Cognitive Errors in Clinical Diagnosis:

Gambler’s Fallacy and Posterior Probability Error

Margaret A. Fitzgerald, DNP, FNP-BC, NP-C, FAANP, CSP, FAAN, DCC, FNAP

Biases in information processing can interfere with sound clinical reasoning and decision-making. A number of biases arise from cognitive shortcuts, or heuristics, which represent fast, intuitive thinking, as opposed to deliberative thinking, which is slower but less prone to bias and error. This article examines two related cognitive biases that result from rapid, intuitive judgments in the absence of deliberate analysis and can lead to diagnostic error: gambler’s fallacy and posterior probability error.

Clinical Vignette

A 67-year-old man presents to the clinic with chest pain, which he reports began earlier that day after he woke up. The clinician recalls that over the past 3 days, she has seen seven patients with chest pain in the clinic, and each has been diagnosed with acute coronary syndrome (ACS). Each of those patients had a similar risk profile as the present patient, including a body mass index that meets the criteria for obesity, a 20+ pack year history of smoking, and hypertension. As the clinician begins to evaluate the patient and formulate a list of possible causes, she considers, given the number of ACS diagnoses she has made in consecutive patients with chest pain, what is the probability that this patient’s pain is a sign of ACS?


In this scenario, the clinician is displaying irrational thinking by considering whether the streak of ACS diagnoses will continue, even though the events in the series of diagnoses are independent and not causally related. This cognitive bias, known as gambler’s fallacy, arises when a person assumes that a deviation from what occurs on average or in the long term will be corrected in the short term.1,2 Such thinking stems from people’s tendency to assume that if a random event has occurred many times in the past, that it will occur less often in the future.3 A common example of gambler’s fallacy is guessing “heads” on a coin toss after “tails” has been tossed 10 times in a row. However, the odds of heads or tails coming up is 50/50 for each coin toss, and previous tosses and results have no bearing on the chance of either outcome. Similarly, there is no causal connection between the previous seven patients who presented with chest pain and the eighth patient who presents in this scenario, since these presentations are all independent, random events.

A related cognitive bias is the posterior probability error, which is the opposite of gambler’s fallacy, in that the person assumes the repeating pattern will continue. For example, a patient who is correctly diagnosed with reflux as the cause of chest pain four times is likely to be diagnosed with reflux when presenting with chest pain a fifth time as the clinician assumes or “bets” that the pattern will continue.4

Thus, these fallacies reflect the beliefs that a random event has a higher probability of occurring because it has not happened for a period of time, and alternatively, that a random event has a lower probability of occurring because it recently happened.5 Behavioral researchers believe there are several reasons why people are prone to the gambler’s fallacy: (1) a dislike of randomness, which triggers a search for patterns in random events; (2) a propensity to make inferences from small samples of information, assuming the sample represents the larger population from which it is are drawn; and (3) a sense that chance is a “self-correcting process” whereby outcomes even out over time.3

Gambler’s fallacy generally occurs when a person makes a snap judgment, relying on fast, automatic intuition rather than measured thinking.1 In the scenario presented here, we do not know whether the clinician’s intuition about the consecutive chest pain/ACS diagnoses was just a passing observation, or whether it led them down a path toward a skewed pre-test probability of ACS. However, clinicians can overcome intuitive thinking, and avoid errors in decision-making, by employing deliberate reasoning when acquiring and processing information. Strategies to overcome the gambler’s fallacy include recognizing the causal independence of random events and that past random events do not influence future events.3

1. Xue G, He Q, Lei X, et al. The gambler’s fallacy is associated with weak affective decision making but strong cognitive ability. PLoS One. 2012;7(10):e47019. doi:10.1371/journal.pone.0047019
2. Msaouel P, Kappos T, Tasoulis A, et al. Assessment of cognitive biases and biostatistics knowledge of medical residents: a multicenter, cross-sectional questionnaire study. Med Educ Online. 2014;19:23646. doi:10.3402/meo.v19.23646
3. The Decision Lab. Why do we think a random event is more or less likely to occur if it happened several times in the past? Accessed July 22, 2022.
4. Croskerry P. 50 cognitive and affective biases in medicine. May 2013. Accessed August 1, 2022.
5. Lyons J, Weeks DJ, Elliott D. The gambler’s fallacy: a basic inhibitory process? Front Psychol. 2013;4:72. doi:10.3389/fpsyg.2013.00072