Game Theory Scene | 21(2008) | Now Playing

lmao this is not game theory

if 2 men say no to your unwanted sexual advances in a hotel should you open another door?

Marilyn vos Savant ;) you know when you know

The Monte hall problem.

My method of going about this is this: You pick door 1 with a probability of 33.33%. Then, the host opens door 3 which is a losing door. Now, If you could pick both door 1 and 2 you would have a 100% chance of winning. So, by simply removing your choice of door one, which had a winning probability of 33.33%, you now have a 66.66% probability of winning by only picking door 2. 100%-33.33%=66.66%.

ah yes the famous moment where the college professor talks about the Monty Hall problem after seeing the Newton's method

I never had a college class that randomly went into probability after seeing Newton's method lmao

For those having trouble understanding:

Let's pretend there are 100 doors instead of simply 3.

We pick door 50.

The game show host shows me that all doors except door 50 and door 63 have goats.

If asked to swap from door 50 to door 63 the obvious choice is to swap!

Damn Matpat getting old

But hey that’s just a theory…

It's called The Monty Hall Paradox
this "paradox" was mentioned also in the series Better Call Saul Season 2 Episode 4

but what if he plays reverse of the reverse pyschology . and the car is behinf Door A ?

This problem is still hotly debated.
For me it is just a math fallacy.
First each door had a 1:3 chance of having a car behind it.
Then the host changed the situation, and thus the problem.
Now each door has a 1:2 chance of having a car behind it.
You can't decide the new situation based on the math from the original situation.

Jesus, nowadays he would not be allowed to throw chalk at a student.

monty hall problem

the only bit that confused me was knowing that, if you guess was correct initally, this is the exact tactic a game show would employ to get you to switch. And if you were to guess incorrectly first, the gameshow would just say "you lose" because, the house always wins.

mathematically hes correct, but gameshows know that, and they make sure they win, just like vegas.

That has to be taught????

By the way, the kid was wrong. Newton didn't steal the method from Raphson. Newton published his method a few years before Raphson reformulated it to the form we use today

After knowing what is behind door no. 3 .it supposed to be limited to doors 1 and 2 only. Meaning the percentage is 50%, why did he say 66.6%?

At first, I did not understand the logic and theory explained in this scene.
However, after going through several comments and explanations online, it did make sense.
I will try to explain some important points to understand the theory.

1) After the door 3 is open, this is just the second part of the same problem.
It is obvious that taken independently, there are then 2 doors and 50% chance of choosing right.
However, it is important to see that as the second part of the same problem / equation and not an independent one.

2) It's statistics and probabilities.
It doesn't mean the right door, in this scene the one with the new car, is door 1, 2 or 3.It's about understanding what choice / what door has the most chances of being the right one.
If we keep doing this experiment thousands of times, what door will be correct the most often.

3) This is something which is not mentioned in the scene but which is implicit.
This is after understanding this and it made sense to me.
When you choose 1 door out of 3, let's say like Ben the door 1, you have 33.3% of chance choosing right (this would be the same if you chose door 2 or door 3).However, that implies that you have 66.7% of choosing wrong.
Those 66.7% mean that the right door is elsewhere, either door 2 or door 3. We don't know which one, but statistically, it would be one of them.
If it's either 2 or 3 and that the game show host indicates it's not door 3, then logically it should be door 2.Consequently, it is in our interest to switch from door 1 to door 2.Again, as explained in 2), it doesn't mean it's 100% correct.
It means switching the door has the most chances of winning and will win the most often if we perform this experiment hundreds or thousands of times.
It is similar to surveys...The larger the sample is, the more accurate / correct the outcome is.

4) To understand better, we can take the example of a deck of cards, 52 cards.
Let's say you pick one without looking at it.
What are the chances of you picking your favorite card, let's say for the example ace of spades?1 chance out of 52, about 2%.It is much more likely that the ace of spades is in the rest of the deck than the card in your hand.
You don't know which card is the ace of spades, but you guess it's somewhere in the deck.
Following probabilities, it is in your interest to switch your card with the rest of the deck.
Now, if you reveal 50 cards out of the 51 cards left in the deck and the ace of spades isn't any of them, you will end up in a similar situation as the 3 doors and the movie scene.
It may appear as a 50%/50%.However, we said earlier that even though we couldn't tell which card it was, it must be in the deck.
In conclusion, it is likely the last card in the deck and it is in your interest to change your initial choice.

How do you know the game show host would also offer the opportunity if you start with a goat?

It's only a relevant example and an increase to 66% if in every scenario the game show host would open a door and re-offers you a choice. So also in case you would start with a goat.

But I want the goat not the car

As a mathematician I’m wondering why is he talking about probabilities in a class of non linear equations, lol

they had sex afterwards

His acting make the scene so much interesting ..

MontyHall Problem.

I remember my Statistics 2 professor telling us something similar about switching and changing your answer, i never really got it

I always wonder why they did not call it Monty Hall problem instead of Game Show problem.

You have three doors: A, B, C. B contains the car, the other two contain goats.
You have an option to choose twice. Once at the start and once after opening a door that contains a goat.

