Do you know the correct answer?

[gypsie]

Is it Schrodinger's car?

permustation.jpg

[AnalogKid]

OK, here's a slightly more detailed version of how I grasped it.

There are two parts to the game, the initial choice and then the decision to swap or not. The crucial bit is what happens in between.

Lets play this out:

You make your first choice, get lucky and pick the car. You don't know it, but Monty knows it and shows you how lucky you were not to choose another door, one that he then demonstrates has a goat behind it. If you swap, you swap the car for the other goat.

Alternatively:

You make your first choice, and unfortunately pick one of the goats. You don't know it, but Monty knows it and shows you how lucky you were not to choose another door, one that he then demonstrates has the other goat behind it. If you swap, you swap your goat for the car.

I.E.

If you stick with your first choice then you are choosing between 1 car and 2 goats, and so have a 1 in 3 chance of picking the car.

If you swap your first choice then you have a 2 in 3 chance of choosing a goat and then swapping it for a car.

[Tom Montgomery]

no, let's not expose lee and paul in goat form.

lol!!

[Tom Montgomery]

.
I think last evening you were all being too hard on CWSmith. He told everyone upfront he had a long hard day at work and that his brain was fried. It was not a good time to pressure him.

[Beowolf]

Is it Schrodinger's car?

No…. That would be my ‘84 Chrysler Laser traveling downhill which appeared to be both running and not running at the same time.

[Boatbum]

Is Nick finally onboard or has he just given up? Don't see anything recently form him.

[Peerie Maa]

Is Nick finally onboard or has he just given up? Don't see anything recently form him.

That is because.

• There is really nothing to add to the "whiteboard" post
• I have been away from the 'puter between that post and now.

[rgthom]

Everyone is just repeating the same arguments and that includes me.

Until someone has a new idea, how about we let this go? Otherwise, we can just number the ideas we have (I think there are two and all the rest are just rephrasings of those two) and throw those numbers instead of doing all this typing.

Let me try something I do not think has been expressed yet. I will try to state it as simply as I can: Your table shows all the combinations, but does not account for probabilities.
When the player chooses a door without the car, Monty has only one choice of door with goat. The probability is 100% he will pick that door.
When the player chooses the door with car, Monty has two choices. Each has 50% probability.
Your table shows all combinations having equal chance. The lines you added have only half the probability of happening.

[Tom Wilkinson]

In a moment of clarity, I realised the key to working out the odds is that if you switch, you will always reverse your original choice.

From there - original choice has 1:3 chance of being right, so switching has a 2:3 chance.

Simples

^this

[Peerie Maa]

So, as yet, no one has tried to disprove post #469 with arguments that address #469.

All anyone has done is restated the original argument that #469 indicates is incorrect.

[Keith Wilson]

The whiteboard, how it should be.

My door = 1/3 chance of a car.
Monty's two doors = 2/3 chance of a car in one or the other, 100% chance of at least one goat.
Monty will always open the door with the goat. This step adds no new information, since we already knew that he had at least one goat.
The remaining door has a 2/3 chance of having the car.

[Dave Wright]

So, as yet, no one has tried to disprove post #469 with arguments that address #469.

All anyone has done is restated the original argument that #469 indicates is incorrect.

I think you and CW have simply been overwhelmed by a barrage of detail. You don't need multiple runs, you don't need tables or convoluted arguments, you don't need to think about Monte Hall or goats. A simple appeal to intuition should do the trick for both of you:

There is a car behind one of three doors.

When you pick one door you absolutely KNOW that there is a greater possibility that the car is actually behind one of the two remaining doors. You simply have to agree with this fact.

You also know that one of these two doors doesn't have a car.

When the door without a car is eliminated the remaining door still has a higher probability of having a car than the door you picked. Once you see this you know what to do.

You switch from your initial pick to this remaining door.

Relax and think about it and it will come to you.

[Peerie Maa]

I think you and CW have simply been overwhelmed by a barrage of detail. You don't need multiple runs, you don't need tables or convoluted arguments, you don't need to think about Monte Hall or goats. A simple appeal to intuition should do the trick for both of you:

There is a car behind one of three doors.

When you pick one door you absolutely KNOW that there is a greater possibility that the car is actually behind one of the two remaining doors. You simply have to agree with this fact.

You also know that one of these two doors doesn't have a car.

When the door without a car is eliminated the remaining door still has a higher probability of having a car than the door you picked. Once you see this you know what to do.

You switch from your initial pick to this remaining door.

Relax and think about it and it will come to you.

Have you read #469?
Address the arguments in that explanation rather than repeating fallacious statements, again.
If there are two options, and you do not have any information telling you which of the two is correct, what are the odds?

