When prospect theory (PT) is applied in a dynamic context, the probability weighting component brings new challenges. We study PT agents facing optimal timing decisions and consider the impact of allowing them to follow randomized strategies. In a continuous-time model of gambling and optimal stopping, Ebert and Strack (2015) show that a naive PT investor with access only to pure strategies $never$ stops. We show that allowing randomization can significantly alter the predictions of their model, and can result in voluntary cessation of gambling.