This work studies the application of genetic algorithms to the domain of game playing, emphasising on learning a static evaluation function. Learning involves experience generation, hypothesis generation and hypothesis evaluation. Most learning systems use preclassified examples to guide the search in the hypothesis space and to evaluate current hypotheses. In game learning, it is very difficult to get classified examples. Genetic Algorithms provide an alternative approach. Competing hypotheses are evaluated by tournaments. New hypotheses are generated by genetic operators. We introduce a new framework for applying genetic algorithms to game evaluation-function learning. The evaluation function is learned by its derivatives rather than learning the function itself. We introduce a new genetic operator, called derivative crossover, that accelerates the search for static evaluation function. The operator performs cross-over on the derivatives of the chromosomes. We have demonstrated experimentally the advantage of the derivative crossover for learning an evaluation function.