Jump to content
Sign in to follow this  
SecretAsianMan

Riddle me this...

Recommended Posts

\o/ !!!

 

It's a wheelbarrow. Boom. I will PM you my address. Can I expect my silver royals and ropes within, let's say, two weeks?

 

Well done! Expect the items to be delivered via wheelbarrow and/or bird.

Share this post


Link to post
Share on other sites

1/3 chance to start with, which you get half right or wrong :wacko:

 

Then a 1/2 chance which booby prize was revealed :frusty:

 

The real answer is that its still a 50/50 chance but probably if you add all the statistics up it'll have a higher probability toooooo... Switch (wild guess, its 50/50 after all)

I've heard the Monty Hall problem several times before, but since a) I actually worked it out rather than being given the answer, and B) we seem to have moved on, I feel justified in stepping in here. I'll put it in spoiler tags in case anyone still wants to work it out for themselves, though.

You start well, Mington, but you make a mistake when you start thinking in halves. There are no relevant 50% probabilities in this problem. The only 50% probability is which of the booby prize doors the host opens in the event that you already had the right door, but since there's a 100% chance the door he isn't opening is also a booby prize, we don't care which he picks.

Here's my attempt at a relatively simple explanation. There are two possible scenarios:

A) You gave the right answer in the first place. In this instance the host opens a random door.

B) You gave the wrong answer in the first place. In this instance the host can only open the one remaining bad door.

In scenario A, you should stick with your choice, but in scenario B the other door is the correct one. These are the only two ways that things can play out. Scenario B is more likely. Since you only have a one-in-three chance of getting it right the first time around, there's a two-in-three chance that the host is giving you important (rather than irrelevant) information when he opens the door, and you should switch. Just because there are only two doors remaining, it doesn't mean that all the probabilities get reset. There's a 67% chance that switching doors will get you the prize.

 

 

I won't comment on the answer, as I am familiar with the problem, but it's interesting how counter-intuitive statistics and probability can be. "Common sense" basically doesn't mean anything in those domains. (Or many domains, but that's a wider discussion)

 

Similar question: say you want to stay at the best hotel out of 3, with the caveat that once you leave a hotel you can't go back to it. You go to the first hotel on your list. Then you go the second hotel and it's better than the first. (We'll assume no hotels are exactly equal) Given that should you now continue on to the third hotel, or stay at this second one?

 

In some ways I think this is even more devious that Monty Hall (although the solution is basically the same) in that it's not interactive at all. Nobody actively does anything, there's not even the potential for any sort of trickery.

Since you say it's essentially the same as the Monty Hall one, I'd assume the answer is that they should continue, but running through it myself it seems like they should stick. There are six possible sequences the hotels could be in before they start, in terms of quality ("1" signifying the best):

1 2 3

1 3 2

2 1 3

2 3 1

3 1 2

3 2 1

Once they determine that the second hotel is better than the first, they can eliminate any scenario where the number in position two is higher (i.e. worse) than the number in position one:

 

1 2 3

1 3 2

2 1 3

2 3 1

3 1 2

3 2 1

This leaves two scenarios wherein the hotel they're currently at is the best, and only one where the final hotel is. On a more intuitive level, it makes sense to me: we know nothing of the quality of the last hotel – it could be best, worst, or between the two – but we know for sure that the middle hotel isn't the worst, because it's already better than the first. It doesn't seem quite as counter-intuitive as the Monty Hall problem. It still seems at first glance like it should be a toss-up, though.

 

 

It's a wheelbarrow. Boom. I will PM you my address. Can I expect my silver royals and ropes within, let's say, two weeks?

God dammit, I was getting really excited reading through two pages'/five hours' worth of posts without anyone getting it, only for you to have posted your answer five minutes before I had a chance. I then spent apparently about half an hour putting this stupid post together. I'm slow.

Congratulations, though.

Share this post


Link to post
Share on other sites

I found it useful to think of a million doors for the Monty Hall. If you randomly pick one out of a million doors, and the host then opens another 999,998 wrong answers, do you still stick with the 1 in a million chance that you chose right the first time?

Share this post


Link to post
Share on other sites

There are several ways of looking at the Monty Hall problem.  The way I like to explain it is you have a 1/3 chance of getting it right the first time in which case switching will get you nothing.  You have a 2/3 chance of getting it wrong the first time in which case switching will give you the prize, so switching is statistically better.

 

The answer of switching yields the best chance also depends on certain conditions to be true, such as the host knowing what's behind every door or his pattern of opening doors not being random.  It's a neat problem and one of my favorites.

Share this post


Link to post
Share on other sites

Another logic one that I'm sure many probably know.

 

A man is walking down a road when he comes to a fork.  At the fork are 2 men, one from Truthtown where everyone always tells the truth, and another from Liarville where everyone always lies.  One path in the fork leads to Truthtown and the other to Liarville.  The man wants to get Truthtown.  What one question can he ask both men to determine which road to take?

Share this post


Link to post
Share on other sites

The biggest riddle of them all.... Who the fuck is Monty Hall

Mystery solved I just google him, this whole time I assumed it was a place :) lol

Thanks for explaining it jimbo, dibs and secret

Share this post


Link to post
Share on other sites

Couldn't you just ask them which road they travelled down to get to the fork? If you asked that then they would both have to point to the Truthtown road.

Share this post


Link to post
Share on other sites

Couldn't you just ask them which road they travelled down to get to the fork? If you asked that then they would both have to point to the Truthtown road.

 

One could argue that they didn't necessarily get to the fork from their respective towns, but you understood the core concept, which is you have to ask them both a question that will result in the same answer.  The more general question I was looking for is "Which road leads to the town you're from" but you essentially got it.

Share this post


Link to post
Share on other sites

The biggest riddle of them all.... Who the fuck is Monty Hall

Mystery solved I just google him, this whole time I assumed it was a place :) lol

 

 

Monty Hall is the American equivalent of your elder statesman Milton Keynes.

Share this post


Link to post
Share on other sites

I found it useful to think of a million doors for the Monty Hall. If you randomly pick one out of a million doors, and the host then opens another 999,998 wrong answers, do you still stick with the 1 in a million chance that you chose right the first time?

 

A really good strategy for all sorts of logical reasoning is to consider extreme cases.

 

Since you say it's essentially the same as the Monty Hall one, I'd assume the answer is that they should continue, but running through it myself it seems like they should stick.

 

I mean the reasoning and the type of problem is the same. (Yes, the answer is to stay where you are) These types of problems are tricky because the "common sense" explanation is based on the state where you have no relevant information, but in the course of the problem you obtain relevant information that changes the probabilities. (Or....elucidates them)

Share this post


Link to post
Share on other sites

Balloonneer? One who balloons? 

 

:(

balloonneer English Noun

balloonneer

  1. Common misspelling of ballooner.

Quadruple score!

 

EDIT: Oh geez, this thread is 7 pages long, I'm out of the thumbs loop.

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
Sign in to follow this  

×