Concept
Combinatorial game theory
Related concepts (17)
Game 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).
Game tree
In the context of Combinatorial game theory, which typically studies sequential games with perfect information, a game tree is a graph representing all possible game states within such a game. Such games include well-known ones such as chess, checkers, Go, and tic-tac-toe. This can be used to measure the complexity of a game, as it represents all the possible ways a 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.
Sequential game
In game theory, a sequential game is a game where one player chooses their action before the others choose theirs. The other players must have information on the first player's choice so that the difference in time has no strategic effect. Sequential games are governed by the time axis and represented in the form of decision trees. Sequential games with perfect information can be analysed mathematically using combinatorial game theory. Decision trees are the extensive form of dynamic games that provide information on the possible ways that a given game can be played.
Go (game)
Go is an abstract strategy board game for two players in which the aim is to surround more territory than the opponent. The game was invented in China more than 2,500 years ago and is believed to be the oldest board game continuously played to the present day. A 2016 survey by the International Go Federation's 75 member nations found that there are over 46 million people worldwide who know how to play Go, and over 20 million current players, the majority of whom live in East Asia. The playing pieces are called stones.
Alpha–beta pruning
Alpha–beta pruning is a search algorithm that seeks to decrease the number of nodes that are evaluated by the minimax algorithm in its search tree. It is an adversarial search algorithm used commonly for machine playing of two-player combinatorial games (Tic-tac-toe, Chess, Connect 4, etc.). It stops evaluating a move when at least one possibility has been found that proves the move to be worse than a previously examined move. Such moves need not be evaluated further.
Game
A game is a structured form of play, usually undertaken for entertainment or fun, and sometimes used as an educational tool. Many games are also considered to be work (such as professional players of spectator sports or games) or art (such as jigsaw puzzles or games involving an artistic layout such as Mahjong, solitaire, or some video games). Games are sometimes played purely for enjoyment, sometimes for achievement or reward as well. They can be played alone, in teams, or online; by amateurs or by professionals.
Minimax
Minmax (sometimes Minimax, MM or saddle point) is a decision rule used in artificial intelligence, decision theory, 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 uncertainty.
Backward induction
Backward induction is the process of reasoning backwards in time, from the end of a problem or situation, to determine a sequence of optimal actions. It proceeds by examining the last point at which a decision is to be made and then identifying what action would be most optimal at that moment. Using this information, one can then determine what to do at the second-to-last time of decision. This process continues backwards until one has determined the best action for every possible situation (i.e.
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. In American English, the game is known as "tic-tac-toe".
Abstract strategy game
Abstract strategy games in contrast to strategy games in general usually have no or minimal narrative theme, outcomes determined only by player choice (with no randomness), and all players have perfect information about the game. 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.