Why You SHOULD Switch Doors (Even if it Feels Wrong) | The Monty Hall Problem

[@roberthobbs6318]

That was really helpful, I always had issues with The Monty Hall problem. This video solved that, and made me think of it in a different way than presented too (well, it's basically the same just worded a bit differently, it just makes more sense to my brain). Each door has a 33% chance of being correct, when you choose your door it's "on hold" (not taken out of the picture altogether) as its contents are still unknown, so all the odds remain the same but your decision can't be changed, for now. So, your door has a 33% chance of being right and the other two "share" the remaining 66% chance of being right (33% each). Now, when the host removes one of the doors, he definitively DOES take it out of the picture, and it's 33% "share" of being correct HAS to go somewhere, so it "donates" it to the other door (it can't go to yours, because yours is on hold), so the one door that was left untouched gets that 33%, giving it a total of 66% chance of being correct, and yours remains with its initial 33% (and gets taken off "hold")!

[@true_cyan9188]

Exactly great way to word it! Ima go ahead and pin this comment cause I think it might help some others!

[@true_cyan9188]

Jk it won’t let me pin comments anymore??

[@roberthobbs6318]

@@true_cyan9188 Thanks, I appreciate that! I just figured it can't hurt to give another example! And it's ok that you can't pin it, I'm sure that at least a few people will come across it!

[@Grumps57]

The 1 in 100 example is the best way of explaining this. Nice work. It isn't the smartest who teach but the one who can dumb it down for the rest of us. Cheers

[@elicareyva]

i got the door in that out of 100 and it scared the shit out of me

[@true_cyan9188]

That was actually me in real time just choosing the door you were thinking about. I can read minds so it was no sweat for me.

[@true_cyan9188]

I feel like this is almost a back handed compliment LMAO but I agree I had plenty of professors that were clearly very very smart but sucked at teaching and they were never my favorite. Always the ones that clearly do know what they are talking about but are capable of just breaking it down into these small building blocks, then it looks so simple.

[@Grumps57]

@ FYI I’m the idiot and you are the good teacher

[@true_cyan9188]

@ I don’t think either of us are idiots, I think anyone willing to learn is never an idiot!

[@Etrancical]

I always love that the easiest way to explain these "paradoxes" is to always take it to the extreme. 100 door analogy is great because imagine choosing a random door and the every other door except one just opens, revealing nothing inside. It's a scary experience irl, but it makes intuitive sense when working with extremes.

[@true_cyan9188]

I didn’t really think about it, but it’s very true that the best way to wrap your head around a lot of the paradox style problems is to view the extremes. Really helps put it into perspective I guess!

[@bluedragonplayer3823]

I’ve literally been mad at this problem for years and this is the first example that’s ever actually explained it to me. Great video 💯

[@true_cyan9188]

LETS GOOOO! I was hoping this would have this effect for at least one person! You have made making this video worth it, thank you!

[@It_Could_Be_Anyone]

Actually I solved the Monty Hall Problem by never being wrong

[@true_cyan9188]

Oh my bad, youre right.

[@esdo1132]

It's incredible that after the first step I didn't get it at all but during the 100 doors example it clicked immediately.

[@true_cyan9188]

LETS GOOOOO! I’m so happy this video is helping people! This problem was keeping me up before I learned about the 100 door approach!

[@EdinoRemerido]

I've found a simplecway to prove this. There are only 3 possible combinations W L L L W L L L W If you always choose the first door in the 1. Variant, switching would makes you loose But in the 2nd staring with a wrong door means the other door is gurranteed to be the right one, and so it is in the 3rd variant.

[@true_cyan9188]

This helps some people but I have seen some people get stuck on trying to understand the “why” part of this math. Still it’s a helpful view point!

[@Alex-ml3bk]

Really really good, well done this is the best explanation ive ever seen

[@true_cyan9188]

Dude thank you so much!

