Abstract: Stochastic model checking is a recent extension and generalization of the classical model checking, which focuses on quantitatively checking the temporal property of a system model. PCTL^* is one of the important quantitative property specification languages, which is strictly more expressive than either PCTL (probabilistic computation tree logic) or LTL (linear temporal logic) with probability bounds. At present, PCTL^* stochastic model checking algorithm is very complicated, and cannot provide any relevant explanation of why a formula does or does not hold in a given model. For dealing with this problem, an intuitive and succinct approach for PCTL^* stochastic model checking with evidence is put forward in this paper, which includes:presenting the game semantics for PCTL^* in release-PNF (release-positive normal form), defining the PCTL^* stochastic model checking game, using strategy solving in game to achieve the PCTL^* stochastic model checking, and refining winning strategy as the evidence to certify stochastic model checking result. The soundness and the completeness of game-based PCTL^* stochastic model checking are proved, and its complexity matches the known lower and upper bounds. The game-based PCTL^* stochastic model checking algorithm is implemented in a visual prototype tool, and its feasibility is demonstrated by an illustrative example.