We examine a logical decision problem, the "Monty Hall Dilemma," in which a large portion of sophisticated subjects insist on an apparently wrong solution. Although a substantial literature examines the structure of this problem, we argue that the extant analyses have not recognized the constellation of cues that guide respondents' answers. We show that insight into subjects' decisions may be obtained by considering problems with similar surface structure to the Monty Hall Dilemma but which are common in environments that they routinely face. In particular, we consider the problem modeled as a game in which actors have possibly opposing interests, and as an environment with information provided by an objective source. We present experimental evidence showing that these comparisons help to explain subject responses.