Two cars, one goat - Page 3 - Fuel Economy, Hypermiling, EcoModding News and Forum

ME_Andy · 02-23-2015, 08:15 PM

Quote:

Originally Posted by Old Mechanic

Irrelevant, the host is always going to choose the goat.

Agreed.

Think of the rest this way: you choose door A (33% likelihood). The host shows a goat in door C. Does seeing the goat in door C give you any motivation to change your answer? Does it have any bearing at all on doors A&B?

No it doesn't. It gave no new information. It's like he's revealing the answer in slow motion-- not helping you at all.

freebeard · 02-23-2015, 09:13 PM

Quote:

You wrote that vos Savant was hot and there was an ad for Asian dating. I forgot, but remembered when it showed me a Philippine dating site.

???? For me link goes to "Marilyn vos Savant Biography, Marilyn vos Savant's Famous Quotes - QuotesSays . COM" like it says on the tin. The picture's link I think I got from the Google search page because the 'CLICK FOR NORMAL VIEW' wasn't working. YMMV.

What are the odds the car was a Pontiac GTO?

niky · 02-23-2015, 11:03 PM

Quote:

Originally Posted by ME_Andy

Yep, the key to all of this (as I understand it) is that the host intentionally makes his choice in a way that doesn't give you any more info.

Wrong. The host always gives more info.

The chance of the host showing A goat is 100%. This is the format of the gameshow.

Once the host shows that goat, he collapses the probabilities, making it much easier to win the game. Just because the other possibilities no longer exist, doesn't mean you shouldn't count them in assigning percentages!

Simplest way to put it:

If Car = Your Door (1/3rd chance), host can open either door. Changing mind = 0% wins.

If Car =/= Your Door (2/3rd chance), host will never open the winning door. The remaining door is the Car. Changing mind = 100% win

100% of 2/3rd is 66% chance of winning, overall.

It's that simple.

And statistical testing backs it up.

If you want long, boring tables, though:

Code:

Car	You	Host	You		Win %, Changed mind
A	A	xxx	xxx	xxx	0.00%
A	A	xxx	xxx	xxx	
A	A	xxx	xxx	xxx	
A	A	B	A	win	
A	A	B	xxx	xxx	
A	A	B	C	lose	
A	A	C	A	win	
A	A	C	B	lose	
A	A	C	xxx	xxx	

B	A	xxx	xxx	xxx	100.00%
B	A	xxx	xxx	xxx	
B	A	xxx	xxx	xxx	
B	A	xxx	xxx	xxx	
B	A	xxx	xxx	xxx	
B	A	xxx	xxx	xxx	
B	A	C	A	lose	
B	A	C	B	win	
B	A	xxx	xxx	xxx	

C	A	xxx	xxx	xxx	100.00%
C	A	xxx	xxx	xxx	
C	A	xxx	xxx	xxx	
C	A	B	A	lose	
C	A	B	xxx	xxx	
C	A	B	C	win	
C	A	xxx	xxx	xxx	
C	A	xxx	xxx	xxx	
C	A	xxx	xxx	xxx	
				Chances	66%

RedDevil · 02-24-2015, 03:05 AM

The thing that makes it hard to get right is that it looks like a lottery.
I won a car in a lottery; the Hyundai I10 in my garage, actually. I know how it feels.

But the contest is not a lottery.
The host can pick a door with a goat because there will always be one door with a goat left after your first choice.

I can break it down as simple as this:
The chance that your first choice is right is 1/3.
The chance that the car is behind one of the other two doors, of which one will be opened to reveal a goat, is 2/3.

The two doors you did not choose still have a combined 2/3 chance of having the car behind them. But when you know which of those two does not have the car, you know the other has the full 2/3 chance.

Got it? No?
Let's change the experiment:

Running the contest with 1.000.000 doors
1 car, 1 million doors.
We send the goats on leave this time.

