About: Solved game

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A solved game is a game whose outcome can be correctly predicted from any position when each side plays optimally. Games which have not been solved are said to be "unsolved". The game-theoretic value is the outcome of a game, when played perfectly from its initial position. In a two-player game it can be a win (W), loss (L) or draw (D) for the first player. A two-player game can be solved on several levels: Strong: The strongest sense of solution requires an algorithm which can produce perfect play from any position, i.e. even if mistakes have already been made on one or both sides.

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rdfs:label	Solved game
rdfs:comment	A solved game is a game whose outcome can be correctly predicted from any position when each side plays optimally. Games which have not been solved are said to be "unsolved". The game-theoretic value is the outcome of a game, when played perfectly from its initial position. In a two-player game it can be a win (W), loss (L) or draw (D) for the first player. A two-player game can be solved on several levels: Strong: The strongest sense of solution requires an algorithm which can produce perfect play from any position, i.e. even if mistakes have already been made on one or both sides.
sameAs	dbr:Solved_game
dcterms:subject	Game Theory
abstract	A solved game is a game whose outcome can be correctly predicted from any position when each side plays optimally. Games which have not been solved are said to be "unsolved". The game-theoretic value is the outcome of a game, when played perfectly from its initial position. In a two-player game it can be a win (W), loss (L) or draw (D) for the first player. A few mancala games have been solved. The game-theoretic value is known for Awari (draw), Kalah (depending on the instance), MiniMancala (draw), Ohvalhu (first-player win). Some trivial games have also been completely analyzed: Micro-Wari and Nano-Wari. A two-player game can be solved on several levels: Ultra-weak: In the weakest sense, solving a game means proving whether the first player will win, lose, or draw from the initial position, given perfect play on both sides. This can be a non-constructive proof (possibly involving a strategy stealing argument) that may not actually help determine this perfect play. Any game using the pie rule is either a draw or a second-player win. Weak: More typically, solving a game means providing an algorithm that secures a win for one player, or a draw for either, against any possible moves by the opponent, from the beginning of the game. Strong: The strongest sense of solution requires an algorithm which can produce perfect play from any position, i.e. even if mistakes have already been made on one or both sides. Given the rules of any two-person game with a finite number of positions, one can always trivially construct a minimax algorithm that would exhaustively traverse the game tree. However, since for many non-trivial games such an algorithm would require an infeasible amount of time to generate a move in a given position, a game is not considered to be solved weakly or strongly unless the algorithm can be run by existing hardware in a reasonable time. Many algorithms rely on a huge pre-generated database, and are effectively nothing more than that.

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