Claude Shannon in the 1940s, though early contributions were made in the 1920s through the works of Harry Nyquist and Ralph Hartley. It is at the intersection of electronic engineering, mathematics, statistics, computer science, Neuroscience, neurobiology, physics, and electrical engineering. A key measure in information theory is information entropy, entropy. Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. For example, identifying the outcome of a Fair coin, fair coin flip (which has two equally likely outcomes) provides less information (lower entropy, less uncertainty) than identifying the outcome from a roll of a dice, die (which has six equally likely outcomes). Some other important measu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
