A paradox—from para, "against," and doxa, "opinion"—is a statement that at first seems surprising, even shocking, because it runs counter to common sense. Studying paradoxes is as much a challenge as it is a diversion. Examining what "appears contradictory" is far from futile: it helps us empathize with those who do not necessarily think as we do, yet are just as reasonable. It gives us a better understanding not of errors in reasoning, but of the reasons behind disagreements. In the Monty Hall paradox, for example, why do so many sensible people insist that "whether you stay with your door or switch makes no difference"? Their reasons are sometimes subtle, and understanding them is part of a complete analysis of the paradox. But what exactly does this paradox say?
Monty Hall: a classic that sparks arguments
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You are standing before three closed doors. Behind one is a fabulous prize—a car, a castle, a lifetime subscription to Tangente…—while an unusual prize lies behind each of the other two. You must choose a door. The host, who knows which door is the "right" one, opens another door, revealing an unusual prize. You may then either open your door, confirming your original choice, or open the third door, changing your original choice. What should you do to maximize your chances of winning the fabulous prize?
Here are your options: stay with your choice because only two doors remain, so you are just as likely to win as you would be if you switched; switch because the third door gives you a better chance of winning; or toss a coin to decide. Think carefully and settle on an answer before reading on…
