Abstract strategy games present a deterministic perfect information environment with which to test the strategic capabilities of artificial intelligence systems. With no unknowns or random elements,only the competitors' performances impact the results. This thesis takes one such game,Lines of Action, and attempts to develop a competitive heuristic. Due to the complexity of Lines of Action, artificial neural networks are utilized to model the relative values of board states. An application, pLoGANN (Parallel Lines of Action with Genetic Algorithm and Neural Networks),is developed to train the weights of this neural network by implementing a genetic algorithm over a distributed environment. While pLoGANN proved to be designed efficiently, it failed to produce a competitive Lines of Action player, shedding light on the difficulty of developing a neural network to model such a large and complex solution space.