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Abstract

Dominion is a deck-building card game that simulates competing lords growing their kingdoms. Here we wish to optimize a strategy called Big Money by modeling the game as a Markov chain and utilizing the associated transition matrices to simulate the game. We provide additional analysis of a variation on this strategy known as Big Money Terminal Draw. Our results show that player's should prioritize buying provinces over improving their deck. Furthermore, we derive heuristics to guide a player's decision making for a Big Money Terminal Draw Deck. In particular, we show that buying a second Smithy is always more optimal than a Silver after turn six, and a gold after turn eight.

Author Bio

Nikolas Koutroulakis is a rising senior from Georgia Southern University. His initial interest in mathematics was peaked upon taking an introduction to predicate calculus in a natural deductive system.

Initially he explored topics related to mathematical logic, including completeness theorems, peano systems, higher order logics, and modal logics. As he progressed through his major, his interest widened to include many topics in algebra, including module and representation theory, tensor algebras, and vector space theory.

Nikolas looks forward to getting his PhD in a branch of theoretical mathematics. He is currently looking at PhD programs that include topics in model theory, mathematical logic, and abstract algebra.

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