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by javajosh
4133 days ago
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Glad it helped! Why it's counter-intuitive-ness is a really, really good question because like 99.9% of people I found this one hard to accept, too. All I can say is that it's an incredibly effective verbal/logical obfuscation that relies on synergistic choice of number of doors and the (in my view) totally bogus part about Monty opening one of the other doors. In fact, some people (in this very thread!) are still analyzing the problem as if the opened door represents new, 'very valuable' information! It is truly just slight of hand to make it seem like you're only picking one door when you are picking two doors. |
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In the "real world" problem there are additional variables to consider, such as whether or not the host would open a door containing a car, whether that would result in a win or a loss, whether the host would offer a switch in all cases, whether if so, there is any additional incentive for switching (which wouldn't adjust the probability of winning, so is a red herring, but "intuitively" it seems that if the host is trying to make you lose by trying to make you switch, probability should go down).
When you try to conflate the real world problem, which actually has multiple different probabilities depending on exact scenario, into an answer to what's generally accepted as the "Monty Hall Problem", some of this gets in the way.
In addition, there are two probabilities in the "Monty Hall Problem" - the first is whether your switch results in a win. The second is the probability that, if you switch, it was the correct choice.