Unlike traditional game playing, General Game Playing is concerned with agents capable of playing classes of games. Given the rules of an unknown game, the agent is supposed to play well without human intervention. For this purpose, agent systems that use deterministic game tree search need to automatically construct a state value function to guide search. Successful systems of this type use evaluation functions derived solely from the game rules, thus neglecting further improvements by experience. In addition, these functions are fixed in their form and do not necessarily capture the game’s real state value function. In this work we present an approach for obtaining evaluation functions on the basis of neural networks that overcomes the aforementioned problems. A network initialization extracted from the game rules ensures reasonable behavior without the need for prior training. Later training, however, can lead to significant improvements in evaluation quality, as our results indicate.