Women, math, and the Monty Hall problem

[Heyo]

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.

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?

Because the Monty Hall Problem "is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal".
It's pure maths, based on a scenario from the show.

Is it that why you went wrong?

 

[anotherneil]

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.

I did 30 rounds & yup, it came up with exactly 2/3 wins from switching doors:

 

[PureX]

Because the Monty Hall Problem "is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal".
It's pure maths, based on a scenario from the show.

Is it that why you went wrong?

It's only a "brain teaser" because the math is divorced from it's intended purpose, and most people don't see this. So they are puzzled by how the math can seemingly defy the logic of reality. And the answer is that math is not real. It's fundamentally representational symbolism, like language.

2 + 2 = 4 is completely devoid of meaning or value until it is applied to something real. The logic 'works' but there is no purpose to it. The same is true of words. And just as we can arrange a set of words that make sense together but tell us nothing, we can arrange a set of numbers and functions that give us a result but that relates to nothing real.

When we assume that we have a 1 in 3 chance of winning the car we are divorcing the mathematics from the reality it was intended to represent. The equation will still produce a result, but the result is no longer related to the reality it was intended to represent. And when people don't realize this is what is happening, they become 'mystified' by it.

That's what is happening here. Then the self-righteousness of ego gets involved and people become intractable 'believers' in their own righteousness no matter what. It become impossible for them to see any other possibility.

 

[anotherneil]

It's only a "brain teaser" because the math is divorced from it's intended purpose, and most people don't see this. So they are puzzled by how the math can seemingly defy the logic of reality. And the answer is that math is not real. It's fundamentally representational symbolism, like language.

2 + 2 = 4 is completely devoid of meaning or value until it is applied to something real. The logic 'works' but there is no purpose to it. The same is true of words. And just as we can arrange a set of words that make sense together but tell us nothing, we can arrange a set of numbers and functions that give us a result but that relates to nothing real.

When we assume that we have a 1 in 3 chance of winning the car we are divorcing the mathematics from the reality it was intended to represent. The equation will still produce a result, but the result is no longer related to the reality it was intended to represent. And when people don't realize this is what is happening, they become 'mystified' by it.

That's what is happening here. Then the self-righteousness of ego gets involved and people become intractable 'believers' in their own righteousness no matter what. It become impossible for them to see any other possibility.

Are you going to test it out for yourself, or not?

 

[PureX]

Are you going to test it out for yourself, or not?

Your "test" is just a flawed equation that produces the result it was designed to produce. But you can't see or accept this because you are a "true believer", now. Your ego won't allow your brain to consider that it might be devorced from the reality it was originally intended to represent.

 

[ImmortalFlame]

Your "test" is just a flawed equation that produces the result it was designed to produce. But you can't see or accept this because you are a "true believer", now. Your ego won't allow your brain to consider that it might be devorced from the reality it was originally intended to represent.

So, you think all of mathematics is a conspiracy theory designed to personally annoy you? And you think it's "our ego" that allows us to accept a widely understood and easily provable mathematical phenomenon, whereas your inability to accept this easily demonstrable fact despite dozens of people explaining it to you and it being accepted by all the world's mathematicians and your insistence that we believe it only because we are weak-minded egotists is... your incredible humility?

I don't know why I continue to try and drain this rock of blood...

 

[9-10ths_Penguin]

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.

FYI: there are only 18 possibilities here (3 doors to choose from × 3 places for the car x 2 options for switching or not). It would be easy enough for you to throw this into a spreadsheet and see whether your bad assumptions are correct.

 

[Heyo]

FYI: there are only 18 possibilities here (3 doors to choose from × 3 places for the car x 2 options for switching or not). It would be easy enough for you to throw this into a spreadsheet and see whether your bad assumptions are correct.

For that, @PureX would have to know what a spreadsheet is. At the current stage of debate, I doubt that.

 

[PureX]

So, you think all of mathematics is a conspiracy theory designed to personally annoy you? And you think it's "our ego" that allows us to accept a widely understood and easily provable mathematical phenomenon, whereas your inability to accept this easily demonstrable fact despite dozens of people explaining it to you and it being accepted by all the world's mathematicians is... your incredible humility?

I don't know why I continue to try and drain this rock of blood...

Math is just a logic system. But logic is meaningless by itself. It has to be applied to something real, to matter. The logic system functions, but has no meaning or purpose, unapplied. Or wrongly applied. Which is what is happening here. The logic functions, but it is bevorced from the reality it is supposed to be related to. But some of you are SO enamored with the logic of the math that you can't see that it's meaningless, because it has been separated from it's intended purpose.

