Open for discusion (stats/probability related)

Gide

Here’s an interesting post I saw on a French forum. I’ll try to translate it as best as I can.

You are on a TV Show and you can win the big prize.
It’s hidden behind one of three doors.
You pick one door.
The Host open one of the two remaining door that he know has nothing behind it

You have the opportunity to change your choice and take the remaining un-open door.

What do you do?

Gide

Pigga

Ill take whats in the Mystery Box

NurseHoliday

This is a good one! Sadly, I am already very familiar with this so I won't spoil it for the others.....but I suspect some others may also be familiar with it (ScottyZ or other math geeks....).
After everyone has had a chance to kick the cat, I will share an interesting (maybe only to me) anecdote about this particular problem and how I came to be so familiar with it.

pkrfce9

Let's see. When you picked your door, you had a 33% chance of picking the right one. When the host shows you one of the other doors is wrong, that means the remaining door now has a 50% chance of being right. Is yours still only 33%? Or is it now 50%??? (Of course, the host always knows which 2 of the doors are losers, so can always show you a door that is a loser. So he's not really giving you any extra information)

I'd rather fight than switch. Or maybe if the host gave me an extra 500 bucks I'd switch...


Here's another classic: There are two doors. One leads to freedom, the other to death. Each one has a guard. One guard always lies and one always tells the truth but you don't know which one is which. You may ask one guard one question to determine the proper door to choose. What is the question?

Unknown

My head hurts. Two great questions, guys... I'm looking forward to reading the answers, as it's becoming apparent that I won't be able to come up with them on my own.

ScottyZ

As NH guessed, I've heard both of these math geekeries before, so I will leave it up to the rest. Bonne chance!

ScottyZ

JuiceMan

Go with your first instinct, its ussually more correct then second guessing yourself

Gide

So far we have 2 persons that won't switch
1 that want the mystery box (or want to grow his post total)
1 that won't commit himself (are you married all_aces .. maybe we seen a trend here)
3 that know the answer (or think they do)

should have made a poll with the question...

Gide

P.s. My day at work is almost done... i'll post the answer before the tourney tonight

Unknown

1 that won't commit himself (are you married all_aces .. maybe we seen a trend here)

No, I'm not married, and I plead the 5th on the other thing...

Zithal

Feel free to add me to the list of people that already know the answer. One poster was on the right track, then fudged up his thinking.

I want to give a clue, but I'm afraid of giving it away, so here's a clue in rot13:

Jung'f gur punapr gung lbh'ir cvpxrq gur jebat qbbe?

http://www.rot13.com/index.php -- awesoma powa!!!!

MickeyHoldem

Add me to the list of "seen it before"... for any non-believers... there is an excellent simulation of the "Monty Hall" puzzle at...

http://www.cut-the-knot.org/hall.shtml

The second logical puzzle has many forms... the most famous is perhaps "The Lady and the Tiger"

Just don't get started on the Knights/Knaves scenario!

MickeyHoldem

Here's an interest prop bet... related to the Monty Hall puzzle...

I will place $100 under 1 of 3 glasses (opaque of course). You pay $120 for a chance to play. You pick a glass... then I remove a glass... then you can choose to switch to the remaining glass if you like. You get to keep what's under the glass you pick!... Do you Play?

ScottyZ

MickeyHoldem wrote:

Here's an interest prop bet... related to the Monty Hall puzzle...

I will place $100 under 1 of 3 glasses (opaque of course). You pay $120 for a chance to play. You pick a glass... then I remove a glass... then you can choose to switch to the remaining glass if you like. You get to keep what's under the glass you pick!... Do you Play?

I'm like that crazy weasel from Looney Tunes.

Yes, yes, yes. Play, play, play. *weasel slurping noise*

ScottyZ

ScottyZ

Damn. You got me.

