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dc.contributor.advisorKrislock, Nathanen_US
dc.contributor.advisorGarivaltis, Alexanderen_US
dc.contributor.authorEsche, Alexanderen_US
dc.date.accessioned2018-10-10T15:21:46Z
dc.date.available2018-10-10T15:21:46Z
dc.date.issued2018
dc.identifier.urihttps://commons.lib.niu.edu/handle/10843/19194
dc.description.abstractIn this paper mathematical programming techniques were used to determine the optimal strategy for playing Magic: The Gathering®. Games with the cards Lightning Bolt, Mountain, and Vexing Devil were evaluated using the minimax algorithm to determine the winner when all information about the cards is assumed known to both players. Computation time was shortened through the use of an evaluation function, a random forest algorithm that had been trained on 1000 completed games. A winning percentage was established for each pair of decks where the number of creatures was less than eight. Using linear programming, the optimal mixed strategy was then calculated. By repeating the simulations, a standard deviation for the winning percentages was estimated. Techniques from robust optimization were then used to determine the optimal strategy under different possible variations. Last, an imperfect information player was constructed that made choices based on guessing the order of the cards in its deck and the composition of the opponent's deck, playing through the perfect information games of these guesses, and making the choice that won in most of these simulations. With decks of eight or fewer creatures, this imperfect information player played below or near a player who used an aggressive heuristic. When the number of possible creatures was increased to 16, the imperfect information player's performance was better than the aggressive heuristic.en_US
dc.format.extent51 pagesen_US
dc.language.isoengen_US
dc.publisherNorthern Illinois Universityen_US
dc.rightsNIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.en_US
dc.subject.lcshGame theoryen_US
dc.subject.lcshProgramming (Mathematics)en_US
dc.subject.lcshRobust optimizationen_US
dc.titleMathematical programming and Magic: The Gathering®en_US
dc.type.genreDissertation/Thesisen_US
dc.typeTexten_US
dc.contributor.departmentDepartment of Mathematical Sciencesen_US
dc.description.degreeM.S. (Master of Science)en_US


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