You pick one door at random. You have 0.0001 % chance of picking the car.
There is a 99.9999 % chance that the car is behind one of the other doors.
There are (at least) 999.998 remaining doors that do not have a car.
Now it comes:
The host opens 999.998 doors, carefully skipping the one door hiding the car (unless you've had the uncanny 0.0001% chance chance of picking the right one at first, in which case he skips a random door)

Will you swap or not?

You should.
Going to high numbers clearly shows how selective the host operates.
With every door he opens he does not increase the chance that your original choice was right, though it may feel that way.

Because unlike a lottery, he does not pick doors at random.
He opens only doors that have no car.

Running a lottery by contrast
If it were a lottery, initially you´d have a 0.0001 % chance that a door reveals a car for each door, just like the contest.

If after half the doors were opened still no car was revealed, then you´d have a 0.00002% chance that any remaining door would have a car.
But you also would have a 50% chance of being out of competition already.

After 999.998 doors and no car shown the remaining two doors, the one you´ve originally chosen and the remaining one, each have a 50% chance of hiding the elusive car.
But you´d only have a 0.0002% chance of getting that far. Over the whole the chance that those particular two doors have the car is still just 0.0001% each.

In the game there is no element of chance after your initial choice.
You have 100% chance to make it to the last 2 doors because the host will not pick the door with the car.
Nothing alters the chance that you did pick right first time.

RedDevil · 02-24-2015, 03:36 AM

Quote:

Originally Posted by freebeard

When I had my IQ tested in high school, they wouldn't tell me the result, because they didn't "want [me] to get a swelled head". Well, they got their way about that.

I've done several IQ tests over the years, and the funny thing is that I score higher with each test.
Apparently, solving IQ tests is a skill, and I get better at it with practise.
I don't think I really got smarter.
But what do I know

jamesqf · 02-24-2015, 12:36 PM

Quote:

Originally Posted by Old Tele man

Uh, spelling wasn't part of those IQ tests, was it (wink,wink)?

Or perhaps he's using the British spelling? https://en.wiktionary.org/wiki/practise I have a bit of trouble with that myself, having read a lot of Agatha Christie &c in my childhood.

hamsterpower · 02-24-2015, 02:49 PM

Quote:

Originally Posted by Old Tele man

Uh, spelling wasn't part of those IQ tests, was it (wink,wink)?

Just blame it on the MS "auto-spell" function -- like I do (ha,ha)!

He may be using Firefox which defaults to english(UK) for the built-in spell checker. Gets me all the time.

Gasoline Fumes · 02-24-2015, 02:59 PM

Quote:

Originally Posted by RedDevil

I can break it down as simple as this:
The chance that your first choice is right is 1/3.
The chance that the car is behind one of the other two doors, of which one will be opened to reveal a goat, is 2/3.

The two doors you did not choose still have a combined 2/3 chance of having the car behind them. But when you know which of those two does not have the car, you know the other has the full 2/3 chance.

Got it? No?

Thanks! Now I finally get it! Did I win a car?

RedDevil · 02-24-2015, 04:35 PM

Quote:

Originally Posted by Gasoline Fumes

Thanks! Now I finally get it! Did I win a car?

What you've won is insight in how first impressions can deceive you.

Kudos to my dad.
I explained the problem to him tonight and before I could finish the sentence about the remaining door he said it had a 2/3 chance of having the car behind it. It is bone trivial to him!
Should I have told him he really needs to think it over?

RedDevil · 02-24-2015, 04:41 PM

Quote:

Originally Posted by jamesqf

Or perhaps he's using the British spelling? https://en.wiktionary.org/wiki/practise I have a bit of trouble with that myself, having read a lot of Agatha Christie &c in my childhood.

I use double-dutch spelling, preferredly...
Yarrrr matey, ye need shoa me haw yer spellin is in Dutch and yer betta do good or ya walk tha plank

Spelling is not a part of IQ tests.
If you end up in Diagon Alley there is still hope.