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> 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:/

by 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.
  - dghf 9mo ago
    How does that contradict what I said? The way the game is set up, one of your choices -- stick or switch -- is guaranteed to win. Your original door will be correct 1/3 of the time and wrong 2/3 of the time. Therefore switching will be the winning move 2/3 of the time.
    - saghm 9mo ago
      Your explanation isn't wrong, but it's never quite resonated with me because it feels almost like a magic trick than something that follows intuition. Like seeing a magician perform a trick, it doesn't quite convey to me the "why" as much as the "what", and even though I know there's no actual magic, I still feel like I'm left having to figure out what happened on my own. The idea that finally made it click for me is that Monty has to choose one of the doors to open, and because he knows which door has which thing behind it, he'll never pick the door with the winning prize. That means the fact that he didn't pick the other door is potentially meaningful; unless I picked the right door on my first try, it's guaranteed to be the one he didn't open, because he never opens the right door on his own. His choice communicates meaningful information to me because it's not random, and that part while seemingly obvious gets left implicit in almost every attempt to explain this that I've seen. Another intuitive way to explain it would be to imagine that the step of opening one door is removed, and instead you're given the option of either sticking with your original door or swapping to all of the other doors and winning if it's any of them. It's much more obvious that it would be a better strategy to swap, and then if you add back the step where he happens to open all of the other doors that aren't what you picked or the right one, it shouldn't change the odds if you're picking all of the other doors. This clarifies why the 100 door case makes it an even better strategy to switch than the 3 door case; you're picking 99 doors and betting that it's behind one. The way people usually describe that formulation still often doesn't seem to explicitly talk about why the sleight of hand that opening 98 of the doors is a red herring though; people always seem to state it as if it's self-evident, and I feel like that misses the whole point of why this is unintuitive in the first place in favor of explaining in a way that clarifies little and only makes sense if you already understand in the first place.
atq2119 9mo ago
> once you open the door, the situation resets That's the root cause error of your thinking. The prizes aren't reshuffled and the host's choice of doors depends on both the player's choice and on information that is hidden to the player. No way you can treat that as a reset.

by tommica 9mo ago

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.
- dghf 9mo ago
  How does that contradict what I said? The way the game is set up, one of your choices -- stick or switch -- is guaranteed to win. Your original door will be correct 1/3 of the time and wrong 2/3 of the time. Therefore switching will be the winning move 2/3 of the time.
  - saghm 9mo ago
    Your explanation isn't wrong, but it's never quite resonated with me because it feels almost like a magic trick than something that follows intuition. Like seeing a magician perform a trick, it doesn't quite convey to me the "why" as much as the "what", and even though I know there's no actual magic, I still feel like I'm left having to figure out what happened on my own. The idea that finally made it click for me is that Monty has to choose one of the doors to open, and because he knows which door has which thing behind it, he'll never pick the door with the winning prize. That means the fact that he didn't pick the other door is potentially meaningful; unless I picked the right door on my first try, it's guaranteed to be the one he didn't open, because he never opens the right door on his own. His choice communicates meaningful information to me because it's not random, and that part while seemingly obvious gets left implicit in almost every attempt to explain this that I've seen. Another intuitive way to explain it would be to imagine that the step of opening one door is removed, and instead you're given the option of either sticking with your original door or swapping to all of the other doors and winning if it's any of them. It's much more obvious that it would be a better strategy to swap, and then if you add back the step where he happens to open all of the other doors that aren't what you picked or the right one, it shouldn't change the odds if you're picking all of the other doors. This clarifies why the 100 door case makes it an even better strategy to switch than the 3 door case; you're picking 99 doors and betting that it's behind one. The way people usually describe that formulation still often doesn't seem to explicitly talk about why the sleight of hand that opening 98 of the doors is a red herring though; people always seem to state it as if it's self-evident, and I feel like that misses the whole point of why this is unintuitive in the first place in favor of explaining in a way that clarifies little and only makes sense if you already understand in the first place.

atq2119 9mo ago

> once you open the door, the situation resets That's the root cause error of your thinking. The prizes aren't reshuffled and the host's choice of doors depends on both the player's choice and on information that is hidden to the player. No way you can treat that as a reset.