Change or not change?
This isn’t a logic puzzle in the strict sense, but it is still a very interesting strategy problem. It suddenly occurred to me:
It goes something like this: you are taking part in a game show such as “Lucky 53,” and, fortunately, you win a prize. The host takes you to three boxes and tells you that one of them contains the grand prize—say, a luxury villa—while the other two contain only consolation prizes—say, a jar of doubanjiang. You may choose any one box at will.
You choose a box, say Box No. 1. At this point the host opens, say, Box No. 3, and lets you and the audience see that it contains a consolation prize. Then the host asks you: do you still stubbornly choose Box No. 1? Or do you switch to Box No. 2?
The question is: what is the best strategy? A. stick with your choice; B. switch; C. it doesn’t matter.
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Hint:
Don’t think too much at first—intuitively, which one would you choose? Then think carefully: what, exactly, should you choose?
Many people, reportedly including quite a few great mathematicians, have fallen flat on their faces on this question!
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Translated from the Chinese original with AI assistance. The original text is authoritative.