ok, firstly John, I just said that the motives of the offerer would always determine the choice you make and not the statistical possibilities based on mathematical calculations.
secondly, Pi... seduce your uncle? I mean it's probably not illegal or anything but come on!
Dublin: I realised the problem with 'matters of opinion' which is why I said "anything specific" in my post. Since George has often criticised my understanding of politics it’s worth reminding him that he predicted that Blair would come out of the Iraq war ‘smelling of roses’ and that the coalition troops would leave Iraq in July :) Oh dear, they don't seem to want to go George!
There are numerous other similar statements and predictions on a variety of topics where Missi has demonstrated the same keen insight and deep understanding of his subject that validates his right to criticise in his elegant, erudite and eloquent manner. ‘F.uck Off you twat’ is somehow almost a mystical revelation when typed by the master himself and seems to subtly express the ebb and flow of that mighty river from which he modestly takes his name.
I think a mighty wind might have been more apt for someone with so much bluster but perhaps those less respectful of the great man might then call him Gusty George - still it's no worse than Watery Win the wet has-bin :)
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Stormy, the genius of that piece will have me chuckling for a long time to come. The next time i get lost in the ambiguity of life, i will think of Cleese and have a good chuckle.
Chuff, chuff, chuffwoooooch, woooooch! Sssssssss, sssssssss! Diddledum, diddledum, diddlealum. Toot, toot. The train now standing at platform eight, tch, tch, tch, diddledum, diddledum. Chuffff chuffffiTff eeeeeeeeeaaaaaaaaa Vooooommmmm.
In other words, my work is done and so I'm I.
Good night, or should i say good morning?
The ambiguity!
opppss yes Ely your right it could be illegal - ok hire some sexy woman to do it for you ... there again she might run off with everything
hummm suppose it wouldn't matter if you are female of male - you could still torture him with a couple of days and nights of emerdale farm - you must understand I have nothing against emerdale farm its just the impact I'm after .... I could sing to him that would work
I have the answer - I know how to find out
*steals stormy's idea from another thread *
Put the uncle in a box with Mississippi and Mykle - he'd soon want out so would have to tell - that would work wouldn't it ?
Thanks Liana. You've given me a very welcome confidence boost. I've always maintained that Maths is relatively easy if you have the right teacher, and that many of the people who claim to be maths-phobic would lose their fear of the subject if things were explained properly. What I like about Maths is that there are few grey areas (well at least in the A level Maths I did at school). An answer is either right or wrong.
In reply to Mykle, I understand exactly what you are saying and I have to say I do not understand why George seems to have a downer on you. In the few posts of yours I've read, I've never found you anything but a reasonable and down-to-earth bloke. As I said on another thread, I was deeply touched by your post about mixed race kids (being of mixed race myself), and anyone who posts like that cannot be all bad.
I genuinely like old Mississippi, but I can't say I always understand where he is coming from.
Damn that's a funny way of looking at it Hen. The number of paths after you picked a box is irrelevant. You are left with a situation where there are only two boxes left, the only question that matters is: do you have your hand on the right box or the wrong box. Remember there were three boxes when you chose that box, do you think it suddenly got more likely to be right.
Notice that your uncle hasn't given you any information about the box you chose, you already knew there was at least one empty box left and him revealing that fact tells you nothing about whether you chose right or you chose wrong. He does, however, tell you quite a bit about the two boxes you didn't choose.
Like I said, this problem has famously baffled some very important mathmaticians, yet my mum (who did no maths beyone O level and forgot most of that) can see right through it.
Dub - screw convincing them, let's go into business as box hustlers. Jesus, if even when you spell it out people don't believe it, how much money can we make out of suckers that we don't try to convince that we're conning them by them sticking with their original choice while we back switch?
Any one of you stickers actually bothered to Google the Monty Hall problem and see that it is a classic probability puzzle that has as its solution, switching is better than sticking by odds of 2 to 1?
Dublin: to be honest, I think a lot of George's posts are designed to liven up the threads and he purposely winds people who he knows will respond. There are a few special cases, like me, who George probably really does dislike but the rest is theatrics :)
That's a completely different point - obviously there are cues you can pick up from the person doing the test; but the question is about strict probability. Which is the key more likely to be in, Box A or one of BoxB&BoxC ?
