Women, math, and the Monty Hall problem

[PureX]

View attachment 100251

Find the missing options ...

1. Lay down on the tracks and let the trolley run you over, so you won't have to decide who else lives or dies.
2. Break off the switch lever and stick it into the trolley wheels to either stop or derail the trolley.
3. Quickly erase the single victim on the top track in the drawing so the switch operator can send the trolley down that track.

 

[Heyo]

Overwhelming evidence shows that Monty will do this regardless of what the contestant does in "phase one".

That is exactly what is happening, except that you are invited to make a choice, and then it is ignored.

What you don't realize is that it is.

The first choice is irrelevant, and is being ignored as a result. It was only offered to confuse folks like you.

No, you just have to stop trying to calculate the odds of choosing doors, and instead focus on the odds of winning the car.

It is, because the first choice is just irrelevant theater.

Well, we have differing hypotheses, what about setting up an experiment to see which hypothesis comports to reality?

 

[PureX]

Without picking a door in phase one, Monty won't open a door and start phase 2.

Overwhelming evidence shows that Monty will do this regardless of what the contestant does in "phase one".

Assume the following game: you don't get to make a first choice. There are three doors, Monty opens one of the doors and reveals a goat. Then you are asked to make a choice. In this scenario, the chances are 50/50.

That is exactly what is happening, except that you are invited to make a choice, and then it is ignored.

What you don't realize is that that is not the game, that is played.

What you don't realize is that it is.

By making a first choice out of three, and Monty then opening a door, the first choice and the second one are related, not independent.

The first choice is irrelevant, and is being ignored as a result. It was only offered to confuse folks like you.

You have to apply Bayes Theorem to calculate the chances.

No, you just have to stop trying to calculate the odds of choosing doors, and instead focus on the odds of winning the car.

The mistake you make is that you assume the second choice to be independent, it isn't.

It is, because the first choice is just irrelevant theater. We know this because no matter what we do, Monty will response the same way regardless. And we will NOT get a car.

 

[Heyo]

Overwhelming evidence shows that Monty will do this regardless of what the contestant does in "phase one".

That is exactly what is happening, except that you are invited to make a choice, and then it is ignored.

It is not ignored.
According to the rules, Monty won't open the door you choose. He will also not reveal the car.
So, in the case that your first choice was a goat, Monty has no choice to ignore anything. He has only one option, to show you the other goat. That is what makes your first choice relevant and related to the second one.

 

[PureX]

Well, we have differing hypotheses, what about setting up an experiment to see which hypothesis comports to reality?

There is no "hypothesis". The reality is the the game and how it's played. And the odds are there for anyone with eyes and brain to recognize. The dispute is that some if you want to calculate the odds of choosing various doors. When the pertinent goal is to calculate the odds of winning the car. These are not the same goal, and this is why some people are confused about the validity of the initial 3-door theatrics.

 

[PureX]

It is not ignored.
According to the rules, Monty won't open the door you choose. He will also not reveal the car.

Thus, proving that your odds of wining the car are ZERO. Not 1 on 3. You're still trying to set the odds for choosing the "right door". While I am setting the odds of winning the car.

So, in the case that your first choice was a goat, Monty has no choice to ignore anything. He has only one option, to show you the other goat. That is what makes your first choice relevant and related to the second one.

None of this matters as Monty will always do the same thing, and you will certainly not win a car. The odds are not 1 in 3 that you will win a car, they are ZERO. The odds of picking the "right door" are irrelevant if you can't win the car no matter what door you pick. ... And if Monty is always going to respond in the same way, anyway. (Which he does.)

 

[Heyo]

There is no "hypothesis". The reality is the the game and how it's played. And the odds are there for anyone with eyes and brain to recognize. The dispute is that some if you want to calculate the odds of choosing various doors. When the pertinent goal is to calculate the odds of winning the car. These are not the same goal, and this is why some people are confused about the validity of the initial 3-door theatrics.

Your hypothesis is that the chance are 50/50, if you switch or not.
My hypothesis is that the chance is 2/3, if I switch.

We can play the game to see who is right.

 

[Whateverist]

He uses the term scientism when he is offended by his special way of knowing, which is intuition, being rejected. It happens frequently with him. He makes some claim supported only by his gut feeling, expects it to be respected, and when it's rebutted, goes on the attack as we see here.

