When first presented with the Monty Hall problem, an overwhelming majority of people assume that each door has an equal probability and conclude that switching does not matter.[9] Out of 228 subjects in one study, only 13% chose to switch.[21] In his book The Power of Logical Thinking,[22] cognitive psychologist Massimo Piattelli Palmarini [it] writes: "No other statistical puzzle comes so close to fooling all the people all the time [and] even Nobel physicists systematically give the wrong answer, and that they insist on it, and they are ready to berate in print those who propose the right answer." Pigeons repeatedly exposed to the problem show that they rapidly learn to always switch, unlike humans.[23]

Most statements of the problem, notably the one in Parade, do not match the rules of the actual game show [10] and do not fully specify the host's behavior or that the car's location is randomly selected.[21][4][24] Krauss and Wang conjecture that people make the standard assumptions even if they are not explicitly stated.[25]

Although these issues are mathematically significant, even when controlling for these factors, nearly all people still think each of the two unopened doors has an equal probability and conclude that switching does not matter.[9] This "equal probability" assumption is a deeply rooted intuition.[26] People strongly tend to think probability is evenly distributed across as many unknowns as are present, whether it is or not.[27]

The problem continues to attract the attention of cognitive psychologists. The typical behavior of the majority, i.e., not switching, may be explained by phenomena known in the psychological literature as:

The endowment effect,[28] in which people tend to overvalue the winning probability of the already chosen – already "owned" – door.

The status quo bias,[29] in which people prefer to stick with the choice of door they have already made.

The errors of omission vs. errors of commission effect,[30] in which, all other things being equal, people prefer to make errors through inaction (Stay) as opposed to action (Switch).

Experimental evidence confirms that these are plausible explanations that do not depend on probability intuition.[31][32] Another possibility is that people's intuition simply does not deal with the textbook version of the problem, but with a real game show setting.[33] There, the possibility exists that the show master plays deceitfully by opening other doors only if a door with the car was initially chosen. A show master playing deceitfully half of the times modifies the winning chances in case one is offered to switch to "equal probability".