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.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.

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-...

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.

> 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.

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"

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.

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.

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?

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.

> 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.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...

> 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