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A medical example is described by Axelsson. Say a doctor performs a test that is 99% accurate, and the patient tests positive for the disease. However, the incidence of the disease is 1/10,000. The patient's actual risk of having the disease is 1%, because the population of healthy people is so much larger than the disease.
For ordinary chess players, prone to inaccuracies and blunders, defeating engine assisted play is only possible if and when cheaters make mistakes, if and when they decide not to use engine assistance. Roughly 0.6% of Chess.com accounts have been closed for cheating.
The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the belief that, if an event (whose occurrences are independent and identically distributed) has occurred less frequently than expected, it is more likely to happen again in the future (or vice versa).