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Notakto
Notakto is a tic-tac-toe variant, also known as neutral or impartial tic-tac-toe. The game is a combination of the games tic-tac-toe and Nim, played across one or several boards with both of the players playing the same piece (an "X" or cross). The game ends when all the boards contain a three-in-a-row of Xs, at which point the player to have made the last move loses the game. However, in this game, unlike tic-tac-toe, there will always be a player who wins any game of Notakto. Notakto is an impartial game, where the allowable moves depend only on the state of the game and not on which player is taking their turn. When played across multiple boards it is a disjunctive game. The game is attributed to professor and backgammon player Bob Koca, who is said to have invented the game in 2010, when his five-year-old nephew suggested playing a game of tic-tac-toe with both players as "X". Play Notakto is played on a finite number of empty three-by-three boards. Then, each player take ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Notakto Boot Trap
Notakto is a tic-tac-toe variant, also known as neutral or impartial tic-tac-toe. The game is a combination of the games tic-tac-toe and Nim, played across one or several boards with both of the players playing the same piece (an "X" or cross). The game ends when all the boards contain a three-in-a-row of Xs, at which point the player to have made the last move loses the game. However, in this game, unlike tic-tac-toe, there will always be a player who wins any game of Notakto. Notakto is an impartial game, where the allowable moves depend only on the state of the game and not on which player is taking their turn. When played across multiple boards it is a disjunctive game. The game is attributed to professor and backgammon player Bob Koca, who is said to have invented the game in 2010, when his five-year-old nephew suggested playing a game of tic-tac-toe with both players as "X". Play Notakto is played on a finite number of empty three-by-three boards. Then, each player take ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tic-tac-toe Variants
Tic-tac-toe is an instance of an m,n,k-game, where two players alternate taking turns on an ''m''×''n'' board until one of them gets ''k'' in a row. Harary's generalized tic-tac-toe is an even broader generalization. The game can also be generalized as a nd game. The game can be generalised even further from the above variants by playing on an arbitrary hypergraph where rows are hyperedges and cells are vertices. Many board games share the element of trying to be the first to get ''n''-in-a-row, including three men's morris, nine men's morris, pente, gomoku, Qubic, Connect Four, Quarto, Gobblet, Order and Chaos, Toss Across, and Mojo. Variants of tic-tac-toe date back several millennia. Historic An early variation of tic-tac-toe was played in the Roman Empire, around the first century BC. It was called Terni Lapilli and instead of having any number of pieces, each player only had three; thus, they had to move them around to empty spaces to keep playing. The game's grid ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Impartial Game
In combinatorial game theory, an impartial game is a game in which the allowable moves depend only on the position and not on which of the two players is currently moving, and where the payoffs are symmetric. In other words, the only difference between player 1 and player 2 is that player 1 goes first. The game is played until a terminal position is reached. A terminal position is one from which no moves are possible. Then one of the players is declared the winner and the other the loser. Furthermore, impartial games are played with perfect information and no chance moves, meaning all information about the game and operations for both players are visible to both players. Impartial games include Nim, Sprouts, Kayles, Quarto, Cram, Chomp, Subtract a square, Notakto, and poset games. Go and chess are not impartial, as each player can only place or move pieces of their own color. Games such as poker, dice or dominos are not impartial games as they rely on chance. Impartial games c ... [...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 pencils (or other writing implements), usually without erasing. They may be played to pass the time, as icebreakers, or to end boredom. In recent times, they have been supplanted by mobile games. Some popular examples of pencil-and-paper games include Tic-tac-toe, Sprouts, Dots and Boxes, Hangman, MASH, Paper soccer, and Spellbinder. The term is unrelated to the use in role-playing games to differentiate 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 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 tur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tic-tac-toe
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] |
Disjunctive Sum
In the mathematics of combinatorial games, the sum or disjunctive sum of two games is a game in which the two games are played in parallel, with each player being allowed to move in just one of the games per turn. The sum game finishes when there are no moves left in either of the two parallel games, at which point (in normal play) the last player to move wins. This operation may be extended to disjunctive sums of any number of games, again by playing the games in parallel and moving in exactly one of the games per turn. It is the fundamental operation that is used in the Sprague–Grundy theorem for impartial games and which led to the field of combinatorial game theory for partisan games. Application to common games Disjunctive sums arise in games that naturally break up into components or regions that do not interact except in that each player in turn must choose just one component to play in. Examples of such games are Go, Nim, Sprouts, Domineering, the Game of the Amazons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bob Koca
