wu :: forums
        (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
      

        riddles >> hard >> $1,000,000 box
        
(Message started by: mingus33 on Jan 15th, 2007, 8:50pm)
Title: $1,000,000 box
Post by mingus33 on Jan 15th, 2007, 8:50pm
you are asked by the game show host to select one box of 3. One of the three contains $1,000,000 and the other two contain nothing.
After you have selected your box, the host removes one of the two remaining boxes and tells you that the box he removed does NOT contain the $1,000,000.
Now he asks you if you would like to keep your box or switch.
what should you do and why?

thanks
tony
Title: Re: $1,000,000 box
Post by Whiskey Tango Foxtrot on Jan 15th, 2007, 9:32pm
I think a similar problem has made its way through the forum before.  I can't come up with a link but I'm pretty sure I've seen it around.
Title: Re: $1,000,000 box
Post by denis on Jan 15th, 2007, 9:33pm
See the Monty Hall riddle in the Easy section of the riddles main page.

http://www.ocf.berkeley.edu/~wwu/riddles/easy.shtml

Its the same puzzle with a slight change in presentation only.

Here is a link to the thread:

http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_easy;action=display;num=1028741912;start=0
Title: Re: $1,000,000 box
Post by hiyathere on Jan 16th, 2007, 11:01am
Did you get this idea out of "Deal or no deal"?
Title: Re: $1,000,000 box
Post by denis on Jan 16th, 2007, 12:17pm
Actually this puzzle existed many years ago before Deal or No Deal was created. It is more of an offshoot of the Monty Hall Show.
Title: Re: $1,000,000 box
Post by rmsgrey on Jan 16th, 2007, 5:02pm
The puzzle pre-dates Monty Hall by some time. Joseph Bertrand's Calcul des probabilites in 1889 contains it (according to The Magical Maze by Ian Stewart)

It's one of the classic examples of the counter-intuitive nature of probability, and has, in various forms, kept cropping up over the years - and has tripped up a number of qualified mathematicians who should have remembered better...
Title: Re: $1,000,000 box
Post by Locke64 on Jan 23rd, 2007, 4:01pm
I first saw this one on Numb3rs. ;)
You [hide]switch[/hide]  I don't have time to explain; I gtg.
Title: Re: $1,000,000 box
Post by Icarus on Jan 23rd, 2007, 5:10pm

on 01/16/07 at 12:17:11, denis wrote:
It is more of an offshoot of the Monty Hall Show.


Which was called "Let's Make a Deal". Monty wasn't actually required to open a gag door and offer a switch, and often just went with the original pick. That changes things considerably.

But if you know your host follows a policy of opening a gag door, then offering a switch to the remaining door, then 2/3 of the time switching is to your advantage.
Title: Re: $1,000,000 box
Post by Locke64 on Jan 23rd, 2007, 6:18pm
Here's the visual way.

A=$1,000,000, B and C=nothing

|A| |B| |C|
1: You pick A, B/C is eliminated, you pick C/B, you lose.
2: You pick B, C is eliminated, you pick A, you win.
3: You pick C, B is eliminated, you pick A, you win.
You win 2 out of the three times.  If you don't switch, however, you only have a one-in-three chance of winning, which is obvious.

I forgot how to do the math version. :(
Title: Re: $1,000,000 box
Post by CowsRUs on Feb 7th, 2007, 8:15pm
I say, Nuke it along with the Statue of Liberty and biobomb the host ;D
Title: Re: $1,000,000 box
Post by JiNbOtAk on Feb 16th, 2007, 3:22am
What if the host would only offer to reveal one door, on the condition that you chose the right one ?
Title: Re: $1,000,000 box
Post by towr on Feb 16th, 2007, 3:53am

on 02/16/07 at 03:22:28, JiNbOtAk wrote:
What if the host would only offer to reveal one door, on the condition that you chose the right one ?
?
Then if he opens a door you know you have the right one?! That sort of gives it away, doesn't it?
Title: Re: $1,000,000 box
Post by rmsgrey on Feb 16th, 2007, 10:47am

on 02/16/07 at 03:53:01, towr wrote:
?
Then if he opens a door you know you have the right one?! That sort of gives it away, doesn't it?

