Women, math, and the Monty Hall problem

[Watchmen]

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.

Were you looking in the mirror when you wrote that?

 

[PureX]

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.

I have often wondered if any of the contestants on that show ever demanded to actually be given the goats.

 

[It Aint Necessarily So]

I was going to say exactly this, and with equal puzzlement.

Thanks for that.

Did you quote what you meant to quote? It sounds like you were responding to these words:

"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."

 

[Watchmen]

Well, to bring it back to the topic of the OP and thread title, I now can't help but wonder if PureX is misidentified on "his" bio and "he" is actually a woman given "his" misunderstanding of the math presented in the Monty Hall Problem. "He" must be a "she."

***I jest! I jest! Just keeping it light hearted while reminding folks of the OP***

 

[Subduction Zone]

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.

That "reasoning" makes no sense at all. No, if there is no switching the odds at set at the start at one in three. If one is given the chance to switch the odds of winning obviously become two out of three.

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.

The person making the choice has no clue. But you keep forgetting that Monty knows. he know that he can always show a goat no matter what the contestant picked. The "theater" is Monty revealing a goat. The choice is really "should I stick with the door I chose or should I switch it for what is behind the other two doors?"

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.

The person trying to win may be bad at math too. The actual odds are that if there is no switching allowed that the odds are one out of three that he will win. If switching is allowed and he switches to the other two doors the odds become two out of three that he will win.

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.

This is either very wrong or very poorly worded. The contestant has no clue as to where the car is. He does not know. Once again, Monty knows. And you are confused by the theater that you kept mentioning earlier. His odds are one out of three that he got the car and two out of three that he did not. Switching means that his odds of winning become two out of three.

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

Projection.

 

[Subduction Zone]

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.

Hopeless word salad. The last refuge of the clueless.

 

[Alien826]

Thanks for that.

Did you quote what you meant to quote? It sounds like you were responding to these words:

"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."

Yes, that was the intention.

Looking back, I think this is what happened. I highlighted the section I wanted to quote then right clicked on "reply", forgetting once again that my normal practice of setting up my response in a separate tab (I'm using Windows) only works when replying via the 'post reply" button. I do that so I can refer back to entire post while composing my response. I cussed under my breath, started again and obvious picked a different paragraph.

 

[PureX]

You seem to be saying now that the arguments resented are logically sound but don't apply to the problem at hand. As usual, you give not argument or explanation - just the claim.

What I am saying is that math is a language of ideological presumptions. We presume, logically, that 2 + 2 = 4. But although this makes sense logically, it tells us absolutely nothing about anything that matters in the real world unless and until we apply it to the real world. Yet in reality, no 2 things are truly equal. That is actually a logical impossibility. The only way two things could be truly equal is if they were the SAME thing. But then they would only be one thing, not two. So when we presume that 2 sheep and two more sheep equate to four sheep we are dismissing all the ways that any two sheep are NOT equal. And therefor that any number of sheep could be equal to any other number of sheep. The equation works perfectly when it exists as an unattached ideal. But for it to work attached to things in the real world we have ignore all the ways in which it doesn't work. Like how it cannot account for the inevitable differences between anything in the real world that it purports to combine, divide, eliminate, etc.,.

People that do not understand that math is not some sacred revelatory force lurking within reality become easily misled by exactly these kinds of misappropriations of the mathematical process. They give the process far more importance than it deserves or warrants. And they fight to maintain their own ignorance regarding how less than accurate mathematics can really be.

This 'puzzler' is a good example of this.

 

[PureX]

Hopeless word salad.

To the clueless, yes, I suppose it is.

 

[Subduction Zone]

To the clueless, yes, I suppose it is.

More projection. You do not understand the math. You do not like simulations. How would you test your claims? Others have shown how they would test theirs.

 

[9-10ths_Penguin]

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?

FWIW, the "Monty Hall Problem" isn't actually a scenario from the show.

I remember reading a summary of a discussion with Monty Hall about it. It was decades ago, but I remember something to the effect of how the specifics would work with Let's Make a Deal rules and he didn't actually have knowledge of what the right guess would ever be (to ensure a fair game, I assume).

The problem matches the general vibe of the show, but the specifics don't quite work, IIRC.

 

[It Aint Necessarily So]

FWIW, the "Monty Hall Problem" isn't actually a scenario from the show.

I remember reading a summary of a discussion with Monty Hall about it. It was decades ago, but I remember something to the effect of how the specifics would work with Let's Make a Deal rules and he didn't actually have knowledge of what the right guess would ever be (to ensure a fair game, I assume).

The problem matches the general vibe of the show, but the specifics don't quite work, IIRC.

I found and watched the end of an episode of Let's Make Deal on YouTube TV, so I can't include a link. It confirms what you and Monty say - the actual show doesn't resemble the format in the Monty Hall Problem.

I couldn't tell the year of the episode, but Monty was relatively young and thin, so probably the 70's. Two contestants got to choose doors.

It turned out that the first door was a weeklong vacation to Acapulco, MX plus $400 "tipping money", valued at $2500.

Door 2 was the most expensive prize, but not even double door 1. It was furniture and a color TV valued at $4200.

Door 3 was Monty's Cookie Jar, which contained $271. That was the only "goat," but not worthless.

The woman chose first and chose door 2. Good guess if you liked the furniture and TV more than the Mexican vacation. The man chose second, and chose door 1, which was the best he could have done.

Nobody was offered a chance to trade for the unchosen door, door 3. Monty revealed the $271 dollars in the Cookie Jar.

Then he looked to the man to reveal door two. The woman gasped, realizing that that meant that she had chosen the most valuable prize, which was then shown to her. That was it.