The much-investigated Monty Hall problem is often regarded as a testament to the woeful state of probabilistic thinking. But there is some evidence that individuals continue to refuse to switch doors with Monty (even in light of additional evidence indicating that their probability of winning has doubled) for reasons that are not related to probabilistic thinking at all. The steadfast refusal to switch can be described as a gut reaction rather than a rational reaction. Having the semblance of superstitions, intuitions involving sticking with your gut are common—refusing to change lanes from a frustratingly slow lane to another lane that is moving briskly (car lanes or grocery lines), refusing to deviate from your first answer choice in a multiple-choice test even upon thoughtful reconsideration, or refusing to exchange lottery tickets even when offered a reward to switch. This study examines the development of a heuristic or rule of thumb about (not) switching with regards to cognitive biases as put forward by decision theorists. These biases influence our thinking, cause us to make incorrect assumptions, and often result in our employing suboptimal strategies that may seem irrational. In this research, experimental treatments allow us to examine how individuals make simple probabilistic decisions when the element of sticking with your first choice is inserted or removed. Additionally, I attempt to examine whether individuals are of "two minds," whether some decisions are based on gut instinct and other decisions are based on rationality. In light of these findings, mathematics educators may be better prepared take cognitive biases into consideration when assessing their students' probabilistic thinking and decisions.