 

[Heyo]

It's only a "brain teaser" because the math is divorced from it's intended purpose, and most people don't see this. So they are puzzled by how the math can seemingly defy the logic of reality. And the answer is that math is not real. It's fundamentally representational symbolism, like language.

2 + 2 = 4 is completely devoid of meaning or value until it is applied to something real. The logic 'works' but there is no purpose to it. The same is true of words. And just as we can arrange a set of words that make sense together but tell us nothing, we can arrange a set of numbers and functions that give us a result but that relates to nothing real.

When we assume that we have a 1 in 3 chance of winning the car we are divorcing the mathematics from the reality it was intended to represent. The equation will still produce a result, but the result is no longer related to the reality it was intended to represent. And when people don't realize this is what is happening, they become 'mystified' by it.

That's what is happening here. Then the self-righteousness of ego gets involved and people become intractable 'believers' in their own righteousness no matter what. It become impossible for them to see any other possibility.

So, you are basically a "maths denier"? You don't believe in abstracting problems or in applying mathematical abstractions to real world problems?

 

[anotherneil]

Your "test" is just a flawed equation that produces the result it was designed to produce.

Wait - is this your way of conceding that the OP is right without having to "concede"?

But you can't see or accept this because you are a "true believer", now.

Nope; I can see or accept this, if it's your way of conceding that the OP is right.

Your ego won't allow your brain to consider that it might be devorced from the reality it was originally intended to represent.

Well, I don't know about that; all I know is that the probability of winning is 2 in 3 by switching doors.

You didn't answer my question: Are you going to test it out for yourself, or not?

Don't use that website's simulator if you don't trust it; set it up for yourself and test it out.

To everyone else: I would like to implore that you please refrain from engaging or continuing to engage in discussion with anyone who doesn't test it out for themselves other than to repeatedly ask them to test it out for themselves, until they come to the realization that this is how science/truth/knowledge/reality works and have no other choice but to test it out for themselves (or run away), otherwise this is just going to go on endlessly.

 

[anotherneil]

For that, @PureX would have to know what a spreadsheet is. At the current stage of debate, I doubt that.

Please, let's not engage in such petty put-downs; I want anyone who's skeptical or doubtful to genuinely test it out for themselves to see what the results are.

 

[ImmortalFlame]

Math is just a logic system. But logic is meaningless by itself. It has to be applied to something real, to matter. The logic system functions, but has no meaning or purpose, unapplied. Or wrongly applied. Which is what is happening here. The logic functions, but it is bevorced from the reality it is supposed to be related to. But some of you are SO enamored with the logic of the math that you can't see that it's meaningless, because it has been separated from it's intended purpose.

You can literally demonstrate that this is true in reality. Are you seriously claiming that the Monty Hall problem cannot be demonstrated?

 

[ImmortalFlame]

Please, let's not engage in such petty put-downs; I want anyone who's skeptical or doubtful to genuinely test it out for themselves to see what the results are.

It's a good sentiment, unfortunately the most important operative word in that sentiment is "genuinely". There are, sadly, some people who are so invested in a specific way of thinking that they will deny any genuine demonstration as in-genuine in some capacity. See above where even a simulation designed to replicate the Monty Hall problem is written off as based on a "flawed equation".

I prefer your optimism to cynicism, though. I would prefer to believe that there is the capacity for reason in all people.

 

[Stevicus]

Because the Monty Hall Problem "is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal".
It's pure maths, based on a scenario from the show.

Is it that why you went wrong?

I think that pretty much nails it: It's a brain teaser. It's not a real life situation, and I can't even imagine what real life applications this could be useful for. Maybe a shell game or three-card Monte, but even among gamblers, those games have a reputation for being notoriously crooked.

I don't think it really matters all that much. Getting a goat isn't that bad. You could sell it and make a few hundred, or maybe keep it as a pet.

 

[anotherneil]

It's a good sentiment, unfortunately the most important operative word in that sentiment is "genuinely". There are, sadly, some people who are so invested in a specific way of thinking that they will deny any genuine demonstration as in-genuine in some capacity. See above where even a simulation designed to replicate the Monty Hall problem is written off as based on a "flawed equation".

I prefer your optimism to cynicism, though. I would prefer to believe that there is the capacity for reason in all people.

Yeah, that's ok; it just reveals to their followers/readers what the deal is.

 

[Heyo]

I think that pretty much nails it: It's a brain teaser. It's not a real life situation, and I can't even imagine what real life applications this could be useful for. Maybe a shell game or three-card Monte, but even among gamblers, those games have a reputation for being notoriously crooked.

I don't think it really matters all that much. Getting a goat isn't that bad. You could sell it and make a few hundred, or maybe keep it as a pet.

The real world application is to show how unreliable our intuition is, especially when it comes to probabilities.
And in the context of a maths lesson, it can introduce to Bayesian probability.

