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Solved Games
A solved game is a game whose outcome (win, lose or tie (draw), 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, perfect play on both sides. This can be a Constructive proof, 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 ...
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Game
A game is a structured form of play, usually undertaken for 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 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 unrestricted play whereas games come with present rules ...
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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 ...
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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'' ...
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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