Let's say that you choose to another door after host shows a different door. Here are the possible scenarios --
{First time Choose A, Second time Choose B, Host open Door C} -> you win,
{First time Choose B, Second time Choose C, Host open Door A} -> you lose,
{First time Choose C, Second time Choose B, Host open Door A} -> you win

Probability of winning went to 67% boom!

Let's say doors 1 - 2 - 3 contain Goat - Car - Goat.

Your first guess 1/3 chance of car, 2/3 chance of guessing a goat. You know this

The information you get when the door opens let's you know not ONLY that there are two doors left and one has the car, but you have to know what the host could NOT do—he could NOT show you the door with the car and he could NOT open the door you first chose. Given you only had a 1/3 chance of correctly guessing the car in the first place, then that means that only 1/3 of the time is it the case that the door(s) he cannot open is BOTH the one you chose AND the one with the car, and THUS only 1/3 of the time would you be wrong to change your guess, ergo 2/3 of the time you'd be correct to change your guess.

The statistic is inversely based simply on the likelihood that your first guess was NOT correct (i.e. 2/3 of the time).

Or to break it down,
Your First choice wast door 1 (goat) = changing your guess [after door 3 is revealed] is correct b/c host could ONLY show you door 3
First choice was door 2 (Car!) = changing is incorrect; the host can reveal door 1 or 3.
First choice was door 3 (goat) = host could ONLY reveal door 1, changing is correct.

Now what's the likelihood you'll be in bed by 2 AM?

Best Explanation:

Scenario 1:
You initially pick the door with the car behind it (1/3 chance).
If you stick with your choice, you win.
If you switch, you lose.

Scenario 2 and 3:
You initially pick a goat (2/3 chance combined for both scenarios).
In both of these scenarios, Monty has to open the other door with a goat.
If you stick with your initial choice, you lose (because you originally chose a goat).
If you switch, you win the car.

The probability breakdown for switching vs. staying is:

Switch: Lose (1/3) vs. Win (2/3)
Stay: Win (1/3) vs. Lose (2/3)

Meaning if you switch you will always have a 2/3 chance of winning (the 1/3 chance of losing is from you switching when you already chose the door with the car)

They forgot to add Kurt Angle to the mix.

I cannot rationalize this even after reading all the comments. I mean why not stick with your orginal choice.

So I didn't get it until it was explained to me this way. You have a 1/3 chance to pick the correct door. Which means the car has a 2/3 chance of being one of the doors you didn't pick. By the host removing 1 of the 2 doors you didn't pick there's a 2/3 chance that it is the other door.

They got one small detail wrong here. When the professor asks how does he know he isn't playing tricks, you can't really play tricks with that gameshow. You will always have that 66.7% chance if you switch.

i disagree

21

The whole interaction with the gameshow host can be simplified down into one single statement: "If you pick the door with the car, you lose". There are two doors without a car behind it, so your odd would be 2/3 (66.6%).

It’s simple math - Capt Ray Holt.

nah, I don't get it

Lived my life based on this movie and heat and that movie till 2016.. what changed????

I had life experience, oh yes, I gambled.. (doesn't work) 😂😢

Gut.. am on 33% hoping to get to 88% from Gut feel..

I say no till, I say yes.... Love too much.. also looking for Ne-yo aka 1% the CR7 and one of you might know him.. 16 year working experience,..mmhh 😂😮JK❤🎉

there are 2 doors.... and there is a goat behind a door, and a car behind the other... pick a door.... I drop my phone on the floor, pick it up and ask you if you want to change your decision.... what do you do?

What does the Monty Hall problem have to do with nonlinear equations or Newton's method? I don't understand Hollywood maths.

I do this with my 10th grade pupils as a maths teacher. Everyone gets an idea to find the best strategy for the monty hall problem by drawing a probability tree for each strategy. Its funny how they sell it as a test to find the only genius in your class.

This scene is not about Game Theory - it's about CONDITIONAL PROBABILITY . There is literally no Game Theoretic component to the solution.

It's literally just the MONTY HALL PROBLEM ... even a few Americans know the difference between Conditional Probability and Game Theory (even if their foreign policy bureaucrats and tech oligarchs understand neither).

I don't know why they don't simply call it by it's name

Here are the possible outcomes (assuming a goat is always revealed):

Pick G1 -> reveals G2 -> switch to car (WIN)
Pick G1 -> reveals G2 -> don’t switch (LOSE)
Pick G2 -> reveals G1 -> switch to car (WIN)
Pick G2 -> reveals G1 -> don’t switch (LOSE)
Pick car -> reveals G1 -> don’t switch (WIN)
Pick car -> reveals G1 -> switch to G2 (LOSE)
Pick car -> reveals G2 -> don’t switch (WIN)
Pick car -> reveals G2 -> switch to G1 (LOSE)

There are 4 winning outcomes, and 4 losing outcomes. Therefore, the statistical probability of winning under these specific conditions is 50%.

The video is titled Game Theory, the class is named Nonlinear Equations, the question is asked is about Probability Theory.

By the mere fact that the show host opens one door (of the 3), it immediately becomes a 50/50 whether or not the show host offers an option to reconsider which door you would prefer.

It doesn't become 33% + 33% = 66% for one of the doors.

This is dumb.