In this paper, we explain why Go is hard to be programmed. Since the strategy of the game is closely related to the concept of alive-dead group, it is plainly necessary to analyze this concept. For this a mathematical model is proposed. Then we turn our research to Tsume-Go problems in which one of the players has always a unique good move and the other has always only two good moves available to choose from. We show that this kind of problems are NP-complete.