Perfect Play
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Perfect Play
A solved game is a game whose outcome (win, lose or draw) can be correctly predicted from any position, assuming that both players play perfectly. This concept is usually applied to abstract strategy games, and especially to games with full information and no element of chance; solving such a game may use combinatorial game theory and/or computer assistance. Overview A two-player game can be solved on several levels: ;Ultra-weak : Prove whether the first player will win, lose or draw from the initial position, given perfect play on both sides. This can be a non-constructive proof (possibly involving a strategy-stealing argument) that need not actually determine any moves of the perfect play. ;Weak : Provide an algorithm that secures a win for one player, or a draw for either, against any possible moves by the opponent, from the beginning of the game. ;Strong : Provide an algorithm that can produce perfect moves from any position, even if mistakes have already been made on one or b ...
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Game
A game is a structured form of play (activity), play, usually undertaken for enjoyment, entertainment or fun, and sometimes used as an educational tool. Many games are also considered to be work (such as professional players of spectator sports or games) or art (such as jigsaw puzzles or games involving an artistic layout such as Mahjong, solitaire, or some video games). Games are sometimes played purely for enjoyment, sometimes for achievement or reward as well. They can be played alone, in teams, or online; by amateurs or by professionals. The players may have an audience of non-players, such as when people are entertained by watching a World Chess Championship, chess championship. On the other hand, players in a game may constitute their own audience as they take their turn to play. Often, part of the entertainment for children playing a game is deciding who is part of their audience and who is a player. A toy and a game are not the same. Toys generally allow for unrestr ...
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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. In game theory, a sequential game has perfect information if each player, when making any decision, is perfectly informed of all the events that have previously occurred, including the "initialization event" of the game (e.g. the starting hands of each player in a card game).Archived aGhostarchiveand thWayback Machine Perfect information defined at 0:25, with academic sources and . Perfect information is importantly different from complete information, which implies common knowledge of each player's utility functions, payoffs, strategies and "types". A game with perfect information may or may not have complete information. Games where some aspect of play is ''hidden'' from opponents - su ...
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Connect Four
Connect Four (also known as Connect 4, Four Up, Plot Four, Find Four, Captain's Mistress, Four in a Row, Drop Four, and Gravitrips in the Soviet Union) is a two-player connection board game, in which the players choose a color and then take turns dropping colored tokens into a seven-column, six-row vertically suspended grid. The pieces fall straight down, occupying the lowest available space within the column. The objective of the game is to be the first to form a horizontal, vertical, or diagonal line of four of one's own tokens. Connect Four is a solved game. The first player can always win by playing the right moves. The game was first sold under the ''Connect Four'' trademark by Milton Bradley in February 1974. Gameplay A gameplay example (right), shows the first player starting Connect Four by dropping one of their yellow discs into the center column of an empty game board. The two players then alternate turns dropping one of their discs at a time into an unfilled colum ...
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Chopsticks (hand Game)
Chopsticks is a hand game for two or more players, in which players extend a number of fingers from each hand and transfer those scores by taking turns to tap one hand against another. Chopsticks is an example of a combinatorial game, and is solved in the sense that with perfect play, an optimal strategy from any point is known. Rules This official set of rules is called ''rollover'' where five fingers are subtracted should a hand's sum exceeds 5 as described below. # A hand is ''live'' if it has at least one finger, and this is indicated by raising at least one finger. If a hand has zero fingers, the hand is ''dead'', and this is indicated by raising zero fingers (i.e. a closed fist). # If any hand of any player reaches exactly five fingers, then the hand is dead. # Each player begins with one finger raised on each hand. After the first player turns proceed clockwise. # On a player's turn, they must either ''attack'' or ''split''. There are two types of splits, ''transfers'' a ...
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Netherlands
) , anthem = ( en, "William of Nassau") , image_map = , map_caption = , subdivision_type = Sovereign state , subdivision_name = Kingdom of the Netherlands , established_title = Before independence , established_date = Spanish Netherlands , established_title2 = Act of Abjuration , established_date2 = 26 July 1581 , established_title3 = Peace of Münster , established_date3 = 30 January 1648 , established_title4 = Kingdom established , established_date4 = 16 March 1815 , established_title5 = Liberation Day (Netherlands), Liberation Day , established_date5 = 5 May 1945 , established_title6 = Charter for the Kingdom of the Netherlands, Kingdom Charter , established_date6 = 15 December 1954 , established_title7 = Dissolution of the Netherlands Antilles, Caribbean reorganisation , established_date7 = 10 October 2010 , official_languages = Dutch language, Dutch , languages_type = Regional languages , languages_sub = yes , languages = , languages2_type = Reco ...
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Amsterdam
Amsterdam ( , , , lit. ''The Dam on the River Amstel'') is the Capital of the Netherlands, capital and Municipalities of the Netherlands, most populous city of the Netherlands, with The Hague being the seat of government. It has a population of 907,976 within the city proper, 1,558,755 in the City Region of Amsterdam, urban area and 2,480,394 in the Amsterdam metropolitan area, metropolitan area. Located in the Provinces of the Netherlands, Dutch province of North Holland, Amsterdam is colloquially referred to as the "Venice of the North", for its large number of canals, now designated a World Heritage Site, UNESCO World Heritage Site. Amsterdam was founded at the mouth of the Amstel River that was dammed to control flooding; the city's name derives from the Amstel dam. Originally a small fishing village in the late 12th century, Amsterdam became a major world port during the Dutch Golden Age of the 17th century, when the Netherlands was an economic powerhouse. Amsterdam is th ...
