Velocity Reviews > Toughest Game Show Question

# Toughest Game Show Question

divya bisht
Guest
Posts: n/a

 01-10-2012
Toughest Game Show Question
(Source : http://hardest-puzzle.blogspot.com/2...-question.html
)

You are on a game show and there are three doors. The presenter tells
you that behind one of doors there is a car and behind the other two
are goats, if you pick the car you win it. After you have picked a
door the presenter opens a different door with a goat behind it, he
then gives you the chance to change what door you open, what should
you do?

http://hardest-puzzle.blogspot.com/2...-question.html

Bill Reid
Guest
Posts: n/a

 01-10-2012
On Jan 9, 8:56*pm, divya bisht <(E-Mail Removed)> wrote:
>
> You are on a game show and there are three doors. The presenter tells
> you that behind one of doors there is a car and behind the other two
> are goats, if you pick the car you win it. After you have picked a
> door the presenter opens a different door with a goat behind it, he
> then gives you the chance to change what door you open, what should
> you do?
>

OH NO, THE DREADED "MONTY HALL" PROBLEM, IT'S BEEN AT LEAST A
USENET!!!!!!!

The answer is that it doesn't matter, your odds are still one
in three no matter what you do...but wait, does it matter if the
presenter knows what's behind the doors and shows you the goat
to make the game more interesting? Let's see what happens with
the "regs" here, might be fun...

---
William Ernest Reid

tom st denis
Guest
Posts: n/a

 01-10-2012
On Jan 10, 9:47*am, Bill Reid <(E-Mail Removed)> wrote:
> OH NO, THE DREADED "MONTY HALL" PROBLEM, IT'S BEEN AT LEAST A
> DECADE SINCE I'VE SEEN THIS MONSTROUSITY REAR IT'S UGLY HEAD IN
> USENET!!!!!!!
>
> The answer is that it doesn't matter, your odds are still one
> in three no matter what you do...but wait, does it matter if the
> presenter knows what's behind the doors and shows you the goat
> to make the game more interesting? *Let's see what happens with
> the "regs" here, might be fun...

Never switch your bet. Pigeons know it.

Tom

Eric Sosman
Guest
Posts: n/a

 01-10-2012
On 1/10/2012 9:47 AM, Bill Reid wrote:
> On Jan 9, 8:56 pm, divya bisht<(E-Mail Removed)> wrote:
>>
>> You are on a game show and there are three doors. The presenter tells
>> you that behind one of doors there is a car and behind the other two
>> are goats, if you pick the car you win it. After you have picked a
>> door the presenter opens a different door with a goat behind it, he
>> then gives you the chance to change what door you open, what should
>> you do?
>>

> OH NO, THE DREADED "MONTY HALL" PROBLEM, IT'S BEEN AT LEAST A
> DECADE SINCE I'VE SEEN THIS MONSTROUSITY REAR IT'S UGLY HEAD IN
> USENET!!!!!!!
>
> The answer is that it doesn't matter, your odds are still one
> in three no matter what you do...but wait, does it matter if the
> presenter knows what's behind the doors and shows you the goat
> to make the game more interesting? Let's see what happens with
> the "regs" here, might be fun...

Stick with the original choice. You can't eat a car.

--
Eric Sosman
http://www.velocityreviews.com/forums/(E-Mail Removed)d

John Gordon
Guest
Posts: n/a

 01-10-2012
In <(E-Mail Removed)> Bill Reid <(E-Mail Removed)> writes:

> The answer is that it doesn't matter, your odds are still one
> in three no matter what you do

It does matter. If you switch, you have a two-in-three chance of winning.

> ..but wait, does it matter if the presenter knows what's behind the
> doors and shows you the goat to make the game more interesting?

The presenter does know. He doesn't open a random door.

