The task of keyhole (unobtrusive) plan recognition is central to adaptive game AI. "Tech trees" or "build trees" are the core of real-time strategy (RTS) game strategic (long term) planning. This paper presents a generic and simple Bayesian model for RTS build tree prediction from noisy observations, which parameters are learned from replays (game logs). This unsupervised machine learning approach involves minimal work for the game developers as it leverage players' data (com- mon in RTS). We applied it to StarCraft1 and showed that it yields high quality and robust predictions, that can feed an adaptive AI.