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The game-show version of the Monty Hall problem isn't ambiguous... people even had the chance to see the show before knowing the mathematical problem. I agree there are different ways to state the problem, but the wording doesn't explain why it confuses people.

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Actually, the strongest criticism that I've heard about the Monty Hall problem is that the game show didn't actually work like that.

I've tried explaining the problem to both people who've seen the show and those who haven't. My experience is that if you've seen the show you'll never accept the question, let alone the answer. Meanwhile, those who never watched the show can be convinced.

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