Monty Hall problem explained. Visit to start learning STEM for FREE, and the first 200 people will get 20% off their annual premium subscription.

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## Jurjen van der Hoek

07.09.2023Is her name really Savant? If so, what a rare coincidence that is!

## GeWij

02.09.20231 in 2 is better then 1 in 3, so that's why changing gives the best odds ? Oké, lets say the host also can't see the cards, and takes one away, this time he might have picked the car. Now anyhow it is again two cards, instead of three, is any logical person still gonna say, now it is better because it is two instead of three? Of course not. I say as soon as there is fiddling in between by somebody, even though i can't pinpoint it (yet), the logic of choosing one out of two is better then one out of three is just out the window.

Ps i would rather have a sheep by the way, by saying "you should" she is also kind of assuming, very unpleasant all in all, this whole mathematical show-ponying it is to me, but could not resist. reacting to it once more .

## Jay L

02.09.2023I don't get it

Isn't this what's going to happen instead?

Your odds of winning is 1 of 3 or 1/3

Now, since the host has shown you the wrong answer, would it make more sense that the mathematical equation has now switched from having a 1/3 odds to 1/2? given that either of the 2 doors has the car behind?

If someone can explain how they got 2/3 better maybe I'll believe it.

## Georg Cantor

02.09.2023UPDATE: It's only the 21st but it's safe to say that the Pinhead of the Month Award goes out to none other than pablorai who, after 35 tries, is trying to convince everyone that if he randomly picks a door from three available and is given another door that MUST have a goat behind it he can double his chances of winning by staying if he reveals it!

Great job!!! You are going be tough to beat next month as well!

## Joy Mahiko

02.09.2023BLM: "This is racist. How dare you be smarter than us"!

## 鄭翔宇

02.09.2023To anyone who still can't get this problem intutitively, here's is a great intuition that hasn't been mentioned elsewhere.

When the host open a door with a goat, this particular choice is not random but rather a reflection of your choice.

If you pick the right door the first time, then switching up or not makes no difference.

However assume you pick the wrong door in the first time, then the opened one must eliminat all the wrong door option.

Another way to look at it without breaking it down into two conditions is, since the door you choose can NOT be revealed by default, the door you choose in the first try must be the worse one in terms of both information and probability, it makes perfect sense to switch up.

(Also any mathematician and statician, or even any one who works with statistic that answers it wrong should be embarrassed. There is a thing called Bayesian statistic and you literally learn the famous Bayes formula in your high school math class.)

## Some random dude

02.09.2023Bruh my brain is frying, this feels like one of those moments mathematics itself is flawed, what if the game host opened the wrong door before the game began amd told you to pick a door, wouldn't it be a 1/2 chance

## Brenda Scally

02.09.2023Her educational mindset is spot on. The best thing I did for one of my children was let him quit in the 11th grade. He pledged to learn as much as he can and he did. He's absolutely brilliant and his needs were not being met. He didn't learn the way they wanted to teach. The American education system is still relatively new, being a few hundred years old. Throughout history, most have learned through apprenticeship, hands on experiential learning.

## Dave Joseph

02.09.2023I really doubt that all statistics professors were ignorant of how to calculate the Monty Hall 3-door problem. A huge number of contestants on the show seemed to know that switching doors was the path to winning.

## Travis Cotter

02.09.2023If you take a multiple question test and you want to show that you know every question. Guess them all wrong because if you don't than it will prove you could have got most of them right and maybe you guessed on a few but to show that you knew every answer you would have to get them wrong. Because if you guessed on a few and got a few right it would prove you could have been guessing at some of the questions. Mr. X

## Finny R

02.09.2023I did not find this problem difficult at all when it was first presented to me when in College. I was puzzled, however, when my brother, who had more college math than I did and was actually teaching college math classes, did not get it. I understand the trap most people find themselves in, but it doesn't take a savant to figure this out. One just has to weigh how the change in knowledge modifies the earlier probability commitment.

## Brainbuster

29.08.2023I had to think about this for 30 mins to realize she is correct. I was certain you still hv a 50/50. But you need to play the game in your mind many times to realize you win, in the end.

Here is my thinking. Please let me know whether my reasoning is incorrect.

3 doors.

2 goats, 1 car.

You randomly pick the car in 1 out of 3 games.

In those games, the other 2 doors each hv a goat. Host reveals where one of the goats is.

Switch your choice, you LOSE… but you lose in only 1 out of 3 games.

You randomly pick a goat in 2 out of 3 games. In 2 out of every 3 games you play, host reveals where the car is (by showing you where the other goat is). Switch your choice, you win the car.

Therefore, this strategy wins the car 2 out of every 3 games (if you play enough times).

## Don Grant

29.08.2023SHE ONLY HAD A 130 IQ. SHE WAS FAKE!!!!!!!!!!!!!!!!!!!!!!

