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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).
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.
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.
For example, one has to buy 13,983,816 different tickets to ensure to win the jackpot in a 6/49 game. Lottery organizations have laws, rules and safeguards in place to prevent gamblers from executing such an operation. Further, just winning the jackpot by buying every possible combination does not guarantee that one will break even or make a ...
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]
Bowditch considers a variant (game 1) of the game with the changes 2 and 3 with a 5-devil. He then shows that a winning strategy in this game will yield a winning strategy in our original game for a 4-angel. He then goes on to show that an angel playing a 5-devil (game 2) can achieve a win using a fairly simple algorithm.
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 ...