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Chess initial position. The game of chess is commonly divided into three phases: the opening, middlegame, and endgame. [1] There is a large body of theory regarding how the game should be played in each of these phases, especially the opening and endgame.
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.
Transpositions are common in chess – a given position can often be reached by different move orders – even move orders with more or fewer moves. The table may also provide percentage of games won by white for each variation, based on the results of the games considered in creating the table.
Separately, game theory has played a role in online algorithms; in particular, the k-server problem, which has in the past been referred to as games with moving costs and request-answer games. [123] Yao's principle is a game-theoretic technique for proving lower bounds on the computational complexity of randomized algorithms , especially online ...
Professional chess players spend years studying openings, and they continue doing so throughout their careers as opening theory continues to evolve. Players at the club level also study openings, but the importance of the opening phase is less there since games are rarely decided in the opening.
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).
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In applied game theory, the definition of the strategy sets is an important part of the art of making a game simultaneously solvable and meaningful. The game theorist can use knowledge of the overall problem, that is the friction between two or more players, to limit the strategy spaces, and ease the solution.