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M,n,k-game
An ''m'',''n'',''k''-game is an abstract board game in which two players take turns in placing a stone of their color on an ''m''-by-''n'' board, the winner being the player who first gets ''k'' stones of their own color in a row, horizontally, vertically, or diagonally.J. W. H. M. Uiterwijk and H. J van der Herik, ''The advantage of the initiative'', Information Sciences 122 (1) (2000) 43-58.Jaap van den Herik, Jos W.H.M. Uiterwijk, Jack van Rijswijck (2002). "Games solved: Now and in the future". Artificial Intelligence. Thus, tic-tac-toe is the 3,3,3-game and free-style gomoku is the 15,15,5-game. An ''m'',''n'',''k''-game is also called a ''k''-in-a-row game on an ''m''-by-''n'' board. The ''m'',''n'',''k''-games are mainly of mathematical interest. One seeks to find the game-theoretic value, the result of the game with perfect play. This is known as solving the game. Strategy stealing argument A standard strategy stealing argument from combinatorial game theory shows t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pente
Pente is an abstract strategy board game for two or more players, created in 1977 by Gary Gabrel. A member of the m,n,k game family, Pente stands out for its custodial capture mechanic, which allows players to "sandwich" pairs of stones and capture them by flanking them on either side. This changes the overall tactical assessments players face when compared to pure placement m,n,k games such as Gomoku. Rules Pente is played on a 19x19 grid of intersections similar to a Go board. Players alternate placing stones of their color on empty intersections, with White always assuming the opening move. The goal of the game is to either align five or more stones of the same color in a row in any vertical, horizontal or diagonal direction or to make five captures. Stones are captured by custodial capture (flanking an adjacent pair of an opponent's stones directly on either side with your own stones). Captures consist of exactly two stones; flanking a single stone or three or more stones ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tic-tac-toe 5
Tic-tac-toe (American English), noughts and crosses (Commonwealth English), or Xs and Os (Canadian or Irish English) is a paper-and-pencil game for two players who take turns marking the spaces in a three-by-three grid with ''X'' or ''O''. The player who succeeds in placing three of their marks in a horizontal, vertical, or diagonal row is the winner. It is a solved game, with a forced draw assuming best play from both players. Gameplay Tic-tac-toe is played on a three-by-three grid by two players, who alternately place the marks X and O in one of the nine spaces in the grid. In the following example, the first player (''X'') wins the game in seven steps: There is no universally-agreed rule as to who plays first, but in this article the convention that X plays first is used. Players soon discover that the best play from both parties leads to a draw. Hence, tic-tac-toe is often played by young children who may not have discovered the optimal strategy. Because of the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ICGA Journal
The ''ICGA Journal'' is a quarterly academic journal published by the International Computer Games Association. It was renamed in 2000. Its previous name was the ''ICCA Journal'' of the International Computer Chess Association, which was founded in 1977. The journal covers computer analysis on two-player games, especially games with perfect information such as chess, checkers, and Go. It has been the primary outlet for publication of articles on solved games, including the development of endgame tablebases in chess and other games. For example, John W. Romein and Henri E. Bal reported in the journal in 2002 that they had solved Awari and, in 2015, David J. Wu reported his solution for the Arimaa Challenge.{{cite journal , first=David J. , last=Wu , year=2015 , title=Designing a Winning Arimaa Program , journal=ICGA Journal , volume=38 , number=1 , pages=19–40 , doi=10.3233/ICG-2015-38104 , url=https://icosahedral.net/downloads/djwu2015arimaa.pdf From 1983 till 2015 ''ICGA Jou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Strategy Games
