brain games mathmatical question..

answer is you should swop boxes

Well, there's a general misunderstanding, perpetuated by that abysmal Kevin Spacey film, that you should swap.

In reality, it depends on what you know about the intentions of the person who gave you the option to change your mind. Proved it on a long country walk, once.

If there is no intent from the person offering the swop then mathematically you should swop the boxes.

Shake both the boxes

It's a definite swap.

Weigh both the boxes

ffs why are you answering your own question 2 minutes later, not much of a brain game with the answer is it

50/50 chance so it makes no difference

because acquiesce, then those can ask why or those can argue it makes no difference etc.

because acquiesce, then those can ask why or those can argue it makes no difference etc.

such as crags

ffs

ok make the boxes three horses & all are 2/1 shots

you take box 1 then box three becomes a non runner that is a rule 4 of 33.333%

66.666% of your box 1 ( which was a 2/1 shot when you picked it ) after the rule 4 makes that a 1.333/1 shot or almost an 11/8 shot.

Hence in that situation you have to change to box 2 as that has to be an odds on shot.

Hope that helps

plus the title is brain games which is the tv show it was just on. So posters could also have watched it.

But you don't seem the  sharpest tool in the box acquiesce. So the title was for the show, and the topic to encourage discussion on it.

It's the Monty Hall problem.  You have a 66.6 percent chance of success if you swap.

It makes no difference (nap)

To put it in simple terms for chit chatters One box has the dosh, one box hasn't. 50/50

Even money shot in my eyes.

Crags.

Imagine how many times you will pick the winning box at the outset; it's obviously a 2 to 1 against shot.  And that's exactly where the odds will stay if you don't swap, sir.

If you pick an empty box at the outset, however, and then swap, the other guy is forced to open the only other empty box.  This is why you now have a 66.6 percent chance of success instead of 33.3 percent.

I'm keeping my box as It's 50/50 chance. To swap and lose would be heart breaking. I do watch DONT you know

Any outcome other than evens each the two is just a clever use of words and/or numbers.

You're a prat who wanted to look clever and instead has been to look an idiot.

Most folk probably agree with you at first, sir.  Until they have that eureka moment, of course, and realise the truth.

Go to google and look up Monty Hall problem.

They should make this into a game show.

A better question might be can topspin be applied to a cueball?

Have you got any more questions and answers male01

Go to google and look up Monty Hall problem.

Where you will find that by phrasing it cleverly you will feel compelled to now swap your even money shot for another even money shot.

Great thread

Akabula:

It has nothing to do with how you phrase the question, sir.  You have a 66.6 percent chance of success if you swap and only 33.3 percent chance if you don't.

The key to understanding this is to realise that the other guy is forced to open the only other empty box if you had originally chosen correctly.  As you will only choose correctly 33.3 percent of the time it stands to reason that it is advantageous to swap.

I'm always going to swap

I'd give anyone 60/40 on their money if they agreed to run it one thousand times and allowed me to swap.

I wouldn't swap but would be interested in seeing it played out like Pokermonster suggests

An interesting thread on chit chat

Pokermonster,

Your analysis is completely correct if you know that the host will always give you the chance to swap.

However, in reality, there's nothing to stop a host thinking "OK, if he chooses the right box on his first go, I'll open one of the others and offer him the chance to swap. If he chooses the wrong box on his first go, I'll go ahead and open it straight away."

In such an instance, you will be right 100% of the time if you don't swap, and 0% of the time if you do.

Well, quite, but it was specifically stated that the swap option would be given.

Well, it wasn't in the OP.

Even if it worked 60/40 in favour of swap I'd still not swap in a one off situation- as that would always be 50/50 . if you see what I mean.

You have a choice of 3 boxes  box 1 box 2 and box 3, in one of them is £100, in  the other two there is nothing.

Say you choose box number 1.

Then box number 3 is opened revealing nothing.

You are then given the option to change your box number 1 to box number 2. Should you swop? Or doesn't it matter?

Your analysis only works if you are made aware before the whole thing starts that there will be the option to swap.

Crags:

It wouldn't be fifty fifty, sir.  You have already ensured it is 2 to 1 with your original pick.

If you wish to make a profit you have to swap, the key to this is if the money is in box three the next stage is obviously null & void, hence you only given the option once the three box is out of the equation, that 2/1 shot ( box 1 )  with one less runner is  still not an even money chance  its still odds against so the right move would be to swap.

That is true, Patra.

It is a classic brainteaser.  I'm sure many a punter has had their fingers burnt betting on even money.

Well I'm keeping my box and that's final!

Its similar to the classic if you had 26 people in a room what are the odds that two actually have the same birthday

In the end on a one-off situation, it's all down to luck!

I'll open the box Michael and stop trying to fox me.

