What's new
By:
USCHO Fan Forum

This is a sample guest message. Register a free account today to become a member! Once signed in, you'll be able to participate on this site by adding your own topics and posts, as well as connect with other members through your own private inbox!

  • The USCHO Fan Forum has migrated to a new plaform, xenForo. Most of the function of the forum should work in familiar ways. Please note that you can switch between light and dark modes by clicking on the gear icon in the upper right of the main menu bar. We are hoping that this new platform will prove to be faster and more reliable. Please feel free to explore its features.

Monty Hall, we have a PROBLEM

owslachief

owslachief

occupe toi de tes oignons
And any other offerings * #

I'm reading this book called "the curious incident with the dog in the nighttime" and the protagonist explains the "Monty Hall Problem". Several thoughts at once:
1. If Let's Make a Deal had offered this scenario to its contestants a dozen or so times, it would lose its insurers and sponsors.
2. I have a healthier respect for the field of statistics and probability
3. PhD's can be pretty lazy
and more besides.

The answer makes no intuitive sense. But s&p is impersonal like all the other maths, and doesn't care about human reason ;).

Goes like this:
You're on a game show where there are 3 doors presented. A car is behind one door, and behind each of the other doors is a goat.
After you pick a door, and before the host (who knows where the car is) opens your chosen door, he reveals what's behind another door - a goat. He offers you the choice of sticking with your first choice, or switching your choice to the other unrevealed door. What choice gives you the better chance of winning the car?
 
Re: Monty Hall, we have a PROBLEM

I'll post my reply in white so it's not a spoiler for others.

When you first pick a door, your chances of it being right are one out of three.

When Monty shows you what's behind one of the other two doors, that action occurs AFTER you already made your choice.

The chances of your choice being right do not change as a result of something that happens subsequently.

Therefore, your chances of being right, if you stick with your original choice, are still one out of three.

Since there is now only one other door available, the chances of THAT door being right must be 1 minus 1/3, or two out of three.

Therefore, you should always pick the other door, not the one you started with. Your chances of winning are twice as good if you switch than if you don't switch.

Most people's intuition gets bollixed up at step 3.
 
Re: Monty Hall, we have a PROBLEM

A couple other ways of thinking of it:

Imagine you pick your door. However, Monty doesn't show you any goats. Instead, Monty offers to trade BOTH his doors for your door. It's the exact same problem. Since there's two goats, we already know for sure that one of them's going to be a goat no matter what.

Or imagine it this way:

There's a million doors. You pick one. Monty opens 999,998 of the other doors to reveal goats, leaving just your door and one other door that he conspicuously skipped for some reason. Hmm, wonder where the car is?

The key to the whole problem is this: Monty knows where the goats are. He will ALWAYS have at least one goat left and will ALWAYS reveal a goat.
 
Re: Monty Hall, we have a PROBLEM

As long as we're playing game theory:

You find yourself in a truel (three-way Mexican standoff from the old westerns.) Your opponents are a man in a white hat and a man in a black hat.

The man in the white hat is the best shot in the West. He hits his target 100% of the time.

The man in the black hat is an average shot. He hits his target 66% of the time.

You are an awful shot. You only hit your target 33% of the time.

However, they have offered you the first shot before they begin shooting.

Who do you shoot?

Answer whited out below:

No one. Waste your bullet. The white and black hat will view each other as the greater threat and one of them will take the other out. You actually have up to a 40% chance of winning this way.
 
Re: Monty Hall, we have a PROBLEM

Twitch Boy said:
As long as we're playing game theory:

You find yourself in a truel (three-way Mexican standoff from the old westerns.) Your opponents are a man in a white hat and a man in a black hat.

The man in the white hat is the best shot in the West. He hits his target 100% of the time.

The man in the black hat is an average shot. He hits his target 66% of the time.

You are an awful shot. You only hit your target 33% of the time.

However, they have offered you the first shot before they begin shooting.

