Monty Hall Dilemma - Winning a GTI on a Game Show

[Dubya]

If you're ever on game show with, say, a GTI as a prize, you may want to know about this . . .

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a GTI; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to switch from door No. 1 to door No. 2?" Is it to your advantage to switch your choice?

As the player cannot be certain which of the two remaining unopened doors is the winning door, most people assume that each of these doors has an equal probability and conclude that switching does not matter.

In fact, all things being equal, the player should switch—doing so doubles the probability of winning the car, from 1/3 to 2/3.

Worth knowing if you ever find yourself in the enviable position of being in the running to win a car!

[MurphyTheElf]

http://en.wikipedia.org/wiki/Special:Random

[team_v]

If you're ever on game show with, say, a GTI as a prize, you may want to know about this . . .

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a GTI; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to switch from door No. 1 to door No. 2?" Is it to your advantage to switch your choice?

As the player cannot be certain which of the two remaining unopened doors is the winning door, most people assume that each of these doors has an equal probability and conclude that switching does not matter.

In fact, all things being equal, the player should switch—doing so doubles the probability of winning the car, from 1/3 to 2/3.

Worth knowing if you ever find yourself in the enviable position of being in the running to win a car!

Schroedinger's cat could apply though.

Your odds will be 1/2 after one of the doors is opened no matter if you stay with your original choice or go with the new door.

[Dubya]

Schroedinger's cat could apply though.

Your odds will be 1/2 after one of the doors is opened no matter if you stay with your original choice or go with the new door.

Apparently not:

http://en.wikipedia.org/wiki/Monty_Hall_problem

[pologti18t]

Your odds will be 1/2 after one of the doors is opened no matter if you stay with your original choice or go with the new door.

Exactly correct.

[cme2c]

Schroedinger's cat could apply though.

Your odds will be 1/2 after one of the doors is opened no matter if you stay with your original choice or go with the new door.

wrong.
combinations are:
(1) (2) (3)
goat goat car

goat car goat

car goat goat

you pick door 1, chances of car, 1 in 3

the fact that the host shows you a goat doesnt change that.

you double your chance of a car by swapping.

I proved this to my sister using cards. She still thinks it's magic.

[team_v]

wrong.
combinations are:
(1) (2) (3)
goat goat car

goat car goat

car goat goat

you pick door 1, chances of car, 1 in 3

the fact that the host shows you a goat doesnt change that.

you double your chance of a car by swapping.

I proved this to my sister using cards. She still thinks it's magic.

In reality though, you still only have a 50:50 chance of having the car behind the door you chose or the door you didn't choose becasue it has to be behind one of them as the other door revealed a goat.


However, schroedingers cat apply's because you never know if you changing doors will change what was behind the doors.

[Dubya]

In reality though, you still only have a 50:50 chance of having hte car behind the door you chose or the door you didn't choose becasue it has to be behind one of them.

However, schroedingers cat apply's because you never know if you changing doors will change what was behind the doors.

Not so, I have to say:

From the outset you have a one in three chance of selecting the door with the car first off.

This means that there is a 67% chance that the car is behind one of the two doors you did not choose and a 33% chance it is behind the one you first chose.

These percentages do no vary after the door with the goat behind it is opened.

We already knew there was a goat behind one of the two doors you did not select; now we just happen to know behind which of the two other doors the goat was hidden.

As the two doors we did not choose initially still have a combined 67% chance of having the car behind them, with the knowledge that the GTI is not behind the door that has been opened, if you swap, your chances of the car being behind your second choice are 67%, not 33% or 50%.

So if you swap, on average, you will win twice as often.

[gareth_oau]

the problem here is that each time time one door is eliminated, you start with a fresh set of variables and probabilities.

so at first choice, your chance was 1 in 3, but once the first door is out of the equation, then its 50:50 for both doors, whether you change or not.

Like tossing a coin, you have a 50:50 chance of getting a tails, but just becuase the first toss revealed a head, doesnt mean the next toss will reveal a tail.

the next toss is still 50:50 for a tail vs a head.

