Mahjong is a four-player, stochastic, imperfect information game. This paper focuses on the Taiwanese variant of Mahjong, whose complexity is higher than that of Go. We design a strong anytime Monte-Carlo-based Taiwanese Mahjong program. First, we adopt the flat Monte Carlo to calculate the win rates of all afterstates/actions such as discarding each tile. Then, we propose a heuristic method, which we incorporate into flat Monte Carlo to obtain the accurate tile to be discarded. As an anytime algorithm, we can stop simulations and return the current best move at any time. In addition, we prune bad actions to increase accuracy and efficiency. Our program, SIMCAT, won the championship in the Mahjong tournaments in Computer Olympiad 2020 and TAAI 2019/2020.