[@xx_Agent_Carolina]

🕵️😁 Never thought about this topic before; it's fantastic intel, ty! 👏👏👏

[@true_cyan9188]

Bruh how I mess that up, good find!

[@xx_Agent_Carolina]

@true_cyan9188 Same way you didn't notice that I'm female, I suppose. 😜 I'll edit now that uv seen it. 🖖

[@true_cyan9188]

@xx_Agent_Carolina you are too kind, thank you!

[@xx_Agent_Carolina]

@@true_cyan9188 🤗 ☺️

[@Llama_charmer]

The way I view this problem is imagine that instead of removing one of the doors after your guess, you are offered the choice to either keep your door or be allowed to open BOTH of the other doors. Ultimately this changes nothing because you know that one or even potentiality both of those doors are empty but if you were given the choice to open two doors or one you'd obviously pick two, why? Because your odds are higher. Removing and opening the door are equal

[@true_cyan9188]

This is a pretty good idea, I don’t think it would work as a complete solution because some people would get stuck on understanding why opening both would be the same as the original problem but for those that do understand the similarities this is a great way to explain it! Great work!

[@Llama_charmer]

@@true_cyan9188 Fair enough, though when i first heard about this problem a while back hearing it explained like this is what made it click for me

[@akavanagh59]

Great explanation, fair play

[@true_cyan9188]

Thank you for your comment!

[@Cube8]

I think it's 50/50. Since the host always removes the wrong one(s) (even if they are 98), it's like the other door(s) don't exist. So you will always be between 2 choices.

[@gavinwilson9472]

I understand why you think this, because that is the intuitive thought process. However, the idea is this: the host will ALWAYS remove a wrong door whether you have chosen a correct one or not. The chance that you chose a correct one in the first place is 33% (because you had three options), but the chance that the remaining door (after the host removes a wrong one) is 66% because it is always correct in the case that you chose a wrong door.

[@true_cyan9188]

The issue with this line of thinking is that the second door will always be correct if your first door is wrong, and since you only have a 1% chance that you got it right, in the 99% chance that you got it wrong the host will then get rid of all of the wrong doors and then keep the right door. So even tho it’s only 2 doors one of them is just the one door you chose while the second door is in a way all of the other doors molded into one

[@Xoeverything-uf4bz]

good work man.

[@true_cyan9188]

Thank you!

[@Grndmstrpotato]

Gonna go crazy on deal or no deal after watching this video

[@true_cyan9188]

Watching this video might disqualify you for fair play violation.

[@SmudgySubset]

This is a great explanation! It's so unintuitive

[@true_cyan9188]

Its a strange thing to wrap your head around. im glad you liked the video!

[@Noah-td1tj]

Wow! This worked!

[@true_cyan9188]

LETS GO! Happy to help!

[@helpmepleeaase]

Does the 33% of the removed door always gets added to the other door instead of my selected door? Or does is sometimes go to mine?

[@true_cyan9188]

It will always go to the other door, the reason for this is because your doors 33% is because it was a 1/3 chance when you first guessed it. After you choose your door, the host functionally chooses both doors he just gets rid of one of them that is wrong so “his” door or the other door will always have the total percentage of all of the doors that you did not choose. Let me know if that helps!

[@helpmepleeaase]

@@true_cyan9188 ah thank you

[@Cube8]

1:06 "Acutally" ... Did you mean _Actually_ ?

[@true_cyan9188]

I did make a typo :/

[@Jok14271]

In the 100 doors i actualy got it right.

[@true_cyan9188]

My friend said he also did, I believe you because it is a wierd thing to lie about but now I’m wondering if i accidentally chose a door that’s more likely to be picked at random, I mean technically I also picked that door.

[@alkinurdotran1053]

its 50/50 so stay

[@true_cyan9188]

Really can’t argue with that logic!

[@alkinurdotran1053]

@@true_cyan9188 Well they dont call me by my name for no reason