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Tic-tac-toe
Tic-tac-toe (American English), noughts and crosses (English in the Commonwealth of Nations, Commonwealth English), or Xs and Os (Canadian English, Canadian or Hiberno-English, Irish English) is a paper-and-pencil game for two players who take turns marking the spaces in a three-by-three grid, one with Xs and the other with Os. A player wins when they mark all three spaces of a row, column, or diagonal of the grid, whereupon they traditionally draw a line through those three marks to indicate the win. It is a solved game, with a forced draw assuming Best response, best play from both players. Names In American English, the game is known as "tic-tac-toe". It may also be spelled "tick-tack-toe", "tick-tat-toe", or "tit-tat-toe". In Commonwealth English (particularly British English, British, South African English, South African, Indian English, Indian, Australian English, Australian, and New Zealand English), the game is known as "noughts and crosses", alternatively spelled ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harary's Generalized Tic-tac-toe
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 (Harary called them "animals") on a grid of squares. It was devised by Frank Harary in March 1977. Harary tic-tac-toe is similar to the m,n,k-games, of which tic-tac-toe and Gomoku are examples; but in tic-tac-toe the first player is trying to complete ''either'' an I-tromino (a horizontal or vertical line of three squares) ''or'' a diagonal line of three corner-connected squares, whereas in Harary's game there is only a single polyomino involved. Categorization of polyominoes by properties of their games Each polyomino corresponds to a generalized tic-tac-toe game: for example, the I-tromino corresponds to the game in which Player 1 is trying to form an I-tromino and Player 2 is trying to stop him. (Note that it is impossible for Player 2 to form an I-tromino before Player 1 does: the strategy-stealing argument applies. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Three Men's Morris
Three men's morris is an abstract strategy game played on a three by three board (counting lines) that is similar to tic-tac-toe. It is also related to six men's morris and nine men's morris. A player wins by forming a mill, that is, three of their own pieces in a row. Rules image:Three Men's Morris variant board.svg, 240px, A board for three men's morris. This pattern has been found carved into the roof of the temple of Kurna. Each player has three pieces. The winner is the first player to align their three pieces on a line drawn on the board. There are 3 horizontal lines, 3 vertical lines and 2 diagonal lines. The board is empty to begin the game, and players take turns placing their pieces on empty intersections. Once all pieces are placed (assuming there is no winner by then), play proceeds with each player moving one of their pieces per turn. A piece may move to any vacant point on the board, not just an adjacent one. According to H. J. R. Murray’s ''A History of Chess ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Tree Complexity
Combinatorial game theory measures game complexity in several ways: #State-space complexity (the number of legal game positions from the initial position) #Game tree size (total number of possible games) #Decision complexity (number of leaf nodes in the smallest decision tree for initial position) #Game-tree complexity (number of leaf nodes in the smallest full-width decision tree for initial position) #Computational complexity (asymptotic difficulty of a game as it grows arbitrarily large) These measures involve understanding the game positions, possible outcomes, and computational complexity of various game scenarios. Measures of game complexity State-space complexity The ''state-space complexity'' of a game is the number of legal game positions reachable from the initial position of the game. When this is too hard to calculate, an upper bound can often be computed by also counting (some) illegal positions (positions that can never arise in the course of a game). Game t ... [...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] |
Nd Game
A ''n''''d'' game (or ''n''''k'' game) is a generalization of the combinatorial 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 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. Game theory An ''nd'' game is a symmetric combinatorial game. There are a total of \frac winning lines in a ''n''''d'' game. For any width ''n'', at some dimension ''d'' (thanks to the Hales-Jewett theorem), there will always be a winning strategy for player X. There will never be a winning strategy for player O because of the Strateg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solved Game
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 or computer assistance. Overview A two-player game can be solved on several levels: Ultra-weak solution : 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 details of the perfect play. Weak solution : Provide one algorithm for each of the two players, such that the player using it can achieve at least the optimal outcome, regardless of the opponent's moves, from the start of the game, using reasonable computational resources. Strong solution : Provide an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paper-and-pencil Game
Paper-and-pencil games or paper-and-pen games (or some variation on those terms) are games that can be played solely with paper and pencil, pencils (or other writing implements), usually without erasing. They may be played to pass the time, as icebreakers, or for brain training. In recent times, they have been supplanted by mobile games. Some popular examples of pencil-and-paper games include tic-tac-toe, Sprouts (game), sprouts, dots and boxes, Hangman (game), hangman, MASH (game), MASH, paper soccer, and Spellbinder (paper-and-pencil game), spellbinder. The term is unrelated to the use in role-playing games to differentiate Tabletop role-playing game, tabletop games from role-playing video games. Board games where pieces are never moved or removed from the board once being played, particularly abstract strategy games like Gomoku and Connect Four, can also be played as pencil-and-paper games. References External links * A Zen Guide to Paper and Pen GamesPencil and Paper Gam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hiberno-English
Hiberno-English or Irish English (IrE), also formerly sometimes called Anglo-Irish, is the set of dialects of English native to the island of Ireland. In both the Republic of Ireland and Northern Ireland, English is the first language in everyday use and, alongside the Irish language, one of two official languages (with Ulster Scots, in Northern Ireland, being yet another local language). The writing standards of Irish English, such as its spelling, align with British English. But the diverse accents and some of the grammatical structures and vocabulary of Irish English are unique, including certain notably conservative phonological features and vocabulary: those that are no longer common in the dialects of England or North America. It shows significant influences from the Irish language and, in the north, the Scots language. Phonologists today often divide Irish English into four or five overarching dialects or accents: Ulster or Northern Irish accents, Western and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sportsmanship
Sportsmanship is an aspiration or ethos that a sport or activity will be enjoyed for its own sake, and with proper consideration for wikt:fairness, fairness, ethics, respect, and a sense of fellowship with one's competitors. A "sore loser" refers to one who does not take defeat well, whereas a "good sport" means being a "good winner" as well as being a "good loser". Analysis Sportsmanship can be conceptualized as an enduring and relatively stable characteristic or disposition such that individuals differ in the way they are generally expected to behave in sports situations. Sportsmanship mainly refers to virtues such as fairness, self-control, courage, and persistence, and has been associated with interpersonal concepts of treating others and being treated fairly, maintaining self-control if dealing with others, and respect for both authority and opponents. Sportsmanship is also looked at as being the way one reacts to a sport/game/player. Four elements of sportsmanship a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
