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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.
In computer chess, the output of an evaluation function is typically an integer, and the units of the evaluation function are typically referred to as pawns.The term 'pawn' refers to the value when the player has one more pawn than the opponent in a position, as explained in Chess piece relative value.
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.
Depth to mate (DTM) – The game can only be won by checkmate. Depth to conversion (DTC) – The game can be won by checkmate, capturing material or promoting a pawn. For example, in KQKR, conversion occurs when White captures the Black rook. Depth to zeroing (DTZ) – The game can be won by checkmate, capturing material or moving a pawn. For ...
An animated pedagogical example showing the plain negamax algorithm (that is, without alpha–beta pruning). The person performing the game tree search is considered to be the one that has to move first from the current state of the game (player in this case) NegaMax operates on the same game trees as those used with the minimax search ...
In game theory terms, an expectiminimax tree is the game tree of an extensive-form game of perfect, but incomplete information. In the traditional minimax method, the levels of the tree alternate from max to min until the depth limit of the tree has been reached. In an expectiminimax tree, the "chance" nodes are interleaved with the max and min ...
Moreover, it is practical because randomized algorithms are capable of "foiling an enemy", meaning an opponent cannot beat the system of game trees by knowing the algorithm used to solve the game tree because the order of solving is random. The following is an implementation of randomized game tree solution algorithm: [5]