Finally - A Monty Hall Problem Explanation that makes sense, even to me!

[Arnold]

Everyone +/- 0.5%

That would be somewhere between 99.5% and 100.5% team_v ... No wonder you have stuck with 50/50 for the Monty Hall Problem.

[ParaBul]

I think this thread can be closed as it is not providing any benefit to forum members who joined to learn more about the brand and their cars.

This is General Discussion, in the General Section, "where you can have your say on anything that doesn't fit in the other sections."

(Emphasis has been added for the purposes of this post).

Nothing about "the brand" or "cars".

If you can't comprehend this then you have no chance with the Monty Hall Problem. Move along - you have nothing to see here.

[team_v]

That would be somewhere between 99.5% and 100.5% team_v ... No wonder you have stuck with 50/50 for the Monty Hall Problem.

It allows for anomalies in the data and statistics and is used regularly in most circumstances.

This is General Discussion, in the General Section, "where you can have your say on anything that doesn't fit in the other sections."

(Emphasis has been added for the purposes of this post).

Nothing about "the brand" or "cars".

If you can't comprehend this then you have no chance with the Monty Hall Problem. Move along - you have nothing to see here.

There has to be some sort of logical limit.
I.e. you don't go and drink 15L of Coke per day just becasue they don't tell you not to....

Arnold and yourself are the only ones who seem interested enough in this discussion and you both came to your conclusions so there is no point in keeping it going in my opinion.

Arnold only keeps this thread alive by posting information he recevied from other people since no one else is respondingin the thread.

[ParaBul]

There has to be some sort of logical limit.

Why?

Arnold and yourself are the only ones who seem interested enough in this discussion and you both came to your conclusions so there is no point in keeping it going in my opinion.

Why does this affect you? We may be the only two posting, but how many may be silently reading? If you're no longer interested, why do you keep coming back?

I'm not denying you your right to an opinion, but I don't understand why you keep posting it when we've acknowledged it, and indicated we don't care.

Arnold only keeps this thread alive by posting information he recevied from other people since no one else is respondingin the thread.

Again, why does this affect you? You seem like the schoolyard bully - two kids are having fun playing a game that you're not interested in, and you're determined to stop them. Why?

You want to shut this thread down because you think it will degenerate into an argument? So far, you're the one trying to start an argument. Perhaps if you go away, this thread will die a quiet death in its own good time?

[Arnold]

The majority.

The breadth of topics on this Forum is so great that it is highly unlikely that more than a very small percentage of threads would be of interest to a majority of forum members.

I am sure you're expected to apply more intellectual rigour than that when giving reasons on behalf of clients in SEPP1 Objections so why not display the same degree of integrity in all aspects of your reasoning?

[Ideo]

The breadth of topics on this Forum is so great that it is highly unlikely that more than a very small percentage of threads would be of interest to a majority of forum members.

I am sure you're expected to apply more intellectual rigour than that when giving reasons on behalf of clients in SEPP1 Objections so why not display the same degree of integrity in all aspects of your reasoning?

Because you're not paying me $200 an hour.

[Arnold]

Everyone +/- 0.5%

I think this thread can be closed as it is not providing any benefit to forum members who joined to learn more about the brand and their cars.

You think this thread should be closed even though it may be of interest to people who joined primarily to learn about VWs but enjoy a broader range of topics that might expand their horizons and stimulate their thinking.

On the other hand, I think this thread should remain open because it has every right to exist in this section, is of interest to an unknown number of people and, apart from which, increases the number of page impressions for banner advertising that helps sustain this as a free forum.

As ParaBul says, not everyone who is interested makes a comment and many many members showed interest and, indeed, fascination with the original Monty Hall (Winning a GTI on a Game Show) thread.

It allows for anomalies in the data and statistics and is used regularly in most circumstances.

Yes, a confidence interval is useful in statistics, but your comment about "everyone" was a generalisation based not on any data or statistics but on your disdain for this thread, which you assume is shared by "everyone".

There has to be some sort of logical limit.
I.e. you don't go and drink 15L of Coke per day just becasue they don't tell you not to....

Your analogy is a curious one as many threads go for hundreds of pages without any "logical" limit and still others idle away with much less interest than this one, their size and the number of readers and contributors self-regulating, as they should.

A better analogy, in terms of your attempts to prevent others on this forum from discussing what interests them, would be that while people would agree that the heavy Coke drinker should not be allowed to force you to drink Coke, very few, if any, in a free society would suggest imposing a legal limit on their consumption, even in the face of such headlines:

Too much Coca-Cola killed mother: coroner

Of course there are much stronger arguments for limiting people's sugar consumption than there are for limiting what people discuss in a civil manner, even if a handful of people take such objection to them doing so.

Arnold and yourself are the only ones who seem interested enough in this discussion and you both came to your conclusions so there is no point in keeping it going in my opinion.

How did you come to that conclusion? A lot of threads have fewer comments and fewer views than this one, which has attracted nearly 1000 views so far.

Arnold only keeps this thread alive by posting information he recevied from other people since no one else is respondingin the thread.