[Dave Wright]

Have you read #469?
Address the arguments in that explanation rather than repeating fallacious statements, again.
If there are two options, and you do not have any information telling you which of the two is correct, what are the odds?

You might eventually be able to use your thoughts here to evaluate many aspects of the way you think.

[Keith Wilson]

Have you read #469??

Have you read 595??

[George.]

Have you read #469?
Address the arguments in that explanation rather than repeating fallacious statements, again.

I read it. There is a logical flaw. There is no such thing as Monty's door. He doesn't choose it until after you have chosen, and he deliberately chooses one with a goat from two possibilities.

When you first choose, the probability is the same for all three doors. Your door gets 33%, and Monty's two doors get 33% each. Once Monty opens one of his doors, the odds between them resolve to 0% for the open door and 66% for the closed door.

[Boatbum]

Nick:

I think it is great that you stick to your guns against overwhelming odds, but it I think it is time to try to disprove your own theory rather than to try to disprove everyone else's. For the sake of intellectual honesty, start with the assumption that you are wrong: Try to find out why that might be the case

[twodot]

The puzzle was solved on page one. The new puzzle is how to get two posters to understand it. It is a vexing puzzle and appears to be unsolvable.

[Decourcy]

It seems to me (and I may be wrong as I’m just, as I’ve said, a wood butcher) that the 50-50 rule only works if the host doesn’t know what’s behind any door either, and has to randomly choose between the two doors that he has, with all doors then revealed after the choices are made.

[Boatbum]

Meantime... one more time... a rough approximation - in graphic form - of 'good news sources'. Ranked for both ideological slant and factual reliability ---

I do recall you posting it before, but according to it the NYT would be one of the trusted neutral sources and if you had taken the time to read my earlier criticism of the NYT you might understand why my feelings about the precision of this chart may be questionable.

There are many criticisms of the Fonts Media chart from the left and the right. My complaint is that among other things it oversimplifies to the point of being useless.


Here is one critique the I find particularly useful.

Mainstream or Utter Garbage?
Another flaw of the balanced, pyramid structure of The Chart is that it fails to take into account the centralization of the media landscape, as described in the Propaganda Model. The corporate monopolizing that we see in the US media, rather than furnishing us with diverse viewpoints across a variety of sources, has collapsed our media ecosystem into a small set of acceptable views, portrayed by dozens of sources that differ only aesthetically. Our media ecosystem, put bluntly, presents an “illusion of choice,” oriented largely to the benefit of a pro-business status quo.

What’s the objective?
Also worth noting is how the “objective, view from nowhere” standard that The Chart reinforces was developed by and for white, cis males, and that enforcing that “neutral” POV can often be fundamentally inequitable..

Consider when a reporter for the City Desk program in Chicago accused Malcolm X of being “personally prejudiced” and incapable of being “academic” in his arguments regarding the Ku Klux Klan, simply because they had burned down his home and murdered his father. Or more recently, when Black journalist Wesley Lowery revealed how he had been “muzzled” by editors at the Washington Post.
In the wake of these events, Lowery has written compellingly on the failures of our current conception of “objectivity” in newsrooms, a conception that The Chart fortifies by design.

The problems of source as shorthand
While the outlet providing an article is certainly an essential consideration when it comes to evaluation, we reject that it is the most important indicator. A media company is not a monolith, but an organization of people. Divergence from editorial direction is common. When the NYT published Senator Tom Cotton’s opinion piece calling for the military be sent in to control protests, or the Wall Street Journal’s Op-Ed questioned Dr. Jill Biden’s use of the “Doctor” title, journalists at both organizations spoke out against pieces.

Sources are also divided into different areas, with different specializations and audiences.This makes it very difficult to generalize a source’s credibility. For example, Buzzfeed and Teen Vogue have published excellent political reporting while also drawing eyeballs through listicles and pop culture pieces.
The simple layout of The Chart does not allow for this kind of context or nuance.

https://acrlog.org/2021/02/23/comple...omment-page-1/

[George Jung]

Sure.

You have a better idea?

[Boatbum]

Sure.

You have a better idea?

Well, originally I was asking Paul Pless for his viewpoint. David G decided to be a part of the discussion and pasted (as he likes to do) this chart. I was trying to have a conversation David G was trying to end one.

[Paul Pless]

one thing i'd like to reinforce about my viewpoint is the importance of consulting multiple sources
and if your view is that the nyt is somewhat left then my suggestion of 'the economist' should easily offset that

[Boatbum]

one thing i'd like to reinforce about my viewpoint is the importance of consulting multiple sources
and if your view is that the nyt is somewhat left then my suggestion of 'the economist' should easily offset that

Fair point. Seems like many like Reuters and AP which more likely give the facts without analysis though it is still possible to slant opinion by what you choose to report and leave out.

