I write programs to play board game variants sometimes. The basic strategy is standard alpha-beta pruning or similar searches, sometimes augmented by the usual approaches to
I would look at a supervised machine learning algorithm such as reinforcement learning. Check out Reinforcement learning in board games. I think that will give you some good directions to look into.
Also, check out Strategy Acquisition for the Game Othello Based on Reinforcement Learning (PDF link) where given the rules of the game, a good "payoff function" can be learned. This is closely related to TD-Gammon ...
During training, the neural network itself is used to select moves for both sides ... The rather surprising finding was that a substantial amount of learning actually took place, even in the zero initial knowledge experiments utilizing a raw board encoding.