Meanwhile : Intuition and probability

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Meanwhile : Intuition and probability

Published: 14 Apr. 2026, 00:05

Audio report: written by reporters, read by AI

Lee Woo Young

The author is an emeritus professor of mathematical sciences at Seoul National University.

Consider a person who, at every step, randomly chooses one of four directions — north, south, east or west — and moves one step accordingly. Will this person eventually return to their starting point? This question, known as the “drunkard’s walk,” is a classic problem in probability theory. Given four possible directions at each step, intuition suggests that the person is more likely to wander away indefinitely than to return, but this judgment turns out to be incorrect.

Anonymous portrait of a French mathematician, physicist, inventor, philosopher and Catholic writer Blaise Pascal (1623-1662) [WIKIPEDIA]

The human brain did not evolve to handle probabilistic thinking with precision. As a result, probability theory contains many problems that seem to counter everyday intuition. One of the most widely known is the “Monty Hall problem,” named after the host of a U.S. television game show. In this scenario, a contestant is presented with three doors. Behind one is a car, while the other two conceal goats. After the contestant selects a door, the host — who knows what lies behind each door — opens one of the remaining doors to reveal a goat and then offers the contestant a chance to change their choice.

At this point, many people assume the odds are now evenly split. Intuition suggests there is no advantage in switching. However, this reasoning is flawed. If the contestant switches, the probability of winning the car is two-thirds. If the contestant stays, it remains one-third. From a probabilistic perspective, switching is clearly the better option.

This does not mean intuition is always unreliable. Many significant discoveries have begun with intuitive insights. However, intuition is especially vulnerable in situations involving randomness. In the case of the drunkard’s walk, the individual will, in fact, eventually return to the starting point. The intuitive mistake lies in equating increasing distance with the impossibility of return. Probability clarifies that even as the path grows longer, the chance of returning persists.

In this way, probability serves as a corrective tool, helping to reduce errors in human intuition and enabling more accurate judgment under uncertainty.

“Man is a thinking reed,” wrote Blaise Pascal (1623-1662) in his posthumous work “Pensées” (1670). The phrase captures the fragile yet reasoning nature of human beings living in uncertainty. It is notable that Pascal, who reflected deeply on the limits of human reason, was also one of the founders of probability theory.

This article was originally written in Korean and translated by a bilingual reporter with the help of generative AI tools. It was then edited by a native English-speaking editor. All AI-assisted translations are reviewed and refined by our newsroom.