I think the horse race metaphor is badly flawed - assuming you know nothing about the horses and can bet on A, B or C. If you back A and then you are told that horse B isn't running and should you bet on horse C or stick, then you may as well stick - there are only two horses running the race, and the odds are 50-50. Because the race is yet to happen.
Providing the selection is made before any of the boxes are opened, the odds are 1/3 that it would be in any of the boxes and 2/3 that it would not be in each box. So no matter which box you pick, it is more likely than not that the box will not be in there.
What causes people problems is that of the other two boxes, you already KNOW that at least one is empty, so your uncle opening it doesn't seem to give you any new information and it seems psychologically that you are making a choice between two boxes, each of which at the beginning had a 1in3 chance of containing the prize, so your brain says, same odds, may as well stick.
It works as a puzzle precisely because our brains work in this way, and we can't see that opening one box and telling you it is empty makes it more likely that the prize is in Box C.
Take out the human or potential for trickery element. Uncle doesn't know which box the key is in and you know that for certain. If the Uncle said to you at the beginning, you can either pick to open two boxes or one, you would ALWAYS, without fail choose to open two boxes.
In making that choice, the odds that the prize would be in ONE of those two boxes (B or C) would be 2 in 3. Suppose YOU open the first box (B) and it is empty. There are two boxes left (A) and (C), but you can't magically suppose that the odds of the prize being in Box C have suddenly gone down from 2 in 3 to 1 in 2. If you were offered the chance to switch at that stage, you would be mad to do so. Because the chance of the prize being in Box A is 1 in 3, and in Box C (which is now a collapsed probability of B and C) is 2 in 3.
What causes people the problem is being able to see that knowing for definite that Box B is empty has no impact whatsoever on the probability at the outset as to which Box the keys were in - it is a 1 in 3 chance that the keys are in any particular box at the beginning and a 2 in 3 chance that the keys are in one of the other two boxes. You get a disguised opportunity to open two boxes rather than one, and you should always take that opportunity.
I was just wondering about the nationality of the mysterious 'uncle'...
If he was a Pakistani... ... there's no way that he would give away an Aston Martin.
If he was an Indian 'untouchable'... ... there's no way that he would have had an Aston Martin, in the first place.
If he was an Irishman... ... there's no way that it would have been an Aston Martin.
If he was an Australian... ... there's no way that he would have known what an Aston Martin was.
If he was an American... ... he'd be too busy going to war.
If he was a Brit... ... he'd be too busy following the American.
If he was a Frenchman... ... he'd be too busy tut-tutting at the American and the Brit.
If he was a German... ... he'd be too busy wondering what might have been.
If he was a Russian... ... he'd be too busy wondering about what, could never have been.
If he was a Moslem-fundamentalist... ... he'd have been too busy dying for the glory of Allah in a suicide bombing mission.
If he was a Jewish-Israeli... ... he'd have been too busy shooting up Palestinian kids.
If he was an African despot... ... he'd be too busy blaming the evil white man for the troubles of Africa.
It's bloody great when you don't give a stuff about political correctness -
everybody should try it now and then.
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Mykle is partly right, with his first sentence, however to consider himself a 'special' case is arrogance beyond belief. There is absolutley nothing about him that is 'special', least of all his attempts to appear more than average in the intelligence department.
I haven't 'sided' with Jon in the box discussion so much as after a cursory examination of the arguments felt that his is the most likely. I think whether or not the uncle knows which box contains the key should be ignored, unless of course the conundrum is more about the relatives than mathematics. I never saw a slide rule that knew who was holding it.
Hen, I think you are starting to get it.
When you do your one-in-25 stab in the dark there is, of course, a one in 25 possibility you have chosen the right horse. But there is a 24 in 25 chance that you have not.
If you have chosen the right horse, then your Uncle is merely going through the motions in presenting you with another horse to choose (which he knows to be a loser).
If, however, you have chosen the wrong horse (which is a 24 in 25 chance - ie very high), then it is a certainty that the final horse your uncle offers you (after he has eliminated the 23 others) will be the winning horse. In other words there is a 24 in 25 chance that your uncle's choice will be the winner.
