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I share your confusion about how ideology clouds judgement but I have a little anecdote. I sometimes give people the Monty Hall problem. When they get it wrong

• orwin 9mo ago
  The N=100 is a 'lazy' (or abstract if you prefer) way to look at it, it doesn't really explain anything. It's hard to show how to explain the problem just writing about it, but by making them choose one of 3, and then making assumptions about which door will reveal the car, and if it is better to switch. You can easily demonstrate that in two out of three situations it is actually better to switch.
  • abetusk 9mo ago
    For the 3 case, since 2/3 is relatively close to 1/2, it's hard to build intuition from just a few examples. The N=100 build intuition very quickly. I disagree that it doesn't explain anything. After playing, people quickly understand that the likelihood that they chose the correct door initially is very small and when all 98 other doors are revealed, the remaining door provides a red flag that their intuition is off. Note that often I would explain the logic behind switching and still have them not believe me. Their intuition wouldn't be shaken by arguments or even small demonstration. Only when actually playing an the N=100 case would they start to understand.
  • 2muchcoffeeman 9mo ago
    Why doesn’t it explain anything when it clearly demonstrates the point?
    • orwin 9mo ago
      Because that's just repeating a point without explaining why the underlying maths works.
• selcuka 9mo ago
  We used to ask job candidates a variation of the door in an infinite wall question [1]. The initial answer of many interviewees is to choose a direction and walk in that way forever, which is understandable, as infinity makes the question weird. What is more interesting is, even after I pointed out that this answer has a 50% chance of finding the door and I'm looking for a 100% solution, some candidates refused to give it a second thought, didn't change their answer, and insisted that this is the best course of action. [1] https://math.stackexchange.com/questions/3915578/door-in-an-infinite-wall-problem https://math.stackexchange.com/questions/3915578/door-in-an-...
• bayarearefugee 9mo ago
  Leave it to people in the tech industry to ask interview questions that confused Paul Erdös for days and expect their interviewees to reason through things during an interview. https://web.archive.org/web/20140413131827/http://www.decisionsciences.org/DecisionLine/Vol30/30_1/vazs30_1.pdf https://web.archive.org/web/20140413131827/http://www.decisi... I'd get the Monty Hall problem question right off the bat, but only because I've encountered it before, not because I can naturally reason through it better than Erdös.
  • deleted 9mo ago
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• billforsternz 9mo ago
  The only reason people get confused about the Monty Hall problem is that the problem description rarely if ever makes it clear that the host knows where the car is and deliberately chooses a different door. It's inconceivable (for example) that Paul Erdos, a world class mathematician, would fail to solve this problem if it were actually communicated clearly.
  • yen223 9mo ago
    It is incredibly annoying that in the case where the host doesn't know where the car is but opens a goat door anyway, the probability goes back to 50-50
    • zephyrfalcon 9mo ago
      But if he doesn't know where the car is, how can he be sure that the door he opens is going to have a goat?
      • yen223 9mo ago
        The scenario is the host doesn't know which door has the car, opens some random door, and that door happens to have a goat behind it. If you were in this scenario, your odds of getting the car doesn't change whether you switch or not
        • auggierose 9mo ago
          That would indeed be annoying, but I doubt it is the case. If you only consider this scenario, it cannot be distinguished by conditional probability from the case that the host knows, and so the math should stay the same. As usual, the problem is not an incredibly difficult problem, but just a failure to state the problem clearly and correctly. Try to write a computer program that approximates the probability, and you'll see what I mean.
          • yen223 9mo ago
• raverbashing 9mo ago
  > I then proceed to give them the example of N=100 doors, opening 98 others, leaving their pick and another closed and then asking them whether that makes a difference. Yeah this is the way I found it the easier to understand intuitively
• tommica 9mo ago
  > They don't trust me or the logic and so dismiss it. This is me, the logic of Monty Hall Doors does not make sense to me, so luckily I found this one: https://www.rossmanchance.com/applets/2021/montyhall/Monty.html https://www.rossmanchance.com/applets/2021/montyhall/Monty.h... After running the process 500 times, the ratio seems insane (using the stay tactic, 67% loss & 33% wins) - it makes me able to accept "that is just how it is then", but absolutely does not explain WHY, because in my mind, once you open the door, the situation resets to 50/50 - so there should be no difference if I stay or switch. The fundamental misunderstanding of statistics is probably what is the problem. It's funny to observe own mind in this process, and how much of a "struggle" there is to convince one-self that what seems logical and sensible is in-fact a wrong interpretation and can only exists due to lack of understanding. > My interpretation is that, before playing the actual game, they refuse to believe me. They don't trust me or the logic and so dismiss it. Once actual stakes are involved, even if it's their pride, only then do they start to be open to arguments as to why their intuition was wrong. That is so true - before the own idea/concept gets put to test, it's easy to be delusional about how correct your own "idea" is. As long as it is in the vacuum of your own brain, you can keep it protected and shielded from all that nasty truth that tries to bully and beat it. There is a reason why a lot of coders do not want others to see their code and do a code review on it...
  • adornKey 9mo ago
    I think in your mind you associate "unknown" strongly with "random" and even "random with equal chances". Just because something is unknown doesn't mean it is random. And if it is random it doesn't mean it is 50/50.
  • dghf 9mo ago
    > the logic of Monty Hall Doors does not make sense to me For me, the core is that you have a 1 in 3 chance of getting it right on your first guess, and nothing can change that. So if you always stick with your original guess, you will win one third of the time.
    • Applejinx 9mo ago
      No no. The thing is, the Monty Hall guy is responding to YOUR choice. So if he has to open a door where you fail, it's a response to what he knows of your choice, so HE knows what YOU chose and is not only revealing the remaining losing choice but also the winning choice. Call it a coin flip except for he always has to call tails. Therefore your choice can either be cadillac or goat, he cannot choose cadillac and has to show a goat, so the remaining option you DIDN'T highlight is that much more likely to be cadillac because it could've been either, but he doesn't get to pick randomly, he had to show which one was NOT the winning one. Hence the result. And since it started out as one pick of three, he responds to you and then you respond to the added information by switching and that's where the 66% odds come from: two moves each responding to each other.
• Angostura 9mo ago
  I remember when I first came across it (someone mentioned it on a business trip) leaving dinner to nip up and write a little random number simulator in Basic on the Z88 that I used for taking notes. Then coming down 15 minutes later" "OMG, you're right"
• bregma 9mo ago
  But what if the car was placed behind one of the doors by aliens? This would be proof that aliens had been visiting and maybe even influencing the production offices of daytime game shows, and possibly even those in prime time. The aliens would have been treated as gods by the producers, forcing them to give away valuable prizes to the contestants to prove their loyalty and worthiness. Consider the possibilities. Of course, there may be other explanations.
• lelanthran 9mo ago
  > I sometimes give people the Monty Hall problem. When they get it wrong, it often falls into the category of staying with the initial pick increases chances or switching has equal odds. I then proceed to give them the example of N=100 doors, opening 98 others, leaving their pick and another closed and then asking them whether that makes a difference. > If they insist that it makes no difference, I then start to play the actual game with them, writing down the prize door before the game starts and then proceeding with the game as normal. Only after a few rounds of them losing do they accept the proofs of what the optimal strategy is. That is all way too much work. I draw a decision tree and let them fill in the fractions for each edge leaving a node (2/3 edges result in this outcome 3 nodes later while 1/3 edges result in that outcome 2 nodes later). If that doesn't work, I'll just give up.
• mda 9mo ago
  Yeah, but Monty Hall problem is so unintuitive even very smart and logical people has hard time accepting it. Even changing it to thousand doors variant doesn't help.
• bazoom42 9mo ago
  The monty hall problem is often stated in such a way multiple interpretations are possible. I don’t know how exactly you state the problem, but have you considered you might have stated it wrongly or ambiguously?
  • abetusk 9mo ago
    Yes. I have stated, explicitly, at the beginning, that the person opening the doors knows where the prize is, will only open doors without a prize and that the prize doesn't change positions. This is demonstrated by the fact that when we actually play the game, I write the door number down on a piece of paper before the game starts. This supposed ambiguity is touted as the key to why the puzzle is so difficult but, in my experience, it makes absolutely no difference.