Combinatorial game theory

Zugzwang (; ) is a situation found in chess and other turn-based games wherein one player is put at a disadvantage because of their obligation to make a move; a player is said to be "in zugzwang" when any legal move will worsen their position.

Jenga is a game of physical skill created by British board game designer and author Leslie Scott and marketed by Hasbro. The name comes from the Swahili word "" which means 'to build or construct'. Players take turns removing one block at a time from a tower constructed of 54 blocks. Each block removed is then placed on top of the tower, creating a progressively more unstable structure. The game ends when the tower falls over.

Minimax (sometimes Minmax, MM or saddle point) is a decision rule used in artificial intelligence, decision theory, combinatorial game theory, statistics, and philosophy for minimizing the possible loss for a worst case (maximum loss) scenario. When dealing with gains, it is referred to as "maximin" – to maximize the minimum gain. Originally formulated for several-player zero-sum game theory, covering both the cases where players take alternate moves and those where they make simultaneous moves, it has also been extended to more complex games and to general decision-making in the presence of u

Nim is a mathematical combinatorial game in which two players take turns removing (or "nimming") 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.

a totally ordered proper class containing the real numbers as well as hyperreal numbers such as infinity and infinitesimals.

search algorithm that seeks to decrease the number of nodes that are evaluated by the minimax algorithm in its search tree

lower bound on the game-tree complexity for chess

branch of game theory about two-player sequential games with perfect information

heuristic search algorithm based on random sampling

tree diagram used to find and analyze potential moves in a game

rapid growth of the complexity of a problem due to how the combinatorics of the problem is affected by the input, constraints, and bounds of the problem

game whose outcome can be correctly predicted

thumb|A move in the game of Chomp, removing two blocks: a player has chosen a block to "eat", and must also eat the block below it. The top-left block is "poisoned" and whoever eats it loses the game. Chomp is a two-player strategy game played on a rectangular grid made up of smaller square cells, which can be thought of as the blocks of a chocolate bar. The players take it in turns to choose one block and "eat it" (remove from the board), together with those that are below it and to its right. The top left block is "poisoned" and the player who eats this loses.

theorem in combinatorial game theory that every impartial game position is equivalent to a position in the game of nim

game in which the allowable moves depend on the current position and not on which of the two players is currently moving

computing, tree data structures, and game theory value

game-theoretic game on an endless chessboard: a devil hinders an angel’s movement, and the angel tries to escape; each turn the angel jumps ≤k squares, and the devil adds a block on an empty square

In mathematics, the nimbers, also called Grundy numbers (not to be confused with Grundy chromatic numbers), are introduced in combinatorial game theory, where they are defined as the values of heaps in the game Nim. The nimbers are the same proper class as the ordinal numbers but endowed with nimber addition and nimber multiplication, which are distinct from ordinal addition and ordinal multiplication.

notion in combinatorial game theory

thumb|A starting setup for the game of Hackenbush Hackenbush is a two-player game invented by mathematician John Horton Conway. It may be played on any configuration of line segments connected to one another by their endpoints and to a "ground" line. Other versions of the game use differently colored lines.

game

argument in combinatorial game theory

Negamax search is a variant form of minimax search that relies on the zero-sum property of a two-player game.

Domineering (also called Stop-Gate or Crosscram) is a mathematical game that can be played on any collection of squares on a sheet of graph paper. For example, it can be played on a 6×6 square, a rectangle, a polyomino, or a combination of any number of such components. Two players have a collection of dominoes which they place on the grid in turn, covering up squares. One player places tiles vertically, while the other places them horizontally. (Traditionally, these players are called "Left" and "Right", respectively, or "V" and "H". Both conventions are used in this article.) As in most game

variation of the game of chess

sequence of moves in a game

in combinatorial game theory

hand game for two 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

negamax algorithm

combinatorial algorithm

game where both players can't move

pencil game

Mathematical studies about the game of go

mathematical game