3 ms·

I'm a mathematician, but I've always wondered when this silver bullet is suggested: am I the only person for whom this exaggerated strategy offers no additiona

by JadeNB 7y ago

I'm a mathematician, but I've always wondered when this silver bullet is suggested: am I the only person for whom this exaggerated strategy offers no additional explanatory value? I know, and can prove mathematically, the right answer, but it's no more intuitive to me with 1000000 doors than with 3.

_asummers 7y ago
The missing part of the explanation (imo), at least the part that helps me explain it in my own brain, is said but not explicit. Imagine the actual mechanics of Monty opening the doors, one by one, and when he gets to that 223,205 door as stated, he skips it, and keeps skipping it. Why _that_ door? What makes it special? I don't think expanding the number of doors without that bit of intuition gives you much.
svara 7y ago
That's interesting - for me it was the first time seeing it explained that way, and it immediately made perfect sense. I think the intuition behind is that, when you initially choose one door out of 1000000, you are almost sure not to have picked the right one, so you ignore the fact that you even chose one. Then, the host opens 999998 doors, but leaves one closed. That door is now really special! Or a different way to look at it: The host gives you partial information about what's between the 999999 doors you didn't choose. Doesn't it seem really unlikely that your intial choice matters given that there are so many doors?
crummy 7y ago
I feel the same way. My gut says, now there are only two closed doors - it's still a 50/50 chance! This explanation offered above makes sense to my "gut" however: https://news.ycombinator.com/item?id=21349295 https://news.ycombinator.com/item?id=21349295
- JadeNB 7y ago
  Yeah, I agree—that was my first time seeing that explanation, and it really helped me to feel the intuition.
mikorym 7y ago
Also a mathematician; also think this is not a real silver bullet. However, I think for those who don't prove the result, the visual intuition of opening 999 998 doors is sensible. The problem to me is more that when you go back down from 1M to 3 doors one can just as well say again "but now we only have three doors". Meaning that a proof of the original problem is the only satisfactory answer; the 1M comparison is maybe for people that don't like proofs and want "evidence".

by JadeNB 7y ago

_asummers 7y ago

The missing part of the explanation (imo), at least the part that helps me explain it in my own brain, is said but not explicit. Imagine the actual mechanics of Monty opening the doors, one by one, and when he gets to that 223,205 door as stated, he skips it, and keeps skipping it. Why _that_ door? What makes it special? I don't think expanding the number of doors without that bit of intuition gives you much.

svara 7y ago

That's interesting - for me it was the first time seeing it explained that way, and it immediately made perfect sense. I think the intuition behind is that, when you initially choose one door out of 1000000, you are almost sure not to have picked the right one, so you ignore the fact that you even chose one. Then, the host opens 999998 doors, but leaves one closed. That door is now really special! Or a different way to look at it: The host gives you partial information about what's between the 999999 doors you didn't choose. Doesn't it seem really unlikely that your intial choice matters given that there are so many doors?

crummy 7y ago

I feel the same way. My gut says, now there are only two closed doors - it's still a 50/50 chance! This explanation offered above makes sense to my "gut" however: https://news.ycombinator.com/item?id=21349295 https://news.ycombinator.com/item?id=21349295

JadeNB 7y ago
Yeah, I agree—that was my first time seeing that explanation, and it really helped me to feel the intuition.

mikorym 7y ago

Also a mathematician; also think this is not a real silver bullet. However, I think for those who don't prove the result, the visual intuition of opening 999 998 doors is sensible. The problem to me is more that when you go back down from 1M to 3 doors one can just as well say again "but now we only have three doors". Meaning that a proof of the original problem is the only satisfactory answer; the 1M comparison is maybe for people that don't like proofs and want "evidence".