If I can find some quotes and the time I might like to start a thread on the strengths and limitations of intuition. (There should be a similar one for reason.)

 

[Alien826]

Thus, proving that your odds of wining the car are ZERO. Not 1 on 3. You're still trying to set the odds for choosing the "right door". While I am setting the odds of winning the car.

None of this matters as Monty will always do the same thing, and you will certainly not win a car. The odds are not 1 in 3 that you will win a car, they are ZERO. The odds of picking the "right door" are irrelevant if you can't win the car no matter what door you pick. ... And if Monty is always going to respond in the same way, anyway. (Which he does.)

Are you seriously suggesting that in real life nobody ever won the car?

And in this highly defined mathematical puzzle (which is what we are discussing) that it's impossible to win the car? After Monty opens the door to the goat, a car is definitely behind one of two doors. All you have to do is pick the right one.

 

[Alien826]

He uses the term scientism when he is offended by his special way of knowing, which is intuition, being rejected. It happens frequently with him. He makes some claim supported only by his gut feeling, expects it to be respected, and when it's rebutted, goes on the attack as we see here.

Then there's the "pearls before swine" stage which comes just before leaving the thread.

 

[PureX]

Are you seriously suggesting that in real life nobody ever won the car?

Not during the theatrics of choosing from the initial three doors.

Please pay attention to the conversation.

And in this highly defined mathematical puzzle (which is what we are discussing) that it's impossible to win the car?

No one ever wins anything by choosing 1 door from among 3. Ever. So there is no reason to include this bit of theater in calculating the odds of winning the car. Because the odds of winning it at this point are ZERO.

After Monty opens the door to the goat, a car is definitely behind one of two doors. All you have to do is pick the right one.

You still are not going to be able to win the car until Monty offers to open the door that you choose from among the two remaining doors. Everything before this point is just irrelevant theater because there is no possibility whatever of you winning (or even losing) the car.

 

[Subduction Zone]

You tell a story using numbers, and then when the numbers reiterate the story you made them tell you think you've proved some truth that you believed from the start. It's the classic confirmation bias of the "scientism" way of thinkIng. And to prove this, just look at how adamantly those who believe in it hold onto their belief. No degree of skepticism whatever. Which is clearly not a scientific view in any sense of that term. It's more akin to religiosity.

The odds don't "remain" 50/50. They simply are 50/50 for the actual result of the choice that the contestant is actually given.

And 1 + 1 = 3 is correct when it's telling a different story than the one you presumed.

Such massive projection.

Just admit that you don't understand it.

 

[Subduction Zone]

There is no "hypothesis". The reality is the the game and how it's played. And the odds are there for anyone with eyes and brain to recognize. The dispute is that some if you want to calculate the odds of choosing various doors. When the pertinent goal is to calculate the odds of winning the car. These are not the same goal, and this is why some people are confused about the validity of the initial 3-door theatrics.

Sorry, but you are wrong about when the odds are set and you are wrong about the theater as well.

The odds are set when the contestant picks his door. The odds are one out of three that he picked the winning door.

There is "theater" involved as well. You seem to keep forgetting that Monty knows where the car is. That is why he can always show a goat. No matter which door the contestant picks there is at least one goat that Monty can show. He is in effect giving the contestant an offer of trading his one door for the other two. His revealing a goat was pure theater that should be ignored.

 

[anotherneil]

For those who believe that your odds of winning don't increase if you switch doors, I challenge you to test it out for yourselves.

Repeat the trials enough times (10 might be enough) to see whether the average outcome approaches 50/50 or 2/3rds.

Come back with your results.

 

[Alien826]

Not during the theatrics of choosing from the initial three doors.

The first choice is part of the whole process. Without that nothing happens because nothing then proceeds. The game doesn't stop there.

No one ever wins anything by choosing 1 door from among 3. Ever. So there is no reason to include this bit of theater in calculating the odds of winning the car. Because the odds of winning it at this point are ZERO.

You still are not going to be able to win the car until Monty offers to open the door that you choose from among the two remaining doors. Everything before this point is just irrelevant theater because there is no possibility whatever of you winning (or even losing) the car.

