We consider the dynamic casino gambling model initially proposed by Barberis (2012) and study the optimal stopping strategy of a precommitting gambler with cumulative prospect theory (CPT) preferences. We illustrate how the strategies computed in Barberis (2012) [Barberis N (2012) A model of casino gambling. Management Sci. 58(1): 35–51.] can be strictly improved by reviewing the betting history or by tossing an independent coin, and we explain that the improvement generated by using randomized strategies results from the lack of quasi-convexity of CPT preferences. Moreover, we show that any path-dependent strategy is equivalent to a randomization of path-independent strategies.