The Monty Hall Puzzle Simplified!

The Monty Hall problem is a classic puzzle in probability. It involves a game show, a prize and a simple choice you need to make to win the prize.

How do you maximise your chances of winning the prize? And are you ready
to make the counterintuitive choice?
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[dominicstevenson]

Thank you for this explanation, I have seen so many other videos that talked about this, but I never understood their explanation.

[DShahdeo]

In a certain novel i saw the explanation as "if there were a thousand doors and one had treasure behind it, and you chose one, and 998 no-treasure doors were broken and you were given a chance to switch, would you?"
In this case it's clear that the probability goes up from 1/1000 to 999/1000 (not 1/2!!!, as it's a 999/1000 chance you chose wrongly initially) after you switch. So in the original monty hall problem, your chances are 1/3rd and then 2/3rd. Never half.

Also this paradox can be solved experimentally.

[samhiltz]

Echoing the "Finally a good explanation." crowd because yeah, finally a good explanation.

[anebr_gameplay]

GOD! I finally got this! Man, I can't tell how perfect and clear this was. Thank You so much

[UnreliableAdviceall]

Im very impressed that you could explain this concept so well in under 60 seconds.

[Arthur_Draws_Things]

Plot twist:
You hear the goat scream from behind the door so you know it’s not that one

[Gruzzly]

Another way to visualize this that helped me - imagine there are a million doors. You choose door #1, the host reveals 999, 998 doors with goats and asks you if you want to switch with the remaining door. Of course you would, because you’ll win the prize unless you happened to make the one-in-a-million guess at the beginning

[D.i.y_electric_hb]

Better way of explanation!
Listen in case 1 probability of getting car was 1/3
And say u picked up 2nd door so probability of car in it was 1/3 but now in case 2
You know that car isnt in 3rd door so the probability of the car in 3rd row is shifted to the 1st door hence probability of car in 1st door is 2/3 and 2nd door is 1/3 hence shifting helps

[mickeyspanish]

No one ever talks about how Monte Hall's real problem was the Nose Candy

[saudk]

This puzzle is very confusing, and this is the first explanation that I understood. 👍

[sat]

Question is from sansad tv math series

[MeetPatel-jcqg]

Well, one cannot of course solely rely upon probability.

[shahadalaslany]

ok if i switch… and the first pick was correct????

[lukewills]

I never understood this 9dea until now

[insignificantfool]

You say the host shows the goat door "instead of opening" the picked door. Doesn't that mean that opening the picked door is at least an option the host has? Because this option is completely missing in the explanation.

[thinkall]

I feel that's wrong explanation.
U strictly chose first door. Manager showed a for with goat. Then why are u arranging the car in all 3 doors for possibilities?

[tamirerez]

The odds will remain 50%-50% no matter how you think.
Doors don't know math.

Math teacher.

[dominicstevenson]

Doesn’t that mean the host would only reveal a door if you have the right answer?

[sonicbreaker]

wrong answer ... the game show doesn't want you to win. so no matter what you do, the game show will SWITCH the car so that you open the door to find a cow.

[AbdullahSaHeL]

Everyone should know that the host will always open only one door before opening any other door, and this door must be: (1) not hiding the prize, (2) not chosen by the contestant before the opening.

1. The contestant will choose door (A).
2. The host will open door (B) immediately after the contestant has chosen door (A), revealing a goat behind this door.
3. Door (C) remains unchosen by the contestant and has not been opened by the host.
4. This implies that either the car or the other goat could be behind door (A) or (C).
5. The contestant has the right to switch their choice to door (C) or stick with the original choice, which is door (A).
6. For some unclear reason, the video host advises switching from door (A) to door (C) to increase the chances of winning the prize (the car).
7. No one will switch between the goats and the prize after the doors are closed and ready for selection or choosing.

Based on the above data, I will present the following methodological observations:

1. Your assumption that the host knows for certain that he will choose the door that does not reveal the desired prize is a form of coercion that directly negates the existence of a choice for the contestant. If there is no choice, it means there is certainly no probability for the contestant!

This means that the total of the choices regarding the doors = 1 + 1 + 1 - (1) = 2, which means the contestant must initially assume that the total of certain probabilities is 1/2 + 1/2.

2. It is important to note that the host opening the door or revealing the cards happened before the contestant executes the choice to reveal what is behind the door he chose. The doors were not opened simultaneously; each door-opening action occurs sequentially, not all at the same time instantaneously.

3. The principle of your answer was based on your assumption that, since the host will assist the contestant by revealing the wrong door, this leads to an additional 1/3 increase in successful probabilities, which will be added to the correct probabilities and removed from the wrong probabilities by the same percentage (all from the host's perspective, not the contestant's perspective).

4. Based on point #3, you implicitly assumed that the host intends to help the contestant by hinting that I (the host) will assist you by opening a door you did not initially choose. Therefore, you, the contestant, should change your choice to the door that you did not choose and that the host also did not open. In other words, if you, the contestant, do not understand that I am hinting to you (without any clear evidence or explicit proof) that you should abandon and change your choice, you will lose.

Therefore, your solution and answer is not convincing at all. According to you, the success is based on trial (not necessarily random) and the probability of 2/3 success is not based on mental math at all.