It does rather depend on whether you know that's what he's doing. If you know that's his strategy, then (assuming you always get the chance to switch) you can still win 2/3
Title: Re: $1,000,000 box
Post by tiber13 on Mar 15th, 2007, 11:24am
dump the first part, part 2 you have 2 boxes, 1 in 2 chances to get the $1kk( $1,000,000)
50%
Title: Re: $1,000,000 box
Post by rmsgrey on Mar 15th, 2007, 12:49pm

on 03/15/07 at 11:24:24, tiber13 wrote:
dump the first part, part 2 you have 2 boxes, 1 in 2 chances to get the $1kk( $1,000,000)
50%

A lot of people think that, which is why the question is a classic. However, the correct answer is that you win twice as often when you switch.

Consider a variant where, instead of opening one of the other boxes, the Host instead always gives you the chance to switch your box for both the others. Better off switching then, right? How about if, when you agree to take the other two boxes instead, you have to pick which one (of those two) you actually want after seeing them both opened? Still a 2/3 chance of winning when you switch, right? How about if the Host doesn't open any boxes, but tells you: "if the prize is in either of these two boxes, it's in this one" after you pick the pair of boxes.


Another variation is to take a pack of playing cards and try and pick the Ace of Spades by the following procedure:
Pick one card and set it aside.
Get someone else to look through the rest of the cards and, if the Ace of Spades is in that pile, set it aside; otherwise, set a random card aside.
You then have two cards, one of which is the Ace of Spades. If you're right, then it doesn't matter where those two cards came from and you have a 50% chance of having the Ace if you don't switch; if I'm right, then the card you picked is only the Ace if you picked it (just under 2% of the time).

If you like, you can try it as an experiment - if you go through the process 100 times, if I'm right, you'll get the Ace roughly twice; if you are it'll be around 50 times.



Of course, there is a variation where you do have the Ace 50% of the time - instead of getting someone to look through the cards to pick which ones to reveal, reveal them randomly until there's only one and the one you picked left - that way about 2% of the time you'll have the Ace; 2% the other card will be the Ace, and 96% you'll have revealed it earlier and have to start over. If you repeat that process until you end up with 2 cards without seeing the Ace, it is then 50% each way of either being the Ace - because you learned something about your card every time you didn't have to start over after revealing a card...
Title: Re: $1,000,000 box
Post by Johan_Gunardi on May 20th, 2007, 8:19pm
[hideb]Switch[/hideb]http://en.wikipedia.org/wiki/Monty_Hall_problem
Title: Re: $1,000,000 box
Post by srn347 on Aug 29th, 2007, 6:59pm
It's a trick, they want you to think that. It's 50-50. Besides, you could have started with the one he gives you the option to switch with and had the same situation.
Title: Re: $1,000,000 box
Post by Aryabhatta on Aug 30th, 2007, 12:59am

on 08/29/07 at 18:59:41, srn347 wrote:
It's a trick, they want you to think that. It's 50-50. Besides, you could have started with the one he gives you the option to switch with and had the same situation.


Wrong again, the 1/0th time.

I feel the strange urge to respond to srn347's posts... I think i should stop now.
Title: Re: $1,000,000 box
Post by towr on Aug 30th, 2007, 1:00am

on 08/29/07 at 18:59:41, srn347 wrote:
It's a trick, they want you to think that. It's 50-50. Besides, you could have started with the one he gives you the option to switch with and had the same situation.

I can't imagine why I'm still bothering to enlighten you; but the situations would not be the same.
Imagine a pack of cards, your goal is to get the ace of spades. You select one card, X, without seeing at; from the other 51 cards I remove 50 cards that are not the ace of spades. Do you stick to your choice, or switch to the other card, Y?
If you had by chance picked Y at the start, how likely do you think it that at the end, the other card would be A?

