Dots and boxes is a pencil-and-paper game for two players. It was first published in the 19th century by French mathematician Édouard Lucas, who called it la pipopipette. It has gone by many other names, including the dots and dashes, game of dots, dot to dot grid, boxes, and pigs in a pen.
John Horton Conway was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branches of recreational mathematics, most notably the invention of the cellular automaton called the Game of Life.
Nim is a mathematical game of strategy in which two players take turns removing objects from distinct heaps or piles. On each turn, a player must remove at least one object, and may remove any number of objects provided they all come from the same heap or pile. Depending on the version being played, the goal of the game is either to avoid taking the last object or to take the last object.
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.
Misère, misere, bettel, betl, beddl or bettler 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.
Winning Ways for Your Mathematical Plays by Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy is a compendium of information on mathematical games. It was first published in 1982 in two volumes.
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.
In combinatorial game theory, a game is partisan if it is not impartial. That is, some moves are available to one player and not to the other.
Col is a pencil and paper game, specifically a map-coloring game, involving the shading of areas in a line drawing according to the rules of graph coloring. With each move, the graph must remain proper, and a player who cannot make a legal move loses. The game was described and analysed by John Conway, who attributed it to Colin Vout, in On Numbers and Games.
Richard Kenneth Guy was a British mathematician. He was a professor in the Department of Mathematics at the University of Calgary. He is known for his work in number theory, geometry, recreational mathematics, combinatorics, and graph theory. He is best known for co-authorship of Winning Ways for your Mathematical Plays and authorship of Unsolved Problems in Number Theory. He published more than 300 scholarly articles. Guy proposed the partially tongue-in-cheek "strong law of small numbers", which says there are not enough small integers available for the many tasks assigned to them – thus explaining many coincidences and patterns found among numerous cultures. For this paper he received the MAA Lester R. Ford Award.
Dodgem is a simple abstract strategy game invented by Colin Vout in 1972 while he was a mathematics student at the University of Cambridge as described in the book Winning Ways. It is played on an n×n board with n-1 cars for each player—two cars each on a 3×3 board is enough for an interesting game, but larger sizes are also possible.
In mathematics, tiny and miny are operators that yield infinitesimal values when applied to numbers in combinatorial game theory. Given a positive number G, tiny G is equal to {0|{0|-G}} for any game G, whereas miny G is tiny G's negative, or {{G|0}|0}.
In combinatorial game theory, a branch of mathematics, a hot game is one in which each player can improve their position by making the next move.
Gathering 4 Gardner (G4G) is an educational foundation and non-profit corporation devoted to preserving the legacy and spirit of prolific writer Martin Gardner. G4G organizes conferences where people who have been inspired by or have a strong personal connection to Martin Gardner can meet and celebrate his influence. These events explore ideas and developments in recreational mathematics, magic, illusion, puzzles, philosophy, and rationality, and foster creative work in all of these areas by enthusiasts of all ages. G4G also facilitates a related series of events called Celebration of Mind (CoM).
Treblecross is a degenerate tic-tac toe variant. The game is an octal game, played on a one-dimensional board and both players play using the same piece. Each player on their turn plays a piece in an unoccupied space. The game is won if a player on their turn makes a line of three pieces in a row.
David Wolfe is a mathematician and amateur Go player.
Blockbusting is a solved combinatorial game introduced in 1987 by Elwyn Berlekamp illustrating a generalisation of overheating.
In combinatorial game theory, cooling, heating, and overheating are operations on hot games to make them more amenable to the traditional methods of the theory, which was originally devised for cold games in which the winner is the last player to have a legal move. Overheating was generalised by Elwyn Berlekamp for the analysis of Blockbusting. Chilling and warming are variants used in the analysis of the endgame of Go.
In combinatorial game theory, a subtraction game is an abstract strategy game whose state can be represented by a natural number or vector of numbers and in which the allowed moves reduce these numbers. Often, the moves of the game allow any number to be reduced by subtracting a value from a specified subtraction set, and different subtraction games vary in their subtraction sets. These games also vary in whether the last player to move wins or loses. Another winning convention that has also been used is that a player who moves to a position with all numbers zero wins, but that any other position with no moves possible is a draw.
Thomas Malin Rodgers was an Atlanta-based businessman and puzzle collector who is remembered as the originator of the Gathering 4 Gardner (G4G) educational foundation, first conceived in 1992. He co-founded G4G with magician and toy inventor Mark Setteducati and UC Berkeley professor Elwyn Berlekamp. Over the past three decades it hosted 14 biennial conferences for aficionados of the recreational mathematician and Scientific American columnist and writer Martin Gardner. Rodgers also edited 6 volumes of Martin Gardner tribute books, published by AK Peters. Rodgers' personal physical puzzle collection was legendary.
