brain teaser

[TrimTheKing]

The best thing to do is get a GCSE mathematics book, look up probability "trees" or "maps" and give it a try.
Not trying to be patronising, its really not that hard when you draw it out and it dawns.

Steve

That's the thing, me and maths have never really seen eye to eye. But when it does 'click' I have one of those eureka moments and beat myself up for ages for not picking it up sooner.

I will investigate...

I was expaining this quandry to SWMBO this morning, and relating it to Deal Or No Deal, which it is clearly based on. Imagine there is £250k left on the board, and 1p. To play devils advocate, the dealer has chosen not to make an offer - you must choose one of the boxes as your prize.

Her answer was to stick with the box she's got. When I pointed out to her that, in that show, the odds of the top prize being in the box she has chosen are 1 in 22 (4.6% chance), and the odds of it being in the other box are 21 in 22 (95.4%), she said that she would still stick with the box she had.

:shock:

So why?

"Because I could bear not winning it if I never had it, but if I had it and then gave it away, i'd be suicidal"

That's women for you :lol:

Cheers

Karl

This is where it loses me Karl. I agree and wholly understand that at the 'start' of the game, those odds make sense. But once all the other boxes are opened except yours and one more, then this is exactly the same as being given 2 boxes at the start and asked to pick one, 50-50, no?.

I know that mathematicians and people with bigger brains than mine will tell me different, but I still don't get it.

I have never trusted maths since I did some research a few years ago which basically said that a massive % of what we believe to be true in maths is unproven. Someone has come along one day and said 'this' is the answer, and because nobody can either prove or disprove it, it becomes so.

Never understood that...

 

[Karl]

This is where it loses me Karl. I agree and wholly understand that at the 'start' of the game, those odds make sense. But once all the other boxes are opened except yours and one more, then this is exactly the same as being given 2 boxes at the start and asked to pick one, 50-50, no?.

No - if you were to choose just 1 box from the two available, then I agree the odds are 50/50.

But the "swap" option isn't the same - because 1 box came from a pool of boxes which, collectively, had a much higher chance of being the ones which contained the top prize - agree?

We know that the odds of the prize being in your box were 1 in 22. So that hasn't changed. The fact that other (opened) boxes have been eliminated doesn't change these odds.

So if your box remains at 1 in 22, and the sum of all probabilities must equal 1, then the odds in respect of the other box must be 21 in 22.

Cheers

Karl

 

[RogerS]

Damned mathmaticians :shock:

http://en.wikipedia.org/wiki/Monty_Hall_problem


How about if you transpose the problem to Russian roulette would you trust the math?

That would depend on the type of gun. There is one model (but I can't remember which one it is and so not prepared to stake my life on it!) that is so perfectly balanced that the weight of the bullet will always make it stop at a point where the bullet is in the lower half of the chamber and so you are 100% guaranteed not to blow your brains out!

 

[jlawrence]

My thoughts:
Since the host will always choose an empty box, the box you're choosing (initially) doesn't have a 1 in 3 chance of winning it has a 1 in 2 chance - the hosts' box can be discounted as it's always empty.
Regardless of which box you choose, after the host has chosen there will be a 50:50 chance of you winning.


edit:
then again perhaps not - doesn't make sense now I've written it down.

 

[The Shark]

Hi guys,
I'm with jlawrence.
I don't pretend to be a teflon head with a massive mathematical brain, but if the first box is taken away and is bound to be empty then to me it is a 50:50 chance on the remaining 2 boxes.

 

[Tom K]

I was never convinced of the arguments either until it was put to me this way.

The key is that the Host knows where the prize is. He is offering you a 50/50 deal, when you made your original choice on a 1/3 deal. He's not opening one box, he's opening ALL the boxes except the Prize box and your choice.

Let's take the case where there are not 3 boxes but 1000 boxes.

You choose no. 483. The probability of you being right is 1:1000

Ah! says the Host, 483, eh? Sure you don't want to change to 219? And he opens all the boxes except 483 and 219.

What do you do then?

You should always swap. You won't always win, but you are more likely to do so.

Cheers
Steve

Thanks for the explanation Steve anyone who didn't understand before this probably still won't :lol: Isn't the answer that you start with a 1:3 chance of picking the winner but after the host opens a box he knows to be empty the remaining box has a 2:3 chance of being the winner?

 

[Karl]

I was never convinced of the arguments either until it was put to me this way.

The key is that the Host knows where the prize is. He is offering you a 50/50 deal, when you made your original choice on a 1/3 deal. He's not opening one box, he's opening ALL the boxes except the Prize box and your choice.

Let's take the case where there are not 3 boxes but 1000 boxes.

You choose no. 483. The probability of you being right is 1:1000

Ah! says the Host, 483, eh? Sure you don't want to change to 219? And he opens all the boxes except 483 and 219.

What do you do then?

You should always swap. You won't always win, but you are more likely to do so.

Cheers
Steve

Thanks for the explanation Steve anyone who didn't understand before this probably still won't :lol: Isn't the answer that you start with a 1:3 chance of picking the winner but after the host opens a box he knows to be empty the remaining box has a 2:3 chance of being the winner?

How do you know that the box which is first to be opened is known to be empty?

The host doesn't play a part in this calculation - he doesn't know which box the prize is.

Steve's example above assumes some collusion by the host in knowing where the prize is, and I don't really understand the example.

Cheers

Karl

 

[Steve Maskery]

Karl, the host DOES know which is the lucky box, but, even ifhe didn't, even if he just happened to pick the lucky box, it wouldn't change the odds. If he accidentally opened the lucky box the game would be over.....

Cheers
Steve

 

[Karl]

I don't see how that relates to the OP though. And in Deal or No Deal, nobody know where the prizes are.

Cheers

Karl

 

[Steve Maskery]

Wel OK, so how about this for the short version.

Option 1. Stick with a decision made with a 1:3 chance of being right.
Option 2. Take the opportunity to make another decision with a 1:2 chance of being right.

I still think it makes sense to think of it as "all the boxes except 2" are eliminated. The odds change in the light of new knowledge.

Cheers
Steve

 

[Tom K]

This interesting brain teaser was suggested at work, several IC design engineers argued over the answer for several days.......

" a game show host as 3 boxs, one has a prize in. The contestant is made to pick a box. The gameshow host then purposefully opens up an empty box leaving 2 (the one the contestant has and the remaining box). Will the contestant have more chance of winning by gambling to swap for the remaining box or sticking with his/her original choice?"


answers on a postcard please......


8)

Steve

It says so Karl :lol:

 

[Karl]

Yes, but it doesn't say that the host KNEW that the box was empty.

 

[Tom K]

How else would you open an empty box purposefully? I put a link in one of my earlier replies to the Monty Hall thing that the question is based on.
Check it out dude and ease up on the meds :lol:

 

[Karl]

Ah - I read it differently.

That he purposefully opened a box, which turned out to be empty.

In any event, it still doesn't change the answer I gave on Page 1.

Cheers

Karl

 

[Tom K]

I would never doubt you Karl just thought Steves explanation confusing.
Its O.K having re-read his answer I think he missed out the "Bishop on a bicycle part" :lol: