**If you think there is not enough information to answer,
make whatever reasonable assumptions you want --
just state what your assumptions are before answering.**

# Brain Teaser

### #1

Posted 10 May 2014 - 05:13 AM

### #2

Posted 10 May 2014 - 05:29 AM

I'd take door #2.......purely to find out how many goats are back there

### #3

Posted 10 May 2014 - 05:39 AM

### #4

Posted 10 May 2014 - 01:03 PM

I would hope for the goat and wait for it to provide me goat cheese.

### #5

Posted 10 May 2014 - 03:55 PM

While I do understand the reasoning behind Savant's logic, which advises that you always switch, I fall into the camp that disagrees.

### #6

Posted 10 May 2014 - 05:17 PM

I believe there is one definitive and provable correct answer,

given two assumptions that aren't stated in the initial question:

* I, the contestant, want the car.

* The host acts in a way to make it the lest likely that I will get the car.

### #7

Posted 10 May 2014 - 05:49 PM

Between the two doors there is still a 50/50 shot at either right? So just hold firm with one. Besides, a goat wouldn't be so bad think of all the fresh milk and cheese! And the car? Bet it's a beater.

### #8

Posted 10 May 2014 - 06:21 PM

Goats?

You did say it was a *game* show?

### #9

Posted 10 May 2014 - 06:28 PM

**The car is actually this rig, both truck & camper -- all shipping charges, taxes, and two years of gas & supplies paid for.**

### #10

Posted 10 May 2014 - 06:31 PM

**The goat is this guy. But you can try to milk him if you really want to.**

### #11

Posted 10 May 2014 - 06:33 PM

The answer to this is not definitive, but by some schools of logic, you should switch.

I subscribe to the school that says it does not make a difference. To me, it boils down to flipping coins to some extent. Even if you flipped heads ten times in a row, you have a 50% chance of flipping it an 11th time even if the chances of flipping heads 11 times in a row is almost nil.

### #12

Posted 10 May 2014 - 06:39 PM

A new GOAT!

The answer to this is not definitive, but by some schools of logic, you should switch.

I subscribe to the school that says it does not make a difference. To me, it boils down to flipping coins to some extent. Even if you flipped heads ten times in a row, you have a 50% chance of flipping it an 11th time even if the chances of flipping heads 11 times in a row is almost nil.

I'm gonna go ahead and say it is definitive -- and you should check your premises.

### #13

Posted 10 May 2014 - 07:10 PM

It's called the Monty Hall Paradox.

### #14

Posted 10 May 2014 - 07:21 PM

I agree with Sensei. With two doors left it's a 50/50 shot. The host asking if you would like to change your choice is irrelevant.

### #15

Posted 10 May 2014 - 07:22 PM

It's totally counterintuitive, but computer simulations have borne out that switching is the proper choice.

This, ganked from wikipedia, helped to convince me:

behind door 1 behind door 2 behind door 3 result if staying at door #1 result if switch to the door offered

**Car** Goat Goat **Car** Goat

Goat **Car** Goat Goat **Car**

Goat Goat **Car** Goat **Car
(apologies for the terrible formatting)**

### #16

Posted 10 May 2014 - 08:15 PM

Say you pick door number 1. There's a 1/3 chance you're right.

Then the host reveals a goat, say behind door 3.

Now, door 2 has a 50% chance of being right, compared to your first odds of 33% at door 1.

This logic is obviously flawed because, at its essence, coin flips have no memory.

### #17

Posted 10 May 2014 - 08:21 PM

That was my logic when I first read about this.

But doing some reading, looking at the chart I posted (poorly), and the fact that a number of simulations have proven out the premise that switching is the correct choice, I changed my mind...

### #18

Posted 10 May 2014 - 08:25 PM

Mayhaps an element of this is that once things are set behind the doors, they are no longer random, as coin flips are?

### #19

Posted 10 May 2014 - 08:29 PM

Mathematicians still argue about it. Well-known mathematicians.

I know that computer simulations suggest switching doubles your chances. We went through this in a stats class, and got 50/50 in 300 trials. So I dunno.

### #20

Posted 10 May 2014 - 08:31 PM

They are like independent coin flips.

Ultimately, you have 2 doors. One has a goat and one has a car.

### #21

Posted 10 May 2014 - 08:48 PM

### #22

Posted 10 May 2014 - 08:50 PM

Just want to add, the premise is not that Monty wants you to lose. That has nothing to do with it. Monty will always open a door that has a goat, and a door that you did not pick.

That is not stated in the problem I posted one way or the other.

### #23

Posted 10 May 2014 - 08:50 PM

As posted it is NOT a statistics problem; it's a game theory question.

### #24

Posted 10 May 2014 - 09:08 PM

SM, do you have any comment on the chart I posted (it's also on the wikipedia "Monty Hall Problem" page if you'd like a more orderly version)?

I'm completely open to the notion that *I'm* missing something myself.

### #25

Posted 10 May 2014 - 09:08 PM

A few marbles, at least.

### #26

Posted 11 May 2014 - 12:04 AM

The host offering you another door is for the audience, not the player. But no amount of the audience wishing you a car behind door one will make it so, if the car is behind door two. OTOH....the audience may be able to make the car appear behind door one in a parallel universe.

### #27

Posted 11 May 2014 - 01:05 AM

I was simply stating that the host is acting pretty much like a robot, according to a set of rules.

How is this classical statistical paradox not a question of statistics?

Tim, I'm working on that chart. The problem for me is that there's so many combinations that I'm having trouble finding the best way to wrap my head around each scenario.

I'm working on a thoughtful answer though!

The best way would be to go through each possible scenario and see how many times you win if you switch vs if you don't. Then tally it up for every possible scenario. Yikes!

My brain is teased! I'm operating under the assumption that I'm wrong, and trying to figure out why.

### #28

Posted 11 May 2014 - 02:24 AM

I'd say fuck it all, and just ride the goat to work.

oh.. wait.. Thats right.. I don't have a job...

I'll just live off of the goat cheese.

### #29

Posted 11 May 2014 - 11:58 AM

Jaba, sorry I thought you later posted that one of the premises is that "the host acts in a way that is less likely for me to win the car."

That is the assumption that I'm making.

I may be using the term "game theory" wrong. But with those assumptions in place I'm pretty sure it's no longer statistics but just pure logic.

Off to breakfast. Will post my "answer" when I get back -- and find out if maybe I'm the one missing something.

I know I'm missing my coffee.

### #30

Posted 11 May 2014 - 12:14 PM

50/50 chance as between the remaining two doors.

### #31

Posted 11 May 2014 - 03:12 PM

It's like each roll of a die is completely independent of any previous or following rolls.

You should be looking at it as an entirely new question.

Doesn't matter if you go with one or two.

### #32

Posted 11 May 2014 - 03:26 PM

Many agree, but just as many (if not more) say that it's not that simple. I can't understand that way of thinking about it though. I'm reading as many explanations as I can and it just doesn't stick for me.

My head!!

### #33

Posted 11 May 2014 - 05:22 PM

**My Initial Assumptions (As I Stated in a Previous Post Above):**

A: This is a stand-alone question. It may look similar to other questions you have seen before, but **this** is the puzzle of **this** thread.

B: The contestant (you) want one of the things (car or goat) more than the other. If not, this really would not be much of a brain teaser.

C: Since the puzzle states that there are two goats but only one car, I'm assuming that the contestant ( I / You ) want the car.

D: I'm assuming the game show host is acting in a way to get you NOT to get the car. Otherwise, if you picked the car on the first try, the host would open that door.

E: On my first pick, I have no special information about which door has the car. My choice is arbitrary and has a 1/3rd probability of being right.

F: The items (car and goats) stay behind the same doors throughout the game-show. They are not rearranged after your first pick.

**Logic to Solve the Puzzle / Brain Teaser:**

1: It is stated that my first pick was Door #1

2: If a goat was behind Door #1, the host would open Door #1 -- making me loose.