On further consideration of the rules, I'll pass on this particular game. :cool:

ScottyZ

Gide

thank mickey for giving the link that give the solution.
I guess that all the peoples that only said that they knew the solution didn't give you a clue that they wanted people voicing their opinion on the problem and try to understand it...

to me you look like a 7 years old who know the answer to a riddle and when someone else ask it he goes " me me me I know it" and he tell the answer before the person telling the riddle even finish it

Gide

btw the link is really good

ScottyZ

Gide wrote:

thank mickey for giving the link that give the solution.
I guess that all the peoples that only said that they knew the solution didn't give you a clue that they wanted people voicing their opinion on the problem and try to understand it...

to me you look like a 7 years old who know the answer to a riddle and when someone else ask it he goes " me me me I know it" and he tell the answer before the person telling the riddle even finish it

Gide

btw the link is really good

I don't see anything wrong with posting a link (or Rot13). People who are still working on the answer don't have to follow that link or decode the message.

Now that there's Google, it's *hard* to ask questions whose answers are hard to find.

ScottyZ

Gide

oups! didn't see it your way scotty... for me identifing it as the monty hall puzzle and giving the link was giving to much info but you are right.. people can still "play/try" to answer it if they want

sorry mickey... look like i'm the 6 years old who don't like his big brother spoiling the fun

Gide

MickeyHoldem

Hmmm...

You are on a TV Show and you can win the big prize.
It’s hidden behind one of three doors.
You pick one door.
The Host open one of the two remaining door that he know has nothing behind it

You have the opportunity to change your choice and take the remaining un-open door.

Who knew mentioning Monty Hall would be such a great clue?

Let's see. When you picked your door, you had a 33% chance of picking the right one. When the host shows you one of the other doors is wrong, that means the remaining door now has a 50% chance of being right. Is yours still only 33%? Or is it now 50%??? (Of course, the host always knows which 2 of the doors are losers, so can always show you a door that is a loser. So he's not really giving you any extra information)

I guess it's OK to post answers... as long as they're not correct... (no offence pkrfce9) but a link to the most well known puzzle on earth (ok... over the top... I know) is not?

Considering the responses that I've seen on other forums when this puzzle gets posted... consider yourself lucky!

Unknown

Well, I looked up the answer to the '2 guards' question on the net, because I was wallowing in suffering, waiting for it to be posted here. I have a problem with the solution. Do not read any further if you don't know the answer, and want to keep trying to work it out....

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The problem is that the answer 'what would the other guard say if I asked him which door leads to death' is based on an assumption that the guard who tells the truth KNOWS that the other guard always lies, and will base his answer on that information. Me and some friends actually came up with this answer, but I wasn't buying it for that reason.... I was hoping for an 'assumption-free' answer. Anyone else feel a little ripped off, or is it just me?

pkrfce9

I was hoping this could be a forum where ideas could be discussed. That is what makes it interesting. Not everyone is a genius and not everyone knows the solution to this classic problem let alone the logic behind it. Simply saying "I know this one" doesn't help those people out. Blurting out the answer without the logic isn't helpful either.

From that perspective, posting the link was very good. It doesn't hit you over the head with the answer but logically walks you through how to figure it out. When you extend the problem to several doors, it is also easier to see why it pays to switch. The multi-stage Monty Hall version of the problem is particularly interesting.

I've heard the problem mentioned before but never analyzed very thoroughly. The link gives you the tools to understand why it is worthwhile to switch. Although, intuitively, I'd hate to switch if I had the correct door. Kind of like Tyson moaning when he gets bluffed out.

So thanks for the link. That is the kind of info I like to see.

Does anyone care to discuss the 'one door to death, one door to freedom' dilemma?

How about "How far can a dog run into the woods?" :rolleyes:

pkrfce9

The guard dilemma is a logic problem. It has to use absolutes to make it work. So one guard always lies and the other always tells the truth. To finish it off, you will always be given the wrong door.

Actually, one guard does not have to know the truthfulness of the other. If your question was "Please ask the other guard which door leads to death and tell me his answer?" Then you'd be ok.

Now do you want to try fuzzy logic on this one? Say one guard tells the truth 75% of the time and the other lies 75% of the time...