If you can accept that, which I think you can, then simply apply the same logic to a 24 horse race, and then to a 23 horse race and so on.
Each time you will find the odds of picking the winner are higher if you choose your Uncle's selection.
Obviously as the number of runners drops, the odds drop. But the odds of your uncle's choice being the winner, will always be higher.
If you take it right down to a three horse race the priniciple still applies.
When your uncle eliminates horse B, he is in effect offering you horse C as a possible winner.
Your initial pick of horse A is a one-in-three stab in the dark. You have a one in three chance of being right. That means you have a two in three chance of being wrong.
You are more likely to be wrong. If you are wrong (a two in three chance), then your Uncle's choice must be the winning horse. Therefore your uncle's offering - horse C - has a two-in-three chance of being the winner.
Mississippi, the uncle knowing in which box the key resides is crucial to this problem.
If he doesn't know, he cannot perform the second part of the conundrum whcih is to eliminate empty box B. How can he know which box is keyless, without knowing which box contains the key?
Wondered when you'd show up John. All I know of Leibnitz is infetismal calculus, and I had to look that up.
Missi is right, it doesn't matter a fig what the uncle knew or even how the box came to be open, all that matters is when it opens.
You're right. We could clean up here. Probably need to repackage the problem, but we've clearly tapped into a rich seam.
There's almost a religious fervour in the way they cling on to their ideas in the face of inescapable logic. Seems like there are quite a few flat earthers out there.
I googled it the other night trying to find the original colomn by Marilyn Vos Savant (I didn't, and it turns out the problem predates her by several years under the name "The Three Prisoners Dilemma").
However I read a couple of very interesting psychology papers on why people stick so forcefully to the 50/50 result, even when it is demonstrated to be wrong. Very interesting but no good answers, like all psychology.
Trivia: One mathmetician did do a version of it at a church fate, and made a fortune.
now THAT'S what I call an explanation. you've really nailled it there Dub, well done. I'm gonna use that when I pull this one out for the family at the weekend.
I see the point, but to me, that actually SEEMS less compelling than the original scenario, whereas your point presumably is that everyone would see the sense in switching horses in this illustration. It just is one of those things where there is a difference between what is there and the pattern the brain tries to put on it. I can see with my logical mind that the horses is a more definitive example, but with my pattern-forming mind I feel much more likely to say 'there's only two horses, its fifty fifty' - the increased numbers somehow make it SEEM less compelling when the reverse is mathematically true.
Interesting.
I understand your point Andrew. It's interesting to see how many different reactions and approaches there are to this problem.
The result seems so counterintuitive. There's something almost creepy about the way it confounds "common sense", which obviously troubles a lot of people - including me I have to say until I got my head round the explanation.
Oh dear, are we still talking about this? OK, let's have a stab.
The point - that I missed when first presented with this problem - is that when you make a decision, you 'lock' the odds that are associated with that decision.
If you have three boxes, one of which contains the car keys, and you choose one of them at random, there is a 1 in 3 chance that the keys are in that box, and a 2 in 3 chance that they aren't. *NOTHING* can ever change that (except opening both boxes that weren't chosen, or opening the box that was). In other words, it is the *decision* that is subject to probability, not the box!!
When one of the boxes is removed, then there is a 1 in 2 chance that the keys are in either of the two remaining boxes. But you aren't just being offered a choice between two boxes - you are betting on whether you made the right decision or wrong decision initially. The box has been removed, but the decision hasn't.
There is nothing about the two boxes that favours one of the other. As an isolated decision, it is a purely a 1 in 2 shot - box A or box B. There is no reason that the two boxes should influence your choice, so you can concentrate solely on betting whether you were right or wrong in your first selection.
Now, if you've made a random choice from three boxes, would you say you made the right choice, or the wrong choice?
OK, I get it now. I was wrong. And what's more, I shouldn't have stated my maths credentials as a way of trying to sway anyone.
Now. I've wasted the whole day. And I don't have the time. So this is the last post I'm ever going to make on these forums.