--
John Gordon A is for Amy, who fell down the stairs
(E-Mail Removed) B is for Basil, assaulted by bears
-- Edward Gorey, "The Gashlycrumb Tinies"

Stephen Sprunk
Guest
Posts: n/a

 01-10-2012
On 10-Jan-12 08:47, Bill Reid wrote:
> On Jan 9, 8:56 pm, divya bisht <(E-Mail Removed)> wrote:
>> You are on a game show and there are three doors. The presenter tells
>> you that behind one of doors there is a car and behind the other two
>> are goats, if you pick the car you win it. After you have picked a
>> door the presenter opens a different door with a goat behind it, he
>> then gives you the chance to change what door you open, what should
>> you do?
>>

> OH NO, THE DREADED "MONTY HALL" PROBLEM, IT'S BEEN AT LEAST A
> DECADE SINCE I'VE SEEN THIS MONSTROUSITY REAR IT'S UGLY HEAD IN
> USENET!!!!!!!
>
> The answer is that it doesn't matter, your odds are still one
> in three no matter what you do...but wait, does it matter if the
> presenter knows what's behind the doors and shows you the goat
> to make the game more interesting? Let's see what happens with
> the "regs" here, might be fun...

Mythbusters recently tested this. You're always better off switching.

S

--
Stephen Sprunk "God does not play dice." --Albert Einstein
CCIE #3723 "God is an inveterate gambler, and He throws the
K5SSS dice at every possible opportunity." --Stephen Hawking

Seebs
Guest
Posts: n/a

 01-10-2012
On 2012-01-10, John Gordon <(E-Mail Removed)> wrote:
> The presenter does know. He doesn't open a random door.

Our spammy friend seems to have a religious objection to an unambiguous
problem statement, and has not specified this.

-s
--
Copyright 2011, all wrongs reversed. Peter Seebach / (E-Mail Removed)
http://www.seebs.net/log/ <-- lawsuits, religion, and funny pictures
http://en.wikipedia.org/wiki/Fair_Game_(Scientology) <-- get educated!
I am not speaking for my employer, although they do rent some of my opinions.

Shao Miller
Guest
Posts: n/a

 01-10-2012
On 1/10/2012 09:47, Bill Reid wrote:
> On Jan 9, 8:56 pm, divya bisht<(E-Mail Removed)> wrote:
>>
>> You are on a game show and there are three doors. The presenter tells
>> you that behind one of doors there is a car and behind the other two
>> are goats, if you pick the car you win it. After you have picked a
>> door the presenter opens a different door with a goat behind it, he
>> then gives you the chance to change what door you open, what should
>> you do?
>>

> OH NO, THE DREADED "MONTY HALL" PROBLEM, IT'S BEEN AT LEAST A
> DECADE SINCE I'VE SEEN THIS MONSTROUSITY REAR IT'S UGLY HEAD IN
> USENET!!!!!!!
>

Learning Algorithms" by David J. C. MacKay from his site:

http://www.inference.phy.cam.ac.uk/mackay/itila/

Or better yet, one can purchase it and have it shipped.

This problem is discussed on page 57, exercise 3.8, if I'm not mistaken.

However, the above-stated details are a little different.

- Shao Miller

Keith Thompson
Guest
Posts: n/a

 01-10-2012
Seebs <(E-Mail Removed)> writes:
> On 2012-01-10, John Gordon <(E-Mail Removed)> wrote:
>> The presenter does know. He doesn't open a random door.

>
> Our spammy friend seems to have a religious objection to an unambiguous
> problem statement, and has not specified this.

The question does say that the presenter opens a door with a goat behind
it.

--
Keith Thompson (The_Other_Keith) (E-Mail Removed) <http://www.ghoti.net/~kst>
Will write code for food.
"We must do something. This is something. Therefore, we must do this."
-- Antony Jay and Jonathan Lynn, "Yes Minister"

James Kuyper
Guest
Posts: n/a

 01-10-2012
On 01/10/2012 04:27 PM, Keith Thompson wrote:
> Seebs <(E-Mail Removed)> writes:
>> On 2012-01-10, John Gordon <(E-Mail Removed)> wrote:
>>> The presenter does know. He doesn't open a random door.

>>
>> Our spammy friend seems to have a religious objection to an unambiguous
>> problem statement, and has not specified this.

>
> The question does say that the presenter opens a door with a goat behind
> it.

Yes, but it doesn't say whether he opened a random door that happened to
have a goat behind it, or whether he deliberately choose a door that he
knew had a goat behind it. The latter is, I believe, the intended
situation in the standard "Monty Hall" problem. A lot of very confusing
discussions about that problem have been based upon choosing a different
assumption. To take the most extreme case: what if the presenter only
bothers opening the second door if you happen to have already chosen the
correct door, and otherwise leaves it closed (obviously, you've not been
informed of this policy)?