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In game theory, Zermelo's theorem is a theorem about finite two-person games of perfect information in which the players move alternately and in which chance does not affect the decision making process. It says that if the game cannot end in a draw, then one of the two players must have a winning strategy (i.e. can force a win).
Algorithmic game theory (AGT) is an area in the intersection of game theory and computer science, with the objective of understanding and design of algorithms in strategic environments. Typically, in Algorithmic Game Theory problems, the input to a given algorithm is distributed among many players who have a personal interest in the output.
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.
Negamax can be implemented without the color parameter. In this case, the heuristic evaluation function must return values from the point of view of the node's current player (Ex: In a chess game, if it is white's turn and white is winning, it should return a positive value. However if it is black's turn, it should return a negative value).
The rating of best Go-playing programs on the KGS server since 2007. Since 2006, all the best programs use Monte Carlo tree search. [14]In 2006, inspired by its predecessors, [15] Rémi Coulom described the application of the Monte Carlo method to game-tree search and coined the name Monte Carlo tree search, [16] L. Kocsis and Cs.
A similar game with larger numbers of cops can be used to define the cop number of a graph, the smallest number of cops needed to win the game. The cop-win graphs are exactly the graphs of cop number equal to one. [22] Bonato and Nowakowski describe this game intuitively as the number of ghosts that would be needed to force a Pac-Man player to ...
It reinforced winning strategies by making the moves more likely, by supplying extra beads. [8] This was one of the earliest versions of the Reinforcement Loop, the schematic algorithm of looping the algorithm, dropping unsuccessful strategies until only the winning ones remain. [4] This model starts as completely random, and gradually learns. [9]
In the game of Chomp strategy stealing shows that the first player has a winning strategy in any rectangular board (other than 1x1). In the game of Sylver coinage, strategy stealing has been used to show that the first player can win in certain positions called "enders". [4] In all of these examples the proof reveals nothing about the actual ...