I didn't think I'd ever say that, but I reckon it's the only way to motivate me to stop. I hate going back on a dramatic pronouncement, so hopefully, I will hate the idea enough not to go back on it,
>> Those one-in-three odds remain attached to that choice throughout the life of the problem <<
>> If he did not allow you to open both boxes and you had to choose between B and C the odds are still 1/3. <<
Look I AIN'T gonna let this go.
When the uncle removes an empty box from the equation an offers you the option of switching boxes, the original offer is cancelled out and a new one made in it's place. The odds ARE '1-in-2'.
>Any one of you stickers actually bothered to Google the Monty Hall problem<
*I shouldn't do this as I'm just passing through*
Yes! And much more math and Physiological dater, that is both for and against the conclusions of the Monty Hall Experiment.
I like this explanation. Imagine you had a Million doors and that the prize was behind one of them. You pike a door, then 999,998 of the door's that don't have a prize behind them are eliminated.
Should you keep you're door or switch to the only remaining door? "It should be obvious to anyone that even though there are only 2 doors left, the odds are far greater that the prize is behind the only remaining door, -(that the player didn't pick).
Because if it as not, it would mean that the player had randomly picked the one door out of a million that had the prize behind it.
What are the odds of that happening?
But as i mentiond... It doesn't really matter what this experiment implies, because when you look at, "Imprecise Probabilities", "The double Split Experiment", Ambiguity Perception" and many other very well research areas of Probability, you fined that this way of applying probability's are limited to this kind of problem.
So, for the three box dilemma, it works, but for problems requiring moor precise useedge of probability's, it doesn't..
*Runs for cover*
Trust me George, the odds are not 1 in 2, the original offer is not cancelled. I wouldn't lie to you about this.
I've got an early night tonight and I'm away for a couple of days, but I'm working on another explanation that will satisfy even you.
Well you can try, but I doubt you'll change my mind on this one. It all hinges on what the offer is and whether the offer is 'changed', constituting a 'new' offer. I say the way the conundrum is worded, I am right. The whole thing is in fact 2 separate offers and the odds are not transferable, but have individual mathematical odds.
So there!
Well for what it's worth Jon, I still see more sense in your explanation than the mathematician's.
I don't think you should bale out either, if for no other reason than it will mean mykle will get twice as much abuse from me than at present. I understand that time is at a premium for you, but it smacks of cowardice to run away when you don't get the response you hope for. Perhaps it would be wiser to stay and change your game-plan to enable you to fare better. You have displayed an impressive degree of resilience in the face of full frontal attacks, though I have to admit I'm more impressed with that than some of your arguments. This whole forum thing is a bit of a catch 22 as I see it. When everyone is playing nicely it becomes so boring it is sleep inducing; when there is a row going on it comes alive, but pisses the more sensitive souls off. So you see, it's a no win thing. I'll keep on saying my bit, please or offend. The amusing part of all this is when the Gen. Diss. sags under the weight of collective torpor I get email from various users pleading with me to liven things up. I do my best!
I think missi is right. Having spoken to my brainiest math's friend. He thinks the trick is in people presuming the probability is carried over, when it blatantly isn't. It has to start afresh. That's how maths goes. So it's 50/50.
I don't understand it myself. Haven't the foggiest.
As far as I'm concerned I don't want anything to do with my uncle's box. I might catch something.
Newcombe's Paradox - as quickly as I can :-
1. A superintelligent being says that it can make very accurate predictions about you - but it is not God, so can't see into future, it is just making a prediction based on what it believes is likely.
2. He produces two boxes , A and B. He tells you that no matter what, inside Box A is £20,000. He tells you that inside Box B is either nothing, or a million pounds.
3. He tells you that you have to choose to take either Box B alone, OR Box A and Box B.
4. Here's the twist - IF he thinks you will take both, then in advance, he will have put nothing in Box B. If he thinks you will only take Box B, then in advance he will have put a million pounds in Box B.
5. What should you do?
The paradox is largely because people make a bloody compelling argument for either, and it is also an illustration of whether you believe in Free Will or Determinism.
(You could always sell the Bottle Imp for lire - it is a bit like a chain letter in that someone at the end is going to get badly knacked, but as long as you never buy it for less than 3 cents, you should be okay. Everyone who buys it will only care that they can sell it to the NEXT person in line. Of course if you are smart, you will think - if I buