Monty Hall Dilemma - Winning a GTI on a Game Show

[Jarred]

You're taking this all very serious arent you Dubya?

Was monty hall a great uncle of yours or something?!

[Rocket36]

Bottom line is, Rocket has said:

He has a 50/50 chance yet he would still switch, but without providing his rationale for doing so.

STOP MISQUOTING ME!!! I have NEVER said the chance of WINNING THIS SCENARIO is 50/50. ALL I have said is that when there are two choices to pick from and you can only pick one, that you have a 50/50 chance of picking the car. AND THAT IS TRUE!!! The chances of winning based on ANY other information are not a factor in that. And I have not once said I would switch based on a 50/50 chance.

If you can't read what I'm saying, don't respond.

[Dubya]

STOP MISQUOTING ME!!! I have NEVER said the chance of WINNING THIS SCENARIO is 50/50. ALL I have said is that when there are two choices to pick from and you can only pick one, that you have a 50/50 chance of picking the car.

And if you pick the car you win, so a 50/50 chance of winning, is what Rocket is saying, if one may be so bold.

Or is Rocket suggesting that "winning" and "picking the car" are not the same?

Or that a 50/50 chance of picking the car does not mean a 50% probability of winning the car?

No wonder people are confused.

AND THAT IS TRUE!!! The chances of winning based on ANY other information are not a factor in that. And I have not once said I would switch based on a 50/50 chance.

But previously:

If I was playing this particular game, I would switch (obviously). That doesn't change the fact that out of two options, the chance of picking one is 50% or 50:50 or 1 in 2.

More confusion.

So on what statistical basis would Rocket switch?

Rocket has already explained how one's chances of picking the car (aka "winning") are 50/50, so why would Rocket switch?

If you can't read what I'm saying, don't respond.

I have no idea what Rocket's position is or the distinction he is attempting to make.

However, once and for all:

Can he kindly explain why he would swtich?

Can he explain what the probabilities are of winning the car:

- if he switches? and

- if he sticks with his initial guess?

That is what this thread is all about.

50/50 does not come into it in terms of "chance" or anything else.

So why does Rocket keep saying there is a "50/50 chance".

And why does Rocket not answer the question or explain why he would "obviously" switch?

All we have seen is 50/50 - nary a mention of 1/3 and 2/3 chances after the first goat is revealed, strongly suggesting Rocket does not subscribe to the theorem that switching after the first goat is revealed doubles the contestant's chances from 33% to 67%. A principle with which Rocket appears to have been arguing against from the outset.

[Rocket36]

OH... MY... GOD...

Pick ONE of these options only:

A or B.

Picked one? OK... You had a 50/50 chance of picking whatever you picked.

Pick ONE of these options only:

Card A (with the car) or Card B (with the goat).

Picked one? OK... You had a 50/50 chance of picking whatever you picked. STOP THINKING ABOUT THE FACT YOU STARTED WITH 3 CARDS!!! That way you might have a chance at understanding this exceedingly basic concept I'm explaining. The fact you have additional information that means you are more likely to pick what you want out of those two, doesn't change the fact that you can only pick ONE OUT OF TWO!

If you still don't get it, then I suggest registering for some primary school classes... I'm done.

[Timbo]

Rocket -- of course we all understand that. Don't be so precious. This is about chances in a game with rules. These rules affect the chances associated with choices at different points in the games, since you are given, not one choice, but two

The game doesn't start with two doors; it starts with three, and you are told that behind one of the doors is a car, and behind the other two are goats. You are asked to pick one door. At this point, your chances of picking a goat are 2 in 3, and of the car, 1 in 3. You pick a door.

The host now picks one of the other two doors, opens it, and reveals a goat. The host knows what is behind each door and the rule is that he'll always reveal a goat.

The host then asks you if you want to keep your original chosen door, or change to the remaining door. What do you do?

Yes, you have a choice of two doors at this stage. But NO, the chance that the door you originally chose hides the car is NOT 1 in 2, or 50:50; it is, as proven, 1 in 3.

This is because THAT door still derives the 2 in 3 chance of hiding a goat associated with your choice in the first round, when there were three doors. Whereas, if you change your choice to THE OTHER DOOR, the chances it hides the car are NOW 2 in 3. Despite what one's intuitive logic makes you think, there is NO 50:50 chance EVER in this game, as explained above and throughout the thread. The End

[Dubya]

OH... MY... GOD...

Pick ONE of these options only:

A or B.

Picked one? OK... You had a 50/50 chance of picking whatever you picked.

Pick ONE of these options only:

Card A (with the car) or Card B (with the goat).[

This is neither the Monty Hall Game nor analogous to it.

Picked one? OK... You had a 50/50 chance of picking whatever you picked. STOP THINKING ABOUT THE FACT YOU STARTED WITH 3 CARDS!!! That way you might have a chance at understanding this exceedingly basic concept I'm explaining. The fact you have additional information that means you are more likely to pick what you want out of those two, doesn't change the fact that you can only pick ONE OUT OF TWO!

When did Rocket stop referring to the Monty Hall Dilemma as it is played and come up with his own game called "Make a choice between two options" and then feel it necessary to explain to everyone ad nauseum that in his game the probability is 50/50 (as if we did not know)?

Rocket should understand load and clear: - we all get it! But does Rocket get the Monty Hall Dilemma? It appears not.

So, back to the real game: the Monty Hall Dilemma.

Why can't Rocket state the chances of a contestant winning the car if he changes or does not change his first guess?