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Vrije Universiteit
The Vrije Universiteit Amsterdam (abbreviated as ''VU Amsterdam'' or simply ''VU'' when in context) is a public research university in Amsterdam, Netherlands, being founded in 1880. The VU Amsterdam is one of two large, publicly funded research universities in the city, the other being the University of Amsterdam (UvA). The literal translation of the Dutch name ''Vrije Universiteit'' is "Free University". "Free" refers to independence of the university from both the State and the Dutch Reformed Church. Both within and outside the university, the institution is commonly referred to as "the VU". Although founded as a private institution, the VU has received government funding on a parity basis with public universities since 1970. The university is located on a compact urban campus in the southern Buitenveldert neighbourhood of Amsterdam and adjacent to the modern Zuidas business district. The University consistently ranks among the top 150 universities in the world by prominent int ...
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Henri Bal
Henri Elle Bal (born 16 April 1958) is a professor of computer science at the Vrije Universiteit, Amsterdam in the Netherlands. He is a well-known researcher in computer systems with a specialization in parallel computer systems, languages, and applications. Education Bal received his engineer's degree from the Delft University of Technology in mathematics cum laude in 1982. Shortly after graduating, he moved to the Vrije Universiteit where he began doing research on optimizing compilers in the Computer Systems group under the direction of Prof. Andrew Tanenbaum. This work was so promising that Tanenbaum encouraged Bal to become a PhD student in his group. Bal's PhD research led to the development of the Orca programming language, one of the first programming languages intended for large-scale cluster computers. Unlike most other parallel programming languages, Orca is based on the shared-data object model, which allows a group of computers to have the illusion that they share ...
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Mancala
The mancala games are a family of two-player turn-based strategy board games played with small stones, beans, or seeds and rows of holes or pits in the earth, a board or other playing surface. The objective is usually to capture all or some set of the opponent's pieces. Versions of the game date back past the 3rd century and evidence suggests the game existed in Ancient Egypt. It is among the oldest known games to still be widely played today. Names and variants The name is a classification or type of game, rather than any specific game. Some of the most popular mancala games (concerning distribution area, the numbers of players and tournaments, and publications) are: * Ayoayo, played by the Yoruba people in Nigeria; similar to Oware * Alemungula or gebeta (ገበጣ)– played in Sudan and Ethiopia. * Ali Guli Mane or Pallanguzhi – played in Southern India. * Bao la Kiswahili – played in most of East Africa including Kenya, Tanzania, Comoros, Malawi, as we ...
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Oware
Oware is an abstract strategy game among the mancala family of board games (pit and pebble games) played worldwide with slight variations as to the layout of the game, number of players and strategy of play. Its origin is uncertain but it is widely believed to be of Ashanti origin. Played in the Bono Region, Bono East Region, Ahafo Region, Central Region, Western Region, Eastern Region, Ashanti Region of Ghana and throughout the Caribbean, oware and its variants have many names - ayò, ayoayo (Yoruba), awalé (Ivory Coast, Benin), wari (Mali), ouri, ouril or uril (Cape Verde), warri (Caribbean) Pallanguzhi (India) wali (Dagbani), adji ( Ewe), nchọ/ókwè (Igbo), ise ( Edo), awale ( Ga) (meaning "spoons" in English). A common name in English is awari but one of the earliest Western scholars to study the game, Robert Sutherland Rattray, used the name ''wari''. Rules Following are the rules for the ''abapa'' variation, considered to be the most appropriate for serious, adult p ...
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Computer Chess
Computer chess includes both hardware (dedicated computers) and software capable of playing chess. Computer chess provides opportunities for players to practice even in the absence of human opponents, and also provides opportunities for analysis, entertainment and training. Computer chess applications that play at the level of a chess master or higher are available on hardware from supercomputers to smart phones. Standalone chess-playing machines are also available. Stockfish, GNU Chess, Fruit, and other free open source applications are available for various platforms. Computer chess applications, whether implemented in hardware or software, utilize different strategies than humans to choose their moves: they use heuristic methods to build, search and evaluate trees representing sequences of moves from the current position and attempt to execute the best such sequence during play. Such trees are typically quite large, thousands to millions of nodes. The computational speed ...
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Endgame Tablebase
An endgame tablebase is a computerized database that contains precalculated exhaustive analysis of chess endgame positions. It is typically used by a computer chess engine during play, or by a human or computer that is retrospectively analysing a game that has already been played. The tablebase contains the game-theoretical value (win, loss, or draw) in each possible position, and how many moves it would take to achieve that result with perfect play. Thus, the tablebase acts as an oracle, always providing the optimal moves. Typically the database records each possible position with certain pieces remaining on the board, and the best moves with White to move and with Black to move. Tablebases are generated by retrograde analysis, working backward from a checkmated position. By 2005, all chess positions with up to six pieces, including the two kings, had been solved. By August 2012, tablebases had solved chess for almost every position with up to seven pieces, but the positio ...
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