3: Therefore there is a CAR behind door #1 **DEFINITIVE ANSWER. This is a logic problem NOT a statistics problem.****You might be playing under a Different Assumption -- which makes it into a Statistics problem:**

D: The game show host's goal is to make the game challenging for me & exciting for the audience**Logic to Solve the Puzzle / Brain Teaser:**

1: It is stated that my first pick was Door #1

2: Whether I have picked a car-door or a goat-door, the host will open a door with a goat behind it -- to keep things interesting.

3: When I picked my first door (Door #1) I had a 1/3rd chance of that being the door with the car.

4: Once the host opens door #3 to show me a goat, he has shown me that door #2 has a 2/3rd chance of having a car behind it.

5: Sticking with a 1/3rd chance instead of moving to a door with a 2/3rd chance is silly.

6: So I switch my pick to door #2, which has a 2/3rd chance.

Note: this is born out by Tim's post about the options.

Sticking with my 1st door give me a 1 in three chance of getting the car

Switching gives me a 2/3rds chance to get the car.

### #34

Posted 11 May 2014 - 05:30 PM

This logic is obviously flawed because, at its essence, coin flips have no memory.

It's like each roll of a die is completely independent of any previous or following rolls.

You should be looking at it as an entirely new question.

This is exactly the point that is wrong. This is **not** like a coin flip. There is memory. The items do not move between picks and the host's action (of opening a door with a goat) is based on data (facts / memory). Therefore it is **not** appropriate (ideal) to treat each pick as an independent event or as a coin-flip.

### #35

Posted 11 May 2014 - 09:07 PM

You have two doors. One has a car, one has a goat. This is a new, independent coin flip in classical terms.

### #36

Posted 11 May 2014 - 09:52 PM

I'm still trying to figure out how door #2 has a 2/3rds chance of being a car after door #3 is revealed a goat.

### #37

Posted 11 May 2014 - 10:36 PM

Whether you pick right or pick wrong on your first try, the host will open a second door with a goat.

If you picked a goat on your first try, the host will open the second goat door.

If you picked the car on your first try, both of the remaining doors have goats and the host will arbitrarily pick a remaining door to open.

In this regard, it's like blackjack. It doesn't matter if the host wants you to win or not. S/he has a set of rules to follow.

### #38

Posted 11 May 2014 - 10:44 PM

### #39

Posted 12 May 2014 - 12:57 AM

Same rules but this time there's a million doors (still only 1 car). You pick one, then the host opens all other doors except one other.

So now there's 2 doors, 1 has a car.

It's almost certain that you did NOT pick the car on your first pick. So, when the host narrows it down to two doors, the chances are that it's the new door (ie, the door you did NOT pick first).

So, you should switch.

3 doors is a funny number though. It's not nearly as obvious, and many do disagree on it.

### #40

Posted 12 May 2014 - 06:29 PM

I concede that it is the classic paradox that is interesting and we'll go with that.

**The Million-Doors is a great illustration. **

### #41

Posted 12 May 2014 - 06:38 PM

Here is an extreme example of why you SHOULD switch.

Same rules but this time there's a million doors (still only 1 car). You pick one, then the host opens all other doors except one other.

So now there's 2 doors, 1 has a car.

It's almost certain that you did NOT pick the car on your first pick. So, when the host narrows it down to two doors, the chances are that it's the new door (ie, the door you did NOT pick first).

So, you should switch.

3 doors is a funny number though. It's not nearly as obvious, and many do disagree on it.

I like this answer. And it most certainly applies if there are a million, or even a hundred doors.

But with 3 doors, my instinct is to stick to my guns since the host is not my friend and my assumption is that he will try to mislead me.

### #42

Posted 12 May 2014 - 06:39 PM

and how the fuck are you gonna get the car out through that narrow doorway?

### #43

Posted 12 May 2014 - 07:33 PM

Julius is right...it's a trick question!

You can't get the car through the door. You should have just been happy with a free goat.

### #44

Posted 12 May 2014 - 07:41 PM

I was totally happy with the free goat. I might even have enough for my daughter's dowry now!

### #45

Posted 12 May 2014 - 07:46 PM

I was totally happy with the free goat. I might even have enough for my daughter's dowry now!

Sweet! My parents got a pregnant cow and her calf from my sister's in-laws when she got married.