 

[It Aint Necessarily So]

The logic functions, but it is bevorced from the reality it is supposed to be related to.

You seem to be saying now that the arguments presented are logically sound but don't apply to the problem at hand. As usual, you give no argument or explanation - just the claim.

The real world application is to show how unreliable our intuition is, especially when it comes to probabilities.

You might find this comment and thread interesting and/or useful: What is intuition and how important is it?

To everyone else: I would like to implore that you please refrain from engaging or continuing to engage in discussion with anyone who doesn't test it out for themselves other than to repeatedly ask them to test it out for themselves, until they come to the realization that this is how science/truth/knowledge/reality works and have no other choice but to test it out for themselves (or run away), otherwise this is just going to go on endlessly.

I'd like to accommodate you, but that doesn't comport with my agenda here, which is to address the inconsistencies in his posting for the benefit of those who enjoy this kind of analysis and commentary. I don't do that for him, at least not anymore, as there is no way to help this person.

Also, he's made it clear that he has no interest in running simulations. He has a belief that is impervious to counterevidence. You cannot change that mind. That should be clear. Therefore, continued posting ought to be for a different reason. Here's a bit more on mine:

This is a fascinating phenomenon to behold and well worth discussing, although PureX cannot benefit from such a discussion given the confirmation bias he's built to defend his erroneous beliefs. That's the sine qua non of a confirmation bias - it cannot be penetrated with evidenced argument. We see it continually with the creationists, flat earthers, Covid anti-maskers and antivaxxers, stolen 2020 election proponents and MAGA thought about Trump. They are all impervious to sound, evidenced counterargument.

Of course, there's always the possibility that he's been trolling from the outset or that he's realized his error somewhere along the line and is too proud to admit it and too stubborn to stop arguing, but I'm proceeding as if he is simply unable make progress due to a cognitive problem. In other words, I'm giving him the benefit of the doubt that he's not being dishonest, that he believes what he says.

Isn't that always the dilemma on this site - is this person sincere and deluded or trolling?

More on my reasons for responding to his posts: What distinguishes this poster from most of the rest for me and increases the fascination factor is that most of the people who fit into any of the above categories almost never say anything that one would call informed or insightful and can't make or understand a sound argument, but this one does when discussing politics, economics, and current events. There is no other poster on RF with whom I agree regularly in one arena and never or almost never in another.

And that is another reason I give him the benefit of the doubt. Why troll the gallery in some arenas but not others? If one likes to troll in this one, why not in those other areas, which some others like to troll in? Why make outrageous comments about math but reasonable ones elsewhere? I say outrageous because it's not just that he doesn't get it. He makes comments such as that nobody ever wins, that there is no chance of winning, and that the simulations are designed to deceive.

*****

On confirmation bias:

In the link below one will find an excellent description of confirmation bias from a YEC who went to university, became a geologist, and became an OEC. Somehow, his experience at university pierced through and he finally saw what he had never seen before. He describes it using the literary device of a demon similar to Maxwell's demon and Descartes demon, which chose what ideas he would be allowed to see and which didn't get in.

I find him sincere and compelling.

The Talk.Origins Archive Post of the Month: February 2002

From the link: "Those who try to help the poor victims escape the ravages of Morton's demon wear themselves out typing e-mails explaining data and facts which never get through the demon's gate."

Sound familiar?

 

[Alien826]

This is a fascinating phenomenon to behold and well worth discussing, although PureX cannot benefit from such a discussion given the confirmation bias he's built to defend his erroneous beliefs. That's the sine qua non of a confirmation bias - it cannot be penetrated with evidenced argument. We see it continually with the creationists, flat earthers, Covid anti-maskers and antivaxxers, stolen 2020 election proponents and MAGA thought about Trump. They are all impervious to sound, evidenced counterargument.

I was going to say exactly this, and with equal puzzlement. I have developed a great respect for @PureX in these areas you list and had a number of very frustrating interactions with him when he gets into this area. Somehow I keep thinking that his demonstrated logical thinking will break through in this discussion if I keep trying.

@PureX, if you are reading this, I'm trying to register a genuine admiration for you (most of the time) and a continuing puzzlement when this area emerges.

 

[PureX]

So, you are basically a "maths denier"?

So, you basically can't read what's in front of you?

You don't believe in abstracting problems or in applying mathematical abstractions to real world problems?

That's what math is for. But once the math becomes divorced from the reality it's supposed to be used to represent, it becomes an empty logical 'circle-jerk'. When you insist that you have a 1 in 3 chance of "picking the car" when in fact you have zero chance of winning the car, you have divorced the math from the reality of the ACTUAL challenge, and it becomes just a useless logic exercise.