In this paper we present our approach of improving the traditional alpha-beta search process for strategic board games by modifying the method in two ways: 1) forgoing the evaluation of leaf nodes that are not terminal states and 2) employing a utility table that stores the utility for subsets of board configurations. In this paper we concentrate our efforts on the game of Connect Four. Our results have shown significant speed-up, as well as a framework that relaxes common agent assumptions in game search. In addition, it allows game designers to easily modify the agent's strategy by changing the goal from dominance to interaction.