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An example is a game Vallejo Pons–Kasparov, Moscow 2004, [19] which was called "a model modern grandmaster draw!" by Kasparov himself in Revolution in the 70s (page 164). 8.Nb3 White opts for a quiet game, but Black has nothing to worry about: 8...Be7 9.Qf3 Nbd7 10.0-0-0 Qc7 where we have reached a set-up very similar to that of the old main ...
Constant sum: A game is a constant sum game if the sum of the payoffs to every player are the same for every single set of strategies. In these games, one player gains if and only if another player loses. A constant sum game can be converted into a zero sum game by subtracting a fixed value from all payoffs, leaving their relative order unchanged.
In both games Fischer played Black and grabbed the pawn. In the first, he reached a secure position with a comfortable material advantage but only secured a draw . In the second, Spassky surprised Fischer with a theoretical novelty and won the game after Fischer defended poorly, allowing Spassky to trap Fischer's queen and handing Fischer his ...
In game theory, a solution concept is a formal rule for predicting how a game will be played. These predictions are called "solutions", and describe which strategies will be adopted by players and, therefore, the result of the game. The most commonly used solution concepts are equilibrium concepts, most famously Nash equilibrium.
An important notion in combinatorial game theory is that of the solved game. For example, tic-tac-toe is considered a solved game, as it can be proven that any game will result in a draw if both players play optimally. Deriving similar results for games with rich combinatorial structures is difficult.
A solved game is a game whose outcome (win, lose or draw) can be correctly predicted from any position, assuming that both players play perfectly.This concept is usually applied to abstract strategy games, and especially to games with full information and no element of chance; solving such a game may use combinatorial game theory or computer assistance.
In game theory, fictitious play is a learning rule first introduced by George W. Brown. In it, each player presumes that the opponents are playing stationary (possibly mixed) strategies. In it, each player presumes that the opponents are playing stationary (possibly mixed) strategies.
In game theory, the homicidal chauffeur problem is a mathematical pursuit problem which pits a hypothetical runner, who can only move slowly, but is highly maneuverable, against the driver of a motor vehicle, which is much faster but far less maneuverable, who is attempting to run him down. Both runner and driver are assumed to never tire.