Whenever I see the three doors in a row on W.M.

Whenever I see the three doors in a row on W.M. Whyte's 1885 tenements on Queen's Drive in Glasgow, I'm always reminded of the Monty Hall Problem. Based on the US game show Let's Make a Deal, this problem shows how poor the intuitive human understanding of probabilities actually is.

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The problem goes something like this: A gameshow host presents a contestant with three doors. Behind one door is a car, behind the other two are goats. If the contestant can pick the door with the car behind it, they win the car. After the contestant picks a door, the gameshow host opens one of the other doors to reveal a goat behind it, and then offers the contestant the chance to swap their chosen door for the other unopened one.

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What should the contestant do to maximise their chance of winning the car?

Intuituvely most people will say stick with the door they originally chose, but probability tells us that the best option is always to swap. This because there's a 66.6% chace the car is behind the other unopened door (and not the 50%, or 33.3% most people intuitively assume it is).

Happy Friday!

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