Probabilities and 50:50 outcomes are only realised over a very large sample.

also, and more importantly accept that Murphys Law is the more powerful law stating that which ever door you choose will have a goat behind it

[Dubya]

the problem here is that each time time one door is eliminated, you start with a fresh set of variables and probabilities.

so at first choice, your chance was 1 in 3, but once the first door is out of the equation, then its 50:50 for both doors, whether you change or not.

Like tossing a coin, you have a 50:50 chance of getting a tails, but just becuase the first toss revealed a head, doesnt mean the next toss will reveal a tail.

the next toss is still 50:50 for a tail vs a head.

Probabilities and 50:50 outcomes are only realised over a very large sample.

also, and more importantly accept that Murphys Law is the more powerful law stating that which ever door you choose will have a goat behind it

Out of respect for the preferences of others, I make no comment as to whether the above comment is correct or not but refer the author to the discussion at:

http://en.wikipedia.org/wiki/Monty_Hall_problem

PS - I do not wish to imply that I have any issue with the comment about "Murphy's Law" except to say that, in my opinion, Murphy was an optimist!

[team_v]

Not so, I have to say:

From the outset you have a one in three chance of selecting the door with the car first off.

This means that there is a 67% chance that the car is behind one of the two doors you did not choose and a 33% chance it is behind the one you first chose.

These percentages do no vary after the door with the goat behind it is opened.

We already knew there was a goat behind one of the two doors you did not select; now we just happen to know behind which of the two other doors the goat was hidden.

As the two doors we did not choose initially still have a combined 67% chance of having the car behind them, with the knowledge that the GTI is not behind the door that has been opened, if you swap, your chances of the car being behind your second choice are 67%, not 33% or 50%.

So if you swap, on average, you will win twice as often.

This is as pointless as the MT vs DSG thread.

You have 3 doors, 33% chance each.
Remove 1 door, only 2 doors remain.
Removing 1 door means that you can no longer use the 1/3 chance breakdown you have used previously and as such must revert back to 1/2 chance unless you actually count choosing the goat as an option.
since you are not going to choose the goat, 1 of the remaining 2 doors has the GTI, the other doesn't so you have a 50% chance no matter which door you choose.


Having said that, you then have to apply Murphy's law stating if you have a 50% chance, 90% of the time you will choose wrong.

And schroedinger's cat also screws with the results.



Bloody Garath beat me to it.
Stupid work getting in the way of my forum viewing time.

[gareth_oau]

team v, you really shouldn't be allowing work to get in the way of priorities - go chat to the boss!

[ccpl]

As stated plenty of times already in this topic, its complete BS.

If you take into account that your original choices include a 1/3 chance of winning, and then the host improves the odds by taking away one of the choices, then yes, given the original odds, you now have a 2/3 chance of winning WITH EITHER DOOR.

But as stated previously, the variables have changed, and so must the odds - so you now have a 1/2 chance of winning.

People try to use mathematics to solve the equation, and just end up complicating the problem - when all they really need is simple arithmetic:

1 + 1 + 1 = 3
3 - 1 = 2

To demonstrate the flawed mechanic, the whole idea of 'switching your door' giving you a 2/3 chance to win, relies on the first mechanic - that you did not choose the prize in the first place (which is an original 1/3 chance). If you happened to win that 1/3 chance, then 'switching your door' gives you a 0/3 (original) and 0/2 (progressive) chance to win.

Should you happen to choose a goat first (2/3 chance), the 'switch mechanic' gives you a 2/3 (original) and 1/2 (progressive) chance to win

HOWEVER

If you take into account that the modified fraction chance values can not exist until the original fraction chance value has been solved (ie: door chosen) - then it becomes obvious that in order to correctly calculate the odds, the variables must be processed first.

Which again is simple maths:

1 + 1 + 1 = 3
3 - 1 = 2

[FJ Steve]

But....but....what if there wasn't a GTI behind the "3rd" door?

In fact...what if they had 3 goats behind the 3 doors.....and only wheeled the GTI up to show you what you missed when you made 2 dud choices....

What's the odds with that?

[team_v]

There are so many variables;

Is the GTI 3 door or 5 door
Manual or DSG
Does it have Dynaudio?
Are the goats the same age?
Are the goats male or female?

Is the goat an option for the GTI?
Can i get the GTI in goat leather trim?

Is it possible to chip the goat?
Is the goat DSG only?