## David Novakovich

29.08.2023I’m not that smart, but I disagree that the second door had better odds than door #1 after opening door #3, because if the contestant had picked door #2 instead, and the host still opened door #3, nothing would have changed situationally. For arguments sake, let’s suppose that the contestant picked mentally, only in his mind, and not vocally, and just as door #3 was opened, before seeing the result, he mentally switched his original pick from door #1 to door #2. Does that now mean that door #1 has the better odds, instead of door #2? Nothing has changed physically at all, so why would the odds change between the remaining two doors? To put it a different way, since door #3 is now eliminated from the exercise, let’s pretend that the original exercise only had doors #1 and #2 to choose from, the exact two remaining doors now. Why would the odds be different between these two scenarios? Maybe this is one of those “on paper” math things, but really doesn’t prove out in reality, or doesn’t have practical relevance?

## Willow Konrad

29.08.2023just to ague for the case of the dummies isn't that like saying, we are not going to update the assessment of the situation given the new knowledge. To me the tennis example serves to serve the more traditional point of view. Wouldn't it be like saying now I know this guy is a Wimbledon champ, I am not going to change the way I see the side of the equation that he is on. Yes any sane person would switch to the champ, but for entirely different reasons. ie with the doors, the unchosen doors side of the equation is not updated with the new information when being compared to the chosen door side. Still I would swap, but only for the reason that a level of abstract thought was introduced to the situation that added to the level of mindfulness in the decision making process, working at a quantum level.

## Gabriel L

29.08.2023um. that problem is silly. if you picked door #1, it is not to your advnatge to open door #2, because if the host

knowswhat is behind the doors, he would try to not let you open the winning door. he either opened door #3 because you picked the door with the good prize or maybe switched one goat door for another goat door. but it is still to your advantage to open door #1## MN

29.08.20233:26 where is the higher chance? Its still 3/6 which is a 50/50 chance…. this is beneficial on a higher yeild.. the question was on 3 doors which is 5050

## Gabriel Rivas

29.08.2023Ok, let me play the lottery 🤦🏻♂️

## Tim Goldich

29.08.2023You all DO know that this woman's ridiculous IQ of 228 has been debunked all over the place, right?

## The Druid Diaries

29.08.2023Is this a joke? It's obvious.

## krishna kanth

29.08.2023write monte carlo simulation .

## Sxmvp

28.08.2023I didn't understand this at all until 3:35, having more doors really makes this much more clear

## MyITRcom

28.08.2023My thinking is the host likely didn't want to be giving the car away on behalf of the company he works for, why he opened door number three, encouraging her to switch the choice. How are the odds any different then the 50/50 chance she already had of being right? So the odds would have seem to change to 50/50 for both door number one and two?

## M.M

28.08.2023Brilliant i have the luck when i buy maybe a new Radio i have a chance it is a broken one 80% so i take the one behind and yes it is a broken one most of the time .allways for real 😉 … Searching solutions to drive around a mistake mostly seem to directly lead to it. akcepting the Chance, right wrong in this small daily decisions takes a lot of pressure . a Mathematical chance in a world where most of mathematics are unseen to the eye seems more like a strong believing. I wait ,the other wil be better , not now .we are manipulated to let the lucky things pass away denying the energetic natural laws we are part of !

## M.M

28.08.2023Living the moment in full awakeness owning the memories to the point of happines. this is what we are made for …some more some less .most intelligent people i had the luck to know a time ,are driven by small imperfections , that make it Impossible to be happy

## laura chamberlain

28.08.2023Somehow this feels like a secret to winning the lotto.

## Smith Smith

28.08.2023I still don't understand this and it's annoying me. If you don't choose door number two then you are choosing door number one all over again. Can someone explain how we know there's a higher chance if you choose door number 2? Has this been run through a simulator?

## Smith Smith

28.08.2023Okay but this would be different if there was no host? If one door would just open at random? If it happened to have the goat and not be the door you chose – then you have option to choose. surely it makes no difference then right?

## Marian L

28.08.2023I read somewhere a very interesting problem. On one wall are three switches, two inactive, and the third operating a light bulb that is in a closed dresser. It is required to find out which is the active switch in a single attempt. You can play with them as you want, you can press two switches at once, even all three, but once you have opened the dresser you are no longer allowed to tuch them.

## GeWij

28.08.2023She is giggling her b*t of on how many people she got fooled.

## Scientific Perspective

28.08.2023I would want to know if the host always offers to let the player change, or only sometimes.