Abstract strategy games admit a number of definitions which distinguish these from strategy games in general, mostly involving no or minimal narrative theme, outcomes determined only by player choice (with no randomness), and perfect information. For example, Go is a pure abstract strategy game since it fulfills all three criteria; chess and related games are nearly so but feature a recognizable theme of ancient warfare; and Stratego is borderline since it is deterministic, loosely based on 19th-century Napoleonic warfare, and features concealed information. Definition Combinatorial games have no randomizers such as dice, no simultaneous movement, nor hidden information. Some games that do have these elements are sometimes classified as abstract strategy games. (Games such as '' Continuo'', Octiles, '' Can't Stop'', and Sequence, could be considered abstract strategy games, despite having a luck or bluffing element.) A smaller category of abstract strategy games manages to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nd Game
A ''n''''d'' game (or ''n''''k'' game) is a generalization of the game tic-tac-toe to higher dimensions. It is a game played on a ''n''''d'' hypercube with 2 players. If one player creates a line of length ''n'' of their symbol (X or O) they win the game. However, if all ''n''''d'' spaces are filled then the game is a draw. Tic-tac-toe is the game where ''n'' equals 3 and ''d'' equals 2 (3, 2). Qubic 3D tic-tac-toe, also known by the trade name Qubic, is an abstract strategy board game, generally for two players. It is similar in concept to traditional tic-tac-toe but is played in a cubical array of cells, usually 4x4x4. Players take turns pla ... is the game. The or games are trivially won by the first player as there is only one space ( and ). A game with and cannot be won if both players are playing well as an opponent's piece will block the one-dimensional line. There are a total of winning lines in a ''n''''d'' game. See also * References Tic-tac-toe {{g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kaplansky's Game
Kaplansky's game or Kaplansky's ''n''-in-a-line is an abstract board game in which two players take turns in placing a stone of their color on an infinite lattice board, the winner being the player who first gets ''k'' stones of their own color on a line which does not have any stones of the opposite color on it. It is named after Irving Kaplansky. General results * ''k'' ≤ 3 is a first-player win. * 4 ≤ ''k'' ≤ 7 is believed to be draw, but this remains unproven. * ''k'' ≥ 8 is a draw: Every player can draw via a "pairing strategy" or other "draw strategy" of ''m'',''n'',''k''-game. See also * ''m'',''n'',''k''-game * Hex (board game) * Harary's generalized tictactoe Harary's generalized tic-tac-toe or animal tic-tac-toe is a generalization of the game tic-tac-toe, defining the game as a race to complete a particular polyomino on a square grid of varying size, rather than being limited to "in a row" construction ... References {{Tic-Tac-Toe Abstract strategy game ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harary's Generalized Tictactoe
Harary's generalized tic-tac-toe or animal tic-tac-toe is a generalization of the game tic-tac-toe, defining the game as a race to complete a particular polyomino on a square grid of varying size, rather than being limited to "in a row" constructions. It was devised by Frank Harary in March 1977, and is a broader definition than that of an m,n,k-game. Harary's generalization does not include tic-tac-toe itself, as diagonal constructions are not considered a win. Like many other two-player games, strategy stealing means that the second player can never win. All that is left to study is to determine whether the first player can win, on what board sizes he may do so, and in how many moves it will take. Results Square boards Let ''b'' be the smallest size square board on which the first player can win, and let ''m'' be the smallest number of moves in which the first player can force a win, assuming perfect play by both sides. *monomino: ''b'' = 1, ''m'' = 1 *domino: ''b'' = 2, ''m'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Connect6
Connect6 (; Pinyin: liùzǐqí; ; ja, 六目並べ; ko, 육목) introduced in 2003 by Professor I-Chen Wu at Department of Computer Science and Information Engineering, National Chiao Tung University in Taiwan, is a two-player strategy game similar to Gomoku. Two players, Black and White, alternately place two stones of their own colour, black and white respectively, on empty intersections of a Go-like board, except that Black (the first player) places one stone only for the first move. The one who gets six or more stones in a row (horizontally, vertically or diagonally) first wins the game. Rules The rules of Connect6 are very simple and similar to the traditional game of Gomoku: * Players and stones: There are two players. Black plays first, and White second. Each player plays with an appropriate color of stones, as in Go and Gomoku. * Game board: Connect6 is played on a square board made up of orthogonal lines, with each intersection capable of holding one stone. In the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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