First you choose a door from three possibilities. Then Monty opens one of the doors of the two you didn't choose. Then you choose either to stick with the door you originally chose or the the Monty didn't open. Three stages involving two choices. All necessary to get the car (or not get it). The first choice is just as much part of it as the second. And, in the described sequence of events choosing the correct final door means you will get the car. Monty has to open it, it's a given.

 

[Stevicus]

Are you seriously suggesting that in real life nobody ever won the car?

In the actual "Let's Make a Deal," the game was never played that way.

 

[Subduction Zone]

In the actual "Let's Make a Deal," the game was never played that way.

That is true. I cannot remember the show well enough to know if Monty ever revealed a "zonk" or not. But that is why it is called the "Monty Hall Problem". It is clearly a fictional Monty Hall that is based roughly upon the show.

 

[ImmortalFlame]

Here's a website when you can demonstrate, without any ambiguity, the truth of the mathematics in this case:

Monty Hall Problem Online. Run the monty hall game and simulation , over and over to understand the probability of this problem.

Monty Hall Problem --a free graphical game and simulation to understand this probability problem.

www.mathwarehouse.com

You can even have the website run the simulation thousands of times. You will get the same result.

At this stage, anybody claiming otherwise is anti-reality.

 

[It Aint Necessarily So]

We know this because no matter what we do, Monty will response the same way regardless.

No, he will not. He will show you a goat door whatever you choose, but if the car is behind door 3 and you choose door 1, Monte will reveal door 2. If you choose door 2 when the car is behind door 3, he'll show you door 1. His response is dependent on your choice and where the car is hidden.

The dispute is that some if you want to calculate the odds of choosing various doors.

That's a trivial problem. The odds of choosing each door is 1 in 3. We're calculating the odds of choosing the correct door and determining the optimal strategy to win playing this game, which is NOT a trivial problem.

Not during the theatrics of choosing from the initial three doors.

That was a reply to, "Are you seriously suggesting that in real life nobody ever won the car?" This is a game on television, so of course its theater. But the Monte Hall problem is NOT theater. It's mathematics.

No one ever wins anything by choosing 1 door from among 3. Ever.

If you mean that you haven't won yet, that is correct, but a trivial observation. You still have another decision to make after which you've either won the car or not.

You still are not going to be able to win the car until Monty offers to open the door that you choose from among the two remaining doors.

If your point is that you don't know that you've won until you see that you've won, that's also a trivial observation and not what the problem is about. It's about winning and the most likely way to do that - not how or when one learns that he has won.

You've won the car after your second decision if it was to take the door with the car behind the curtain whether by keeping or swapping your original choice. You find out that you've won a few seconds later.

And you won't know that when Monte offers to open the door you chose - "You chose door number 3. Let's what's behind the curtain" - but rather, after he actually does it - "You've won a brand-new car!" which is also a trivial observation.

 

[PureX]

It is not ignored.
According to the rules, Monty won't open the door you choose. He will also not reveal the car.

Then according to the rules, there is zero chance of winning the car by choosing one of three doors. Not a 1 in 3 chance. And not a 2 in 3 chance, either. Zero chance.

So, in the case that your first choice was a goat, Monty has no choice to ignore anything. He has only one option, to show you the other goat. That is what makes your first choice relevant and related to the second one.

But you can't know this, because you never find out what's behind the door you chose. If you don't know what's behind the door you chose, you can't know what's behind the other door that Monty didn't open. Monty does, but you still don't. All Monty's revealing one goat tells you is that there remains one goat and one car. But you still have no way of knowing which door hides which item.

You're trying to look at this 'from above', and not from the perspective of the person trying to win the car. But the whole purpose of determining the odds is that the contestant wins the car. The odds you're calculating are not related to the actual odds of the contestant trying to win the car. So it becomes an irrelevant math problem, devorced from the real world scenario it was intended to help illuminate.

There is no escaping the fact that choosing one of three doors has zero chance of the contestant winning the car. Yet you keep insisting that it gives the contestant a one in three chance of "picking the car". But picking the car or not picking the car is irrelevant when he is not allowed to know whether he picked the car, and he will not win the car whether he picked it or not. He learns nothing, and he gets nothing. This "pick" was completely irrelevant to his winning the car.

Why do you and others keep ignoring the blatant reality of this?