Well, my 60/40 offer stands if anyone wants to take me up on it.

I'd swap.

Right PM I'll take you on. £600 to £400 in my favour.
I've got the boxes set up and will let you know the outcome some time tomorrow night.

Okay, I accept.  How can we make this thing work?

It's started. I'm at box 6 and looking favourite.

You cannot play solo, somebody has to act as the unbiased quizmaster.

My wife is doing that. Box 11 now and I'm still favourite.
I hope your not one of these people who goes back on their word.

No, I'm certainaly not.  By the same token, I hope you're not one of those who is economical with the truth.

1 in 3 chance you are correct
2 in 3 chance you are incorrect

You are going to be incorrect more than you are correct

If incorrect, then the box opener is forced to open the only other empty box. Therefore the money is the remaining box (the one NOT chosen and the one NOT opened).

If correct, then the box opener can open any of the other two.

Since you are going to be incorrect more times than you are correct, it is advantageous to swap as the money will be in the remaining box.

Let me know the result after box 1000, Akabula, and we'll settle up.

OK PM
I have to say I'm feeling lucky and on a good run, box 32 and it's 31-1 in my favour.
You can put that down to variance.

As you're on a lucky streak, perhaps we could up the ante and I'll travel to play the game in person?

the OP doesn't mention that the "host" or whoever picks the 2nd box isn't allowed to pick the winning box.

Are the boxes different colour's because that could make a big difference.

the % of the awap is not 50/50 its 2/3 or 66.66%

awap = swap

i have proof that this is the answer forget all the ponderables about weight colour etc

read the effing ?

Sep 3, 2014 -- 11:18PM, erse2 wrote:

the OP doesn't mention that the "host" or whoever picks the 2nd box isn't allowed to pick the winning box.

you have a choice of 3 boxes  box 1 box 2 and box 3, in one of them is £100, in  the other two there is nothing.

Say you choose box number 1.

Then box number 3 is opened revealing nothing.

You are then given the option to change your box number 1 to box number 2. Should you swop? Or doesn't it matter?

what the puffin hell are you  puffin talking about

like someone else said up there ^ monty hall, do the swap.

There is a vital piece of information missing from the OP. The missing info is that the person offering the choice of boxes KNOWS which box contains the money...and then opens the first box knowing that it contains nothing.
So you swap your box, which had (and STILL HAS!) a one-in-three chance of winning for the another box which now has a one-in-two chance.

But this only applies if the person offering and opening the boxes KNOWS where the money is. It is NOT pure chance as one might first think.

No the person offering the choice does not have to know, it is better
to swap and this is the case when both players don't know.

Actually it is dependent of course on the 2nd box being empty.
If this was done say 100 times would it be an advantage to always
go 2nd if no swops are allowed and the person going first has a one
in 3 chance?

^^^ no that wouldn't work, you need to be offered the swop, after
the second box is empty.

When box 3 is taken away you are left with a 1 in 2 chance that box 1 has the money and similar odds that box 2 contains the cash.

I remember watching this conundrum on Marcus Du Sautoy's show with Alan Davies as his guest a few years ago and it took me ages before I twigged:

https://www.youtube.com/watch?v=o_djTy3G0pg

Fought against this for a while. Only made sense when someone explained with more boxes.

Pick a box out of 100, 98 empties get removed, dont know what odds on the other box but loads better than my 99/1

^^^ most elegant clarification

Ok then. I agree that the person opening the boxes does NOT need to know which are empty. But this would mean that once in every three repetitions of the game the first box opened would be the prize box...thereby totally ruining the whole point of the puzzle!

Nailedontip. Yes it is much easier to see with more original  boxes. But some of these posters don't realise that, with 100 boxes, the puzzle wouldn't work 99 times out of !00. Unless the box-opener KNOWS which are the empty ones!

Also at the start there is a 2  in 3 chance that the box with money will
have been picked. If when the second box is empty does this increase
the chance of the 1st being right and so it would be better not to swop

To convince someone, put a pack of cards face down, ask them to pick out, say, the ace of spades.
Now, they are 51/1 to pick it, ok?
Now, you take the other 51, look through them, pick one and show him the other 50.
Now, is he still 51/1 or is he evens?
If he thinks evens be generous and give him 5/4.

Lfc. So is it OK if the first box opened contains the prize? What do you do then? Start again?What happens after 24 ti8mes of picking the prize box first? All go home?

naydam i was going on the assumption that the contents are unknown but that
the box that is opened has of course to be empty...there is no point swapping then :-)

But if the box is empty shkuld you not swop because there was origionally
a 66% cbance that one of you would be right. Therefore increasimg your chances
if the other is seen to be empty.

does the fact that the second box is  thatempty mean that there is now a 66% chance that youhave
the right box because that is what it was for the 2 boxes