What is the correct answer to the "Monty Hall Dilemma"?

[Darth]

I just read this thread:

http://www.vwwatercooled.org.au/forums/f40/monty-hall-dilemma-winning-gti-game-show-42135.html

Which solution do you think is correct?

The thread was closed before a consensus was reached.

I gather there is a limit on how long threads can be.

[team_v]

I just read this thread:

http://www.vwwatercooled.org.au/forums/f40/monty-hall-dilemma-winning-gti-game-show-42135.html

Which solution do you think is correct?

The thread was closed before a consensus was reached.

I gather there is a limit on how long threads can be.

I think it was actually closed because people were arguing with each other and bitching/flaming.

The main issue was that you end up changing the odds if you remove an option however the argument claims that the odds are better as you have removed an option but continues to use the old odds.

This argues the fact that you would still include another door even though you know it won't have a winning prize behind it in your selection (which technically you would, however in reality no one would choose that door if you wanted to win the GTI)

[Darth]

I think it was actually closed because people were arguing with each other and bitching/flaming.

Really? A few bad apples behave badly and everyone who's enjoying the discussion is penalised and denied the opportunity to participate in a stimulating discussion?

I thought Rules allowed discussions to stay open as the disruptive ones could be sidelined with penalties. Doesn't that happen here?

In terms of your answer to the puzzle, does that mean if there were a billion doors when you made your choice (instead of three), and only two doors remained, you'd have a 50/50 chance of the door you picked out of a billion being correct?

Or is it the case that it is only a 50/50 chance if you choose RANDOMLY between the two remaining doors (without knowing which door was chosen first)?

IE:

Chances of the GTI being behind one of the two remaining doors equals 100%.

Chances of randomly picking the correct door first go from the two remaining doors 50%.

Chances of you picking the correct door first go when there were n doors equals 1/n or, say, 1 in a billion, when n = 1 billion.

Chances of the only door remaining being the correct door = 1-n/n, or 999,999,999/1,000,000,000 or 99.999999999% (almost certain).

So chances are, you would have been wrong when you originally chose your door from a billion available doors, so the other door is more likely to be the one with the car.

So it is only 50-50 if you do not know which door you, or the person choosing, chose in the first place.

It's a bit like if when there are two doors remaining, the host whispers the correct door to the contestant. While there's still only a 50-50 chance of choosing the correct door randomly, there is a 100% chance if the contestant remembers what the host told him.

Similarly, if the contestant remembers which door he chose first, he will realise it only has a 1/n chance of being right whereas the only other remaining door has a 1-n/n chance of being correct. Whereas the odds for someone who does not know or can't remember are back to just 50-50.

So the same scenario can have different probabilities:

one set of probabilities for a person who does not know what went on beforehand (ie which door was chosen initially); and

another set of probabilities for a person who does know which door was chosen randomly from the greater number of original options and so is far less likely to be the winning door.

So if you do know which door was selected in the first place, switching is the way to go as the chances of the first choice being right are set by the probability that prevailed at the time the selection was made. Which stands to reason.

I guess the proof of this is that if you tried this one in a billion game with a billion people you would only expect one person, on average to win.

But if the chances of winning at the end were 50-50 whether you switched or stuck with your original choice, then you would expect half the contestants, or 500,000,000 people, to win! That would mean, somehow, against all odds, half a billion people had correctly chosen the correct one-door-in-a-billion that hid the GTI. Wow - that would be in incredible result. (Emphasis on the word incredible!)

Therefore, I think the theory shows that all but one in a billion will win if they switch, but virtually no one will win if they do not switch. So switching increases your odds of winning by a factor of 1-n.

Use the Force and you will see!

Cheers
Darth Veyron

[Buller_Scott]

this is dubya with a new username, isnt it?

[Darth]

this is dubya with a new username

Hi Dubya.

Any ideas on Monty Hall?

Cheers
Darth Veyron

[schoona]

Klaus?
Rocket 36?
Corey R?

Even though it was closed, there's plenty of long and detailed explanations in that thread!

[Darth]

Klaus?
Rocket 36?
Corey R?

Even though it was closed, there's plenty of long and detailed explanations in that thread!

But a consensus was illusive for some reason!

The contributors to the original thread must not have explained things clearly enough.

Maybe Buller_Scott could explain it better!

[VW Convert]

But a consensus was illusive for some reason!

The contributors to the original thread must not have explained things clearly enough.

Maybe Buller_Scott could explain it better!

Now perhaps you should re-open one of the old chip wars threads, you could have the trifecta then.

[Darth]

Now perhaps you should re-open one of the old chip wars threads, you could have the trifecta then.

You think? Do you have a link?

Seriously, I'm not a fan of chips - way too much cholesterol.

[schoona]

Of course there isn't giong to be a consensus because there are 2 ways to think and no-one can qualify either way. It wouldn't be what it is if there was a definitive answer?

[Blitzen]

What is this puss?? Who gives two sh*ts about it?? It was closed for a reason.
Why don't we leave the crap discussions in the Mk6 DSG thread...

Are you going to send PM's out to people that don't agree with you on this one too??

[Darth]

What is this puss?? Who gives two sh*ts about it?? It was closed for a reason.
Why don't we leave the crap discussions in the Mk6 DSG thread...

Are you going to send PM's out to people that don't agree with you on this one too??

Why so nasty, Blitzen? And what's it to you? I gather you trawl the Forum so you can comment on threads that hold no interest for you.

[Darth]

Of course there isn't giong to be a consensus because there are 2 ways to think and no-one can qualify either way. It wouldn't be what it is if there was a definitive answer?

Was that a question? If so, there is a definitive answer and it is above. And those who do not understand it can simulate the problem with three playing cards.

[Blitzen]

Why so nasty, Blitzen? And what's it to you? I gather you trawl the Forum so you can comment on threads that hold no interest for you.

You will notice that my title on this forum is 'Volkswagen Antagonist'. I neither trawl, nor give two fcuks what you think...

I hold no interest in this thread as it holds no relevance to this forum, especially as you, a noob on here, takes it apon himself to PM other members to force his opinions on them.

Contribute to the forum in a constructive way, or bugger off. Either way, I don't care. If you have more question of me, I will be at GAF.

Now, I'm going to get another beer.

[VW Convert]

Contribute to the forum in a constructive way, or bugger off. Either way, I don't care. If you have more question of me, I will be at GAF.

Well said mate.

In the short time Darth has been on here he has gone out of his way to stir up controversy, we don't need members with that attitude.