Bob, BOB, or B.O.B. may refer to: Places *Mount Bob, New York, United States *Bob Island, Palmer Archipelago, Antarctica People, fictional characters, and named animals *Bob (given name), a list of people and fictional characters *Bob (surname) *Bob (dog), a dog that received the Dickin Medal for bravery in World War II *Bob the Railway Dog, a part of South Australian Railways folklore Television, games, and radio * ''Bob'' (TV series), an American comedy series starring Bob Newhart * ''B.O.B.'' (video game), a side-scrolling shooter *Bob FM, on-air brand of a number of FM radio stations in North America Music Musicians and groups *B.o.B (born 1988), American rapper and record producer *Bob (band), a British indie pop band *The Bobs, an American a cappella group *Boyz on Block, a British pop supergroup Songs * "B.O.B" (song), by OutKast * "Bob" ("Weird Al" Yankovic song), from the 2003 album ''Poodle Hat'' by "Weird Al" Yankovic *"Bob", a song from the album ''Brighter Than Cr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knight (chess)
The knight (♘, ♞) is a piece in the game of chess, represented by a horse's head and neck. It moves two squares vertically and one square horizontally, or two squares horizontally and one square vertically, jumping over other pieces. Each player starts the game with two knights on the b- and g-, each located between a rook and a bishop. Movement Compared to other chess pieces, the knight's movement is unique: it moves two squares vertically and one square horizontally, or two squares horizontally and one square vertically (with both forming the shape of a capital L). When moving, the knight can jump over pieces to reach its destination. Knights capture in the same way, replacing the enemy piece on the square and removing it from the board. A knight can have up to eight available moves at once. Knights and pawns are the only pieces that can be moved in the chess starting position. Value Knights and bishops, also known as , have a value of about three pawns. Bishops utili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Misère
Misère ( French for "destitution"), misere, bettel, betl, or (German for "beggar"; equivalent terms in other languages include , , ) is a bid in various card games, and the player who bids misère undertakes to win no tricks or as few as possible, usually at no trump, in the round to be played. This does not allow sufficient variety to constitute a game in its own right, but it is the basis of such trick-avoidance games as Hearts, and provides an optional contract for most games involving an auction. The term or category may also be used for some card game of its own with the same aim, like Black Peter. A misère bid usually indicates an extremely poor hand, hence the name. An open or lay down misère, or misère ouvert is a 500 bid where the player is so sure of losing every trick that they undertake to do so with their cards placed face-up on the table. Consequently, 'lay down misère' is Australian gambling slang for a predicted easy victory. In Skat, the bidding can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Games
A mathematical game is a game whose rules, strategies, and outcomes are defined by clear mathematical parameters. Often, such games have simple rules and match procedures, such as Tic-tac-toe and Dots and Boxes. Generally, mathematical games need not be conceptually intricate to involve deeper computational underpinnings. For example, even though the rules of Mancala are relatively basic, the game can be rigorously analyzed through the lens of combinatorial game theory. Mathematical games differ sharply from mathematical puzzles in that mathematical puzzles require specific mathematical expertise to complete, whereas mathematical games do not require a deep knowledge of mathematics to play. Often, the arithmetic core of mathematical games is not readily apparent to players untrained to note the statistical or mathematical aspects. Some mathematical games are of deep interest in the field of recreational mathematics. When studying a game's core mathematics, arithmetic theory i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paper-and-pencil Games
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 pencils (or other writing implements), usually without erasing. They may be played to pass the time, as icebreakers, or to end boredom. In recent times, they have been supplanted by mobile games. Some popular examples of pencil-and-paper games include Tic-tac-toe, Sprouts, Dots and Boxes, Hangman, MASH, Paper soccer, and Spellbinder. The term is unrelated to the use in role-playing games to differentiate 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 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 tur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Game Theory
Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Study has been largely confined to two-player games that have a ''position'' that the players take turns changing in defined ways or ''moves'' to achieve a defined winning condition. Combinatorial game theory has not traditionally studied games of chance or those that use imperfect or incomplete information, favoring games that offer perfect information in which the state of the game and the set of available moves is always known by both players. However, as mathematical techniques advance, the types of game that can be mathematically analyzed expands, thus the boundaries of the field are ever changing. Scholars will generally define what they mean by a "game" at the beginning of a paper, and these definitions often vary as they are specific to the game being analyzed and are not meant to represent the entire scope of the field. C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