[George Jung]

Sorry; I guess my take was one you've now answered. I expect it's really quite difficult to not bring at least part of one's perspective into reporting, but - some seemingly are better than others. As you, and Paul have noted - look at multiple sources.
'The Truth' is in there, somewhere.

[coelcanth]

Nick,
your diagram in post #469 is of a different game, or at least is a diagram of only the second half of this game, AFTER the player has already chosen their first door.

your diagram is correct in that we know, yes, at this point in the game the player has a 1 in 2 chance of picking door One and a 1 in 2 chance of picking door Three.
they will never pick door Two because Monty has opened it, as you show. that much is indisputable.

but, it's what's BEHIND either door that matters for the FINAL outcome of the TOTAL game
behind door One is a 1 in 3 chance of there being a car (remember ?? we chose that door from a pool of THREE possibilities !)
sometimes there will be a car, but more often there will be a goat

behind door Three there will be a 2 in 3 chance of finding the car !

but how can that be if there are only two doors left in the game ?? because the door that Monty opened is always a goat door. we always knew that it would be.
but the fact is, Monty HAD two doors, and he simply opened one that was not a winner. one of his doors always has to contain one goat. but when he did have the two doors of three, his piece of the pool was bigger and that is simply why the winner is 66% likely to be behind one of his doors.

[George Jung]

Looks like this thread - fun as it was - is damn near on life support.

[Boatbum]

Nick,
your diagram in post #469 is of a different game, or at least is a diagram of only the second half of this game, AFTER the player has already chosen their first door.

your diagram is correct in that we know, yes, at this point in the game the player has a 1 in 2 chance of picking door One and a 1 in 2 chance of picking door Three.
they will never pick door Two because Monty has opened it, as you show. that much is indisputable.

but, it's what's BEHIND either door that matters for the FINAL outcome of the TOTAL game
behind door One is a 1 in 3 chance of there being a car (remember ?? we chose that door from a pool of THREE possibilities !)
sometimes there will be a car, but more often there will be a goat

behind door Three there will be a 2 in 3 chance of finding the car !

but how can that be if there are only two doors left in the game ?? because the door that Monty opened is always a goat door. we always knew that it would be.
but the fact is, Monty HAD two doors, and he simply opened one that was not a winner. one of his doors always has to contain one goat. but when he did have the two doors of three, his piece of the pool was bigger and that is simply why the winner is 66% likely to be behind one of his doors.

Well said

[jpatrick]

What are the odds in this scenario: Contestant makes choice. Let's say he open door A ... Monty opens a door that isn't door A ... There are now two doors that are unopened. Monty brings in a new contestant who hasn't been watching. He tells the contestant they can have the item behind door A or choose the other unopened door and take that item. He says one item is a car and the other is a goat. What are the odds for the new contestant?

I think those odds are 50/50. If that's right, then the first contestant ought to be able to get those odds also. But maybe to do so, the first contestant has to flip a coin in order to reset their brain from the original problem?

It's all very confusing, I admit. And frustrating because I've long forgotten the math skills I thought I'd have forever. sigh........ Maybe we're all goats, in the end?

Jeff

[coelcanth]

the first contestant cannot possibly have the same odds because when he chose his door there were more goats in the mix !!
nobody can have 50/50 odds for that matter, because when the door first was chosen its odds were set in stone !
the odds then were 1 in 3 that a CAR would be behind that door, and so they remain

[Paul Pless]

Looks like this thread - fun as it was - is damn near on life support.

i hope tom comes up with a new challenge for us each sunday
gonna be hard to top this one though
he has set the bar high right out of the gate

[birlinn]

the first contestant cannot possibly have the same odds because when he chose his door there were more goats in the mix !!
nobody can have 50/50 odds for that matter, because when the door first was chosen its odds were set in stone !
the odds then were 1 in 3 that a goat would be behind that door, and so they remain

In which case, surely there is a 1 in 3 chance there is a car behind the door?
And there was a 2 in 3 chance of there being a goat at the start?

[peb]

If you switch, you only lose if you had chosen correctly. You had a 33% chance of that. It's is as simple as that. Cannot be explained better.

[twodot]

If you switch, you only lose if you had chosen correctly. You had a 33% chance of that. It's is as simple as that. Cannot be explained better.

Very nice, a less than twenty word proof.

[Tom Montgomery]

Nick:

I think it is great that you stick to your guns against overwhelming odds, but it I think it is time to try to disprove your own theory rather than to try to disprove everyone else's. For the sake of intellectual honesty, start with the assumption that you are wrong: Try to find out why that might be the case

Or actually play the game 50 or 100 times as I did and then try to figure out why you get the results you will certainly get.