For the Monty Hall problem the only difference is that it's equivalent to a three card game, and not a full deck one. But the end situation would still not be the same if you had picked the other; and switching is still better on mathematical grounds.

However based on prior experience I have little hope you'll actually consider any argument contrary to the answer you set your mind on.
Title: Re: $1,000,000 box
Post by JiNbOtAk on Aug 30th, 2007, 4:25am

on 08/30/07 at 00:59:00, Aryabhatta wrote:
I feel the strange urge to respond to srn347's posts... I think i should stop now.


I know the feeling, it's like when you have an itch between your shoulderblades; you could never reach it to scratch it properly, but it doesn't mean you'll stop trying.  ;D
Title: Re: $1,000,000 box
Post by mikedagr8 on Aug 30th, 2007, 4:29am
Oh yes, now that's a metaphor I have to use.
Title: Re: $1,000,000 box
Post by JiNbOtAk on Aug 30th, 2007, 4:47am

on 08/30/07 at 04:29:04, mikedagr8 wrote:
Oh yes, now that's a metaphor I have to use.


I think the word you're looking for is simile.  But I could be wrong. :P
Title: Re: $1,000,000 box
Post by mikedagr8 on Aug 30th, 2007, 4:53am
Wouldn't surprise me if your correct. I generally can't remember all the terms like alliteration and all that crap. All I know is that I'll be using it.

Guess what, you are.
Title: Re: $1,000,000 box
Post by SMQ on Aug 30th, 2007, 4:55am

on 08/29/07 at 18:59:41, srn347 wrote:
It's a trick, they want you to think that. It's 50-50.

If it's really 50-50, why would "they" try to trick you, since it wouldn't matter if you switched or not? :P

--SMQ
Title: Re: $1,000,000 box
Post by srn347 on Aug 30th, 2007, 10:08am
So your answer to the riddle would be wrong. And perhaps it's an idiom.
Title: Re: $1,000,000 box
Post by Aryabhatta on Aug 30th, 2007, 1:52pm

on 08/30/07 at 01:00:49, towr wrote:
I can't imagine why I'm still bothering to enlighten you;


It is clear that srn347 is only capable of talking and not listening.

I suggest we just ignore him.
Title: Re: $1,000,000 box
Post by Hippo on Aug 31st, 2007, 2:03pm

on 08/30/07 at 13:52:09, Aryabhatta wrote:
It is clear that srn347 is only capable of talking and not listening.

I suggest we just ignore him.


This is exactly what I have been thinking about ... I have strength feeling this is common idea of lot of us.

P.S.: I had feeling there followed some other posts of towr, but he deleted them as irrelevant....
Title: Re: $1,000,000 box
Post by towr on Sep 18th, 2007, 11:23pm

on 08/31/07 at 14:03:04, Hippo wrote:
P.S.: I had feeling there followed some other posts of towr, but he deleted them as irrelevant....
Yes, that's right.
Perhaps I could go as far as deleting everything from the 16th reply down, since it adds little to the topic to this thread. But ending on the note of ignoring him seemed fitting.

And note, srn347, if you post anything with a font size over 3, I will delete it on sight now. I will no longer even consider the infinitesimal possibility it contains anything worth replying to.
Title: Re: $1,000,000 box
Post by srn347 on Sep 20th, 2007, 7:14am
Why? And that last one was 2002/1000, which is less than 3.
Title: Re: $1,000,000 box
Post by towr on Sep 20th, 2007, 7:50am

on 09/20/07 at 07:14:37, srn347 wrote:
Why?
Because it only serves to annoy. If you want to emphasize something there's bold or italic, even underlining, each of which is better than what amount to childish attention seeking.
And there's an end to my tolerance if there isn't any sign of a desire to improve one's behaviour after having been asked to several times.
Title: Re: $1,000,000 box
Post by srn347 on Sep 20th, 2007, 4:35pm
Or all at once.


Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright © 2000-2004 Yet another Bulletin Board