General Game Playing (GGP) contest provides a research framework suitable for developing and testing AGI approaches in game domain. In this paper, we propose a new modification of UCT gametree analysis algorithm working in cooperation with a knowledge-free method of building approximate evaluation functions for GGP games. The process of function development consists of two stages: generalization and specification. Both stages are performed autonomously by the system and do not require human intervention of any kind. Effectiveness of the proposed method is proved in three exemplar games selected from the GGP games repository.