## Matt Bendzinski

27.08.2023So maybe this is incorrect but the chart at 3:25 is wrong. Because door number 3 HAS a goat, game 3 and game 6 are no longer possible. Therefore, the only two options are Door 1 has goat OR Door 2 has goat. So it is still 50/50 shot. The incorrect assumption is that the puzzle gets more info, however the probability changes to 50/50. Pick door 1 or door 2. Each holds the same probability of being either a goat or a car.

## M Zeeshan

27.08.2023I have a question.Actually i want to know about ml8m .its a cordword .what is the meaning of this

## Paul Spence

27.08.2023No. Did no one hear of Baysean probability. Once the 3rd door was written off the probabilities changed. Remove door 3 with no other data the probability of the prize being behind the other two doors is equal.

## The

27.08.2023i used to think the goat was the prize lol i'd be happy to have a goat 😂😂

## VectorAlphaAI

27.08.2023She was the smartest human being on Earth. That is amazing. She definitely could have done anything.

## joey lucius

27.08.2023This is dumb. Filled with procedural and semantic confusion. She went to language because she's good at confusing people.

## trallfraz

27.08.2023I don't care about her I.Q. or her logic, I only care about the game show resolve, which by the way, you didn't bother showing……so which door had the car and who was actually, or even mathmatically, correct??????????? Usually one can only assume their first choice is the best choice, and on the game show the contestants are usually correct, however, they go ahead and choose door #2 which ends up being worse than a goat!!!! (just saying)

## inefekt

27.08.20233:24

This table is incorrect. Possibilities three and six do NOT exist if the host has revealed a goat to be behind door three. How can a car be behind door three if there is a goat, therefore it is incorrect, those possibilities should be disregarded. The whole point of the exercise is that the host is revealing a door that he KNOWS contains a goat. Therefore the result is that there is a 50/50 chance of winning whether the person switches or not. The professors writing to her were correct, she is not. So much for your genius…

## Mad Dog Fargo

27.08.2023I had to think about this one… It isn't about YOUR selection pool, it's about MONTE's! 100% of the time he reveals a GOAT, but he does NOT have an equal pool 100% of the time.

1/3 of the time your initial choice is CAR, Monte can open 2 GOAT doors. Switching has a 100% chance of being WRONG.

2/3 of the time your initial choice is GOAT, Monte can open the 1 other GOAT door. Switching has a 100% chance of being RIGHT.

This means 2/3 of the time, switching is the best choice. It is actually pretty simple once you REVERSE your perspective. Kinda like a reverse proof to check your answer.

## Mc Chicken

26.08.2023I still have a peoblem with this setup. The options with theee doors makes it no less transparent. But the chance increase exponential with more doors added.

Its the same way with atoms and the distribution of high and low entropi.

We simply don't get monkeys writing Hamlet the more endless atoms there is at disposal in the universe.

## John Lee

26.08.2023Actually, no. She is wrong.

I'll explain why she was confused.

I also did well on the IQ test. Kind of a joke really.

Whether she picked the door with the car or not, the host will leave her with a 50/50 chance.

Neither remaining doors has the better chance with the info of having just one door revealed.

It is as if the game only had two doors to begin with. One with a goat, the other a car.

People mis understand. Her chances of picking the car gets better after a door is eliminated BUT her chances does NOT get better by switching doors. Switching her choice is irrelevant. The host gave her the better odds by eliminating a choice, she can't improve on that by switching doors. If she did she would have odds beyond 50/50 in a game of only two choices. Why can't people see this?

Time line

She has 1 in 3 chance of winning the car – 33%

Host eliminates a door. Now she has 1 in 2 chance – 50%

She switches doors, still 1 in 2 – 50%

She keeps her choice – 50%

In a game with only two possibilities with no insight to the correct choice it is IMPOSSIBLE to better the odds than 50%.

## Teacher Mark

26.08.2023I'm leery of any explanation that uses this two set idea. Odds can not shift. I think when the host reveals a goat, he has ended the game and started a new one instead. In this game he knowingly removes a goat from only two of the doors while avoiding the car if it should be there. Only now you're asked to pick. His manipulation of those two doors just leaves a game where one door of the two remaining doors is twice as likely to have the car, since he removed one possibility of it having a goat.

## Manny Ricketson

26.08.2023Has mathematics gotten so bad this day and age this problem is like a fraction

## Manny Ricketson

26.08.2023When i started school kids in the first drade had piano and trigonometry

## Manny Ricketson

26.08.2023Grade

## silverriffs

26.08.2023This is all hinged on the assumption that he’ll always show you a goat

## Dedan Kabuga

26.08.2023I had to google if savants are named for Marilyn.

## Jebbie Kanfer

26.08.2023I agree with her

## Newsthink

26.08.2023Did you manage to solve the puzzling problem?If not, Brilliant can help you out!Visit https://brilliant.org/Newsthink/ to learn math, science, and computer science for FREE, and the first 200 people will get 20% off their annual premium subscription.