Who do you shoot?
Click to expand...


Hmm...without having viewed your answer, i surmise you "accidentally" shoot yourself someplace where it won't do any lasting harm, and then ask to be disqualified because of your injury??
 
Re: Monty Hall, we have a PROBLEM

Twitch Boy said:
A couple other ways of thinking of it:

Imagine you pick your door. However, Monty doesn't show you any goats. Instead, Monty offers to trade BOTH his doors for your door. It's the exact same problem. Since there's two goats, we already know for sure that one of them's going to be a goat no matter what.
Click to expand...

When Monty reveals the goat it's both a red herring and an odds-enhancer. The contestant would tend to eat the herring. He thinks his odds have been raised to 50%, when in fact he's been given a chance to double his 33%.
 
Re: Monty Hall, we have a PROBLEM

Game Theory is awesome. It messes with your mind so much. :D
 
Re: Monty Hall, we have a PROBLEM

You just died.

Don't worry, no matter what you believed during life, there IS an afterlife.[SUP]1[/SUP] and it's totally non-sectarian, too! All you need is a good heart and a clear mind.

The reason no one comes back, is that right after you die, you are given a choice.

Before you there are two doors. They are absolutely identical in every respect, there is no way to distinguish one from the other.....until you pass through!

One is the door to heaven, and the other is the door to hell.

In front of each door, there is a guardian. The door to heaven is guarded by an angel. It embodies everything good, which means it always tells the truth.

The door to hell is guarded by a devil. It embodies everything evil, including duplicity.[SUP]2[/SUP] It looks just like the angel in every respect, except that it always lies.

You have one question and can ask only one of the two guardians your question. What question do you ask to ensure you open the door to heaven?








[SUP]1[/SUP] I think it was Bertrand Russell, though it may have been a different famous logician, who said: "if you are not sure whether there is an afterlife or not, it is more logical to believe that there is. If you believe that there isn't and you are wrong, the consequences are much more severe than the converse."

[SUP]2[/SUP] The most insidious thing the devil ever did was to trick us into believing he does not exist.
 
Re: Monty Hall, we have a PROBLEM

FreshFish said:
You just died.

Don't worry, no matter what you believed during life, there IS an afterlife.[SUP]1[/SUP] and it's totally non-sectarian, too! All you need is a good heart and a clear mind.

The reason no one comes back, is that right after you die, you are given a choice.

Before you there are two doors. They are absolutely identical in every respect, there is no way to distinguish one from the other.....until you pass through!

One is the door to heaven, and the other is the door to hell.

In front of each door, there is a guardian. The door to heaven is guarded by an angel. It embodies everything good, which means it always tells the truth.

The door to hell is guarded by a devil. It embodies everything evil, including duplicity.[SUP]2[/SUP] It looks just like the angel in every respect, except that it always lies.

You have one question and can ask only one of the two guardians your question. What question do you ask to ensure you open the door to heaven?
Click to expand...

Answer in "white"
You ask one of the guardians whether both of them always tell the truth.
 
Last edited:
Re: Monty Hall, we have a PROBLEM

A different, correct, answer in white:

You ask one of the guardians which door the OTHER one would say led to heaven.
 
Re: Monty Hall, we have a PROBLEM

The following problem has driven me nuts, and I've never solved it. The phone rang or it was time to fix dinner or something always came up.....

Any takers?

Five friends, Andrew, Bernard, Claude, Donald and Eugene, each have a son and a daughter. Their families are so close that each has married his daughter to the son of one of his friends. Consequently, the daughter-in-law of the father of Andrew's son-in-law is the sister-in-law of Bernard's son, and the son-in-law of the father of Claude's daughter-in-law is the brother-in-law of Donald's daughter. But although the daughter-in-law of the father of Bernard's daughter-in-law has the same mother-in-law as the son-in-law of the father of Donald's son-in-law, the situation is simplified by the fact that no daughter-in-law is the sister-in-law of the daughter of her father-in-law. Who married Eugene's daughter?
Click to expand...
 
