GomokuGomoku, also called Five in a Row, is an abstract strategy board game. It is traditionally played with Go pieces (black and white stones) on a Go board. It is played using a 15×15 board while in the past a 19×19 board was standard. Because pieces are typically not moved or removed from the board, gomoku may also be played as a paper-and-pencil game. The game is known in several countries under different names. Players alternate turns placing a stone of their color on an empty intersection. Black plays first.
Game treeIn 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.
Combinatorial game theoryCombinatorial 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.
PSPACE-completeIn computational complexity theory, a decision problem is PSPACE-complete if it can be solved using an amount of memory that is polynomial in the input length (polynomial space) and if every other problem that can be solved in polynomial space can be transformed to it in polynomial time. The problems that are PSPACE-complete can be thought of as the hardest problems in PSPACE, the class of decision problems solvable in polynomial space, because a solution to any one such problem could easily be used to solve any other problem in PSPACE.
Abstract strategy gameAbstract 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.
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.
Hex (board game)Hex (also called Nash) is a two player abstract strategy board game in which players attempt to connect opposite sides of a rhombus-shaped board made of hexagonal cells. Hex was invented by mathematician and poet Piet Hein in 1942 and later rediscovered and popularized by John Nash. It is traditionally played on an 11×11 rhombus board, although 13×13 and 19×19 boards are also popular. The board is composed of hexagons called cells or hexes.
Ply (game theory)In two-or-more-player sequential games, a ply is one turn taken by one of the players. The word is used to clarify what is meant when one might otherwise say "turn". The word "turn" can be a problem since it means different things in different traditions. For example, in standard chess terminology, one move consists of a turn by each player; therefore a ply in chess is a half-move. Thus, after 20 moves in a chess game, 40 plies have been completed—20 by white and 20 by black.
XiangqiXiangqi (; ˈʃɑːŋtʃi), commonly known as Chinese chess or elephant chess, is a strategy board game for two players. It is the most popular board game in China. Xiangqi is in the same family of games as shogi, janggi, Western chess, chaturanga, and Indian chess. Besides China and areas with significant ethnic Chinese communities, this game is also a popular pastime in Vietnam, where it is known as cờ tướng, literally 'General's chess'. The game represents a battle between two armies, with the primary object being to checkmate the enemy's general (king).
State space (computer science)In computer science, a state space is a discrete space representing the set of all possible configurations of a "system". It is a useful abstraction for reasoning about the behavior of a given system and is widely used in the fields of artificial intelligence and game theory. For instance, the toy problem Vacuum World has a discrete finite state space in which there are a limited set of configurations that the vacuum and dirt can be in. A "counter" system, where states are the natural numbers starting at 1 and are incremented over time has an infinite discrete state space.
