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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.
A third example of Parrondo's paradox is drawn from the field of gambling. Consider playing two games, Game A and Game B with the following rules. For convenience, define to be our capital at time t, immediately before we play a game. Winning a game earns us $1 and losing requires us to surrender $1.
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In this example game, both players know the payoff matrix and attempt to maximize the number of their points. Red could reason as follows: "With action 2, I could lose up to 20 points and can win only 20, and with action 1 I can lose only 10 but can win up to 30, so action 1 looks a lot better." With similar reasoning, Blue would choose action C.
Although the term is used less precisely in games such as chess, it is used specifically in combinatorial game theory to denote a move that directly changes the outcome of the game from a win to a loss. [2] [3] Putting the opponent in zugzwang is a common way to help the superior side win a game, and in some cases it is necessary in order to ...
[1] [2] The objective of each player is to lose all of their pieces or be stalemated, that is, a misère version. In some variations, a player may also win by checkmating or by being checkmated. Losing chess was weakly solved in 2016 by Mark Watkins as a win for White, beginning with 1.e3.
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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. [125] Yao's principle is a game-theoretic technique for proving lower bounds on the computational complexity of randomized algorithms , especially online ...