Rocket seems to state these probabilities as 50/50 because there are only two closed doors to choose from.

As many have explained, this is incorrect.

So, Rocket, in the Monty Hall Dilemma we have been discussing here, what are the odds if you stick and if you switch after the first goat is revealed?

Unless Rocket explains, many will be left with the distinct impression that:

- Rocket does not understand the theory of this particular game (never mind his expertise on his "A or B" game); and

- Rocket is convinced some people do not understand the concept of 50/50 when guessing between two options.

At this stage, Rocket's refusal to explain the chances of each option and just repeat "50/50" certainly points to Rocket not accepting that the odds are 33/67 after the first goat is revealed and not 50/50 as he keeps on saying.

I guess we can put him down as a non-switcher, which of course is his right, as he has said nothing about 33% or 67% - dares not to by all appearances.

If you still don't get it, then I suggest registering for some primary school classes... I'm done.

So much for keeping things civil, as Rocket opined earlier...

slightly OT but I have to say it's quite cool that this can be so hotly discussed by so many without tempers/attitudes flaring - keep going guys! LOL!

Not so cool now, Rocket. Or rational.

I suppose we live in faint hope of Rocket addressing the questions posed to him.

[Timbo]

If this thread is how you people get off ...

Actually, I do get off on this but not in the way you clearly like to spend your time imagining . If you watch any TV shows like Survivor, The Mole and their ilk, have bought a car at a Pickles auction or even gone out 'on the pull' with some mates, then you have -- most likely unwittingly -- been playing or observing these games. What's more, they can be scripted, and you'll be manipulated -- most likely without you even being aware!

I find that very interesting. That outcomes are often not just a random chance, but the played-out result of each of us following (or not following) 'rules' we may not even be conscious of existing, perhaps at the behest of a controller . Women can be very good at this....
the "Prisoner's Dilemma", and you'll see what I mean

[Dubya]

Now that's the best idea all day! Done and done! I can't stand people that put words in other people mouths, make assumptions about what they're thinking or how they're rationalising. And how about addressing people directly rather than in the third person

I do not believe I attributed to Rocket any concepts he did not utter himself.

What I did was try to understand was what Rocket was saying (which was not easy) in the course of which I had to draw some conclusions, such as that:

- picking the car was the same as winning; and

- a 50/50 chance of picking the car was the same as a 50% probability of winning.

This did not seem like putting words into his mouth.

Rocket has made a big issue of the distinction between the 50/50 "chance" and the "odds", without letting readers know what these odds are. 2:1? Something else?

Apart from being the inverse of the probability, how are the "odds" different from the "chance" of winning?

No idea? Or can Rocket spell it out once and for all?

Rocket was also asked for his rationale for switching.

Rocket has not provided this even though he says it is "obvious" that he would switch.

Why is it obvious?

We are not all rocket scientists.

Will Rocket not deign to explain why he would switch?

He has been asked the question several times.

All we know for sure is that Rocket understands the concept of 50/50.

(BTW, first person might suit Rocket if he were the only person reading this, but third person is more appropriate for posts that are being read by others, as opposed to PMs.)

I gather Rocket has now joined team_v in a logic-free zone and leaving behind their profound thoughts on Monty Hall for posterity.

[Jarred]

seriously bro.


LET IT GO.

he's not watching anymore. and we all lost interest after page 10!

[gldgti]

I cant believe the length of this thread, but to see if anyone is still watching, the explanation is very simple and infact I am surpised at the level of the ruse. Heres my explanation, choose to believe it or not.

Indeed, the second choise is all that counts. 50/50 is the final chance. So where is this 66.6666% number coming from? Well thats quote easy too.

If you switch, and you are shown a Goat, then there is a cumulative 67% chance that AT SOME POINT IN THE GAME, YOU CHOOSE THE GTI. This is definately not the same as winning the GTI.

As many have already said, whether you switch or not is still a 50/50 for the car. If there are any highschool maths teachers reading this, i stress - please emphasise the old coin tossing theory.

The head maths teacher at my Highschool had a trcik where he could write a proof that 0=1. I cant remember it, but it was a good trick. So is this.

[Buller_Scott]

guys guys guys guys! when's the next nsw / vic combined drive day or bbq?

there are two games being played, i think the problem is that the mathematicians (self proclaimed perhaps and including myself) are sticking to their guns with their reasoning, and at least in my case, overlooking/ taking for granted some key aspects of the scenario.

gld said it good, and as schoona told me in the poll thread, the ''riddle'' works in a macro context whereas im analysing the math in a micro one.

it was a pretty rad thread- lots of good stuff back and forth, but at the end of the day we're part of a fuggin' VW community- does there really need to be any bad blood?

[Treza360]

Right this thread is now just going around and around in circles and I'm going to close it.

As a closing point, I would just like to say that those who are quoting primary and high school statistics need to understand that at that level, they only teach you the very basics and in some cases they are quite wrong.

For example I'd say most of you know from primary and high school that you can't find the square root of a negative number right (your maths teacher told you so right)? Wrong! Your maths teacher told you this so you can grasp the basic concepts.

It's the same with your 50:50 odds for two choices. Your maths teacher said that given two choices this is always the case. However they did not bring into account Conditional and Baysean statistics (what this problem applies to) as this is much to complex for most adults let alone school kids.

It's a shame that people can't accept that some things are outside their realm of knowledge. It's also sad that people are to lazy to play an online game for 10 minutes to challenge their perceived knowledge and maybe learn something that most people aren't even aware of let alone understand.

Such is life hey...

Cheers,
Trent