This study proposes a new mathematical game called Polyomination which involves the competitive placement of polyominoes to capture area. The game playing agents used are able to encode both their strategy and the game pieces they will play with. Strategy is encoded in a finite state representation called a binary decision automata which has access to a variety of pieces of information abstracted from the game state. Playing pieces are encoded by a developmental representation. An extensive parameter study is performed. The elite-fraction used by the evolutionary algorithm that trains the agents is found to be relatively unimportant. The number of states in the automata and the maximum number of squares used to build polyominoes are found to have a significant impact on competitive ability. The polyomino playing pieces are found to evolve in a strategic manner with playing pieces specializing for area-occupation, area-denial, and cleanup in which small pieces can fill in small remaining areas. This study serves as an initial study of Polyomination, intended to serve as a springboard for the design of simpler, related games.
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