There's a paradox!

But instead of sending off-topic posts containing spurious reasons for closing this thread, why not apply your acuity to explaining to all of the poor mistaken "33/67" souls how the Monty Hall Problem provides 50/50 odds in the "two-door" phase of the game even though you have acknowledged that a person sticking with their first choice in a one-in-three type game will only win 33 times in a hundred?

Surely, if it is 50/50, the contestant would win 50 times in a hundred, and in the card game analogy this would be evidenced by the contestant's marker being found on 50 Aces if left on their original selections, not the 33 Aces on which you've agreed it would be found.

It would be a shame if you were unwilling or unable to articulate your reasons in support of 50/50 as shamelessly as you have put your arguments for this thread being closed.

[Arnold]

... why not display the same degree of integrity in all aspects of your reasoning?

Because you're not paying me $200 an hour.

Noted, with thanks.

PS - Everyone comments voluntarily on this forum and yet presumably aims to conduct themselves with integrity, despite not being paid to do so.

[Arnold]

And here is an explanation with which even team_v should not have an issue:

When the number of doors / playing cards is reduced to two, the contestant has a 50% chance of picking the winning door / Ace if they do so randomly.

While their first pick has a 33% chance of being a winner and the other door / card a 67% chance of being the winner, if the contestant played the game 100 times and at random variously switched from and stuck with their first choice so that half the time they switched and half the time they stuck, they would, on average, win 50% of the time.

However:

A contestant that always stuck with their first choice would, on average, win 33% of the time; and

A contestant that always switched to the other door / card would, on average, win 67% of the time.

So each contestant's chances of winning depend on how they choose to play the game (randomly/emotionally or logically).

However, in this game, the probability of each of the two options are an uneven 33/67 not an even 50/50, just as the probabilities are uneven in many situations even though there are only two possible outcomes (e.g. Federal elections, tennis matches etc etc) where the 100% probability of one of them winning (presuming a draw is not possible) is not divided evenly between each of the two possible outcomes even though a random guess will deliver a punter a 50% chance of success if repeated enough times, i.e. over enough contests/games.

Hopefully that is an explanation that makes sense to anyone who still thinks each of the two remaining doors / playing cards has an even or 50/50 chance of being the winner.

Anyone who still does not understand feel free to send another PM.

[Arnold]

Hey Scotty (Buller_Scott) and Team_v

I was wondering if the penny had dropped with either of you two given you have been among the strongest proponents of the 50/50 argument on the various Monty Hall threads. Not that there is anything wrong with that, although I noticed that Rocket36, once of the most vociferous objectors to the correct answer (impugning people's intelligence) changed his handle! Not sure to what name.

One of the nice things about this thread is that, being based on pure logic, unlike most threads here, there is actually a right answer. As proponents of the wrong answer in the various threads, I was wondering if you had turned the corner. In case not, here is one more attempt at an explanation, personalised for someone in the market for a $10k car (which itself is a sign of intelligence):

There are three doors and behind one is a $10k car and each of the other two doors conceals a goat.

Picking randomly, you therefore have a 33% chance of getting a $10k car and 67% chance of a getting a goat.

If you play this game 100 times by picking a door and sticking with that choice, you should, on average, win 33 cars, right?

If, after you have randomly picked one of the three doors, you learn which one of the doors conceals one of the two goats but stick with your first choice, you will still win 33% of the time, right? Or, if all three doors get blown open simultaneously, you'd still win 33% of the time as the order in which the doors are opened does not affect the chances of your first pick being right. Probability is still 1 / number of doors, right?

However, each of you has argued in various threads that once you know which one of the two doors conceals one of the two goats, the probability of picking the winning door goes to 50/50. That is, you have argued that, because there are only two doors remaining, the door you randomly picked from three options now has a 50% chance of being the winner.

But how do your chances of winning go from 33% to 50% just because you find out that one of the other two doors conceals a goat? You already knew that one of those doors concealed a goat and this has not changed.

Do you truly believe that you will win 50 cars in 100 attempts at a 1 in 3 random guess just because one of the goat doors is opened early but only 33 cars if all of the doors are opened simultaneously?

Are you able to explain how the early opening of one of the goat doors effectively converts 17 goats into cars (when the game is played 100 times) to increase the number of successful first picks from 33 to 50 (and increase the probability from 1 in 3 to 1 in 2)?

I only ask because even people who stridently object to the correct answer to the Monty Hall Problem are eventually struck by the inescapable logic of the correct answer and I was wondering if, after all of this time, you had experienced that pleasurably heady mix of enlightenment and humility upon realising the correct answer.

Or can you explain how, in 100 plays of the game, 17 goats change into cars when one of the goats is revealed early in order to provide 50 wins in 100 instead of the statistically expected, and probable, 33 wins in 100?

If this does not make sense, think of 100 sets of triplets of cards comprising two Jokers and one Ace face down on a table. Randomly nominate one triplet from each. You'd expect to have picked the Ace 33 times. Does this somehow change to 50 times if the "host" reveals one Joker from each triplet and gives you the chance to switch from your original choice?