Re: Monty Hall, we have a PROBLEM

FreshFish said:
The following problem has driven me nuts, and I've never solved it. The phone rang or it was time to fix dinner or something always came up.....

Any takers?
Click to expand...
You realize that A, B, C, D & E are all bigots because they did not allow same sex marriages. :)
 
Re: Monty Hall, we have a PROBLEM

Lynah has the right answer. First time I heard that one was some years ago and it took me a little while to figure out, but the trick is to figure out a question where both the angel and devil will give the same answer.
 
XYZ said:
Lynah has the right answer. First time I heard that one was some years ago and it took me a little while to figure out, but the trick is to figure out a question where both the angel and devil will give the same answer.
Click to expand...
Not to quibble, but two correct answers were given.
 
Re: Monty Hall, we have a PROBLEM

owslachief said:
Not to quibble, but two correct answers were given.
Click to expand...
I agree. Owslachiefs answer is also "correct" in that it will give you the information you seek in this particular problem. The problem statement gives you 3 key pieces of information:

1) there is a truth teller
2) there is a liar
3) the truth teller is in front of the heaven door (so the liar is in front of the other).

Given those 3 pieces of info, owslachef's answer works perfectly. I've seen a similar problem statement that omitted item #3 above: the guardians are just standing together, off to the side, and not associated with either door. In that case, owslachef's answer doesn't work - his question will tell you which is the liar and which is the truth teller, but then you would need to ask a second question to find out which door to choose, as that information is not "linked" to which guardian is which. The answer I gave works whether the guardians are associated with the doors or not.

Interestingly, if the guardians are not assigned to particular doors and you ask the question I gave, you would be able to choose the correct door, but you would still *not* be able to identify which guardian was the liar.
 
Re: Monty Hall, we have a PROBLEM

You're in an auction with one other person. Up for bids is a crisp $100 bill. There's a catch, however: the losing bidder must pay his bid as well and gets nothing.

Bidding starts at $1.

What is the optimal bid?

$99. (Or $100, if the opponent is spiteful.)

Someone bids $1, and is in line to make $99 profit. Someone else bids $2, putting him in line to make $98 profit. The original bidder can either lose his $1 or up his bid to $3, making $97 profit. The other guy can lose his $2 or up his bid to $4, making $96 profit.

Rinse and repeat until someone bids $99. The other bidder can lose his $98 or bid $100 and break even. The other guy can now lose $99 or bid $101, losing $1. The other guy can lose $100 or bid $102, losing $2. Repeat ad infinitum.

The only "winning" move is to immediately bid $99 and make $1. However, if spite is taken into consideration your opponent can bid $100, break even, and screw you over...
 
Re: Monty Hall, we have a PROBLEM

LynahFan said:
I agree. Owslachiefs answer is also "correct" in that it will give you the information you seek in this particular problem. The problem statement gives you 3 key pieces of information:

1) there is a truth teller
2) there is a liar
3) the truth teller is in front of the heaven door (so the liar is in front of the other).

Given those 3 pieces of info, owslachef's answer works perfectly. I've seen a similar problem statement that omitted item #3 above: the guardians are just standing together, off to the side, and not associated with either door. In that case, owslachef's answer doesn't work - his question will tell you which is the liar and which is the truth teller, but then you would need to ask a second question to find out which door to choose, as that information is not "linked" to which guardian is which. The answer I gave works whether the guardians are associated with the doors or not.

Interestingly, if the guardians are not assigned to particular doors and you ask the question I gave, you would be able to choose the correct door, but you would still *not* be able to identify which guardian was the liar.
Click to expand...
Isn't there a scenario where you ask a liar if he/she is telling the truth and if they say No, it's the truth, but they can't tell the truth so they end up in an infinite loop?
 
You must log in or register to reply here.
Back
Top