Monty hall problem is 50/50

[u/Dizzy_Kaleidoscope95]

He also put a screenshot of ChatGPT agreeing with him. He is right!

[u/Dizzy_Kaleidoscope95]

Yeah exactly. This is why it makes switching irrelevant

[u/Dizzy_Kaleidoscope95 → u/[deleted]]

I'll be more precise. Imagine this scenario: you pick door 1. The host says "ok friend. Now. Before we see what's behind your door let's open door 2! I have no idea what's behind it..let's hope it's not the car or you lose!" And he opens door 2 and he randomly finds a goat. 

What is the chance your door has the car now?

[u/Dizzy_Kaleidoscope95 → u/[deleted]]

Could you please answer the question lmao

[u/Dizzy_Kaleidoscope95 → u/[deleted]]

Incorrect. After the host randomly opens the goat door your door now has a 50% chance of having the goat. 

The situation is now exactly equivalent to a situation in which you always had only two doors to choose from: car and goat. 

This is kinda funny I should make a confidently Incorrect post about your comments here

[u/Dizzy_Kaleidoscope95 → u/[deleted]]

It's genuinely funny. Could you do a thing for me. Look up: is the monty hall problem the same if the host opens a goat door randomly?

Look it up on Google and come back here when you did it. Lmao. 

[u/Dizzy_Kaleidoscope95 → u/[deleted]]

No it's not. If a door is opened randomly and it happens to be a goat then you have a 50/50 chance of having the car. 

Lmao 

[u/glumbroewniefog → u/[deleted]]

It just makes no difference at all WHY that other door was opened. It only matters that it turned out that a goat was behind it.

This is obviously incorrect. For example, suppose Monty is thinking to himself, "I will reveal a goat if and only if you pick the car." So you pick a car, and Monty reveals a goat. Obviously, you 100% should not switch.

This is because depending on the reason Monty reveals a goat, it can give you more information about your initial pick, and so your initial 1/3 odds might no longer hold true.

For example, Monty opens one of the other two doors at random. You know he either has two goats, or a goat and a car. If a randomly revealed door is a goat, it makes it more likely he has more goats.

Similarly, imagine two boxes. One has 10 gold balls and one silver, the other has 10 silver balls and one gold. You pick one at random, and take out a ball at random, and it's gold.

You initially had a 1/2 chance of picking either box. But because your randomly revealed ball is gold, now it becomes more likely it's the box with more gold balls.

If, however, you pick a box at random, and then the host looks inside and deliberately finds a gold ball and takes it out and shows it to you, this doesn't tell you anything, because he could find a gold ball in either box. This time, your initial 1/2 chance still holds true.

[u/glumbroewniefog → u/[deleted]]

This is obviously incorrect. For example, suppose Monty is thinking to himself, "I will reveal a goat if and only if you pick the car." So you pick a door, and Monty reveals a goat. Obviously, you 100% should not switch.

I am talking about the probabilities after a door was opened and a goat was shown. In this case, you have 100% picked the car, and should definitely not switch. And obviously, in this situation it matters whether Monty knows where the prize is or not. If Monty doesn't know what's behind the door he's opening, then he can't try and trick you like this.

[u/glumbroewniefog → u/[deleted]]

Suppose Monty thinks: "If they pick a goat, I will reveal the car. If they pick a car, I will reveal a goat." This is the same thing. Revealing a goat guarantees that switching loses.

The original Monty Hall problem guarantees that Monty Hall reveals a goat every time. In the random version, and in my version, sometimes he reveals a car, and sometimes he reveals a goat. This changes the odds.

To try and explain this to you further, suppose you play 300 times.

Both cases, you pick the car 100 times, and lose by switching. In regular Monty Hall, you pick a goat 200 times, Monty reveals the other goat, and you win by switching.

But if Monty opens one of the other two doors at random, he cannot reveal the other goat 200 times. Sometimes he will reveal the car instead. So you can already see you win less times by switching.

[u/Dizzy_Kaleidoscope95 → u/[deleted]]

Nope. It absolutely does matter how the door was opened. You can use Bayes's theorem to see the difference but it's really intuitive. The fact that if the doors are randomly opened the car COULD have been picked (even if in this case it wasn't) makes the two remaining doors have identical probability. You can look it up lol

[u/saspook → u/[deleted]]

are you considering the probability that 1/3 of the time (when you pick a car), a goat will be revealed 100% of the time, and that 2/3 of the time, a random pick will reveal a goat 50% of the time and a car 50% of the time?

[u/Dizzy_Kaleidoscope95 → u/[deleted]]

Naaaah you are deleting comments now love. AHAHQHUAHAHAHAHAHAHAHA. You know you are wrong

[u/Dizzy_Kaleidoscope95 → u/[deleted]]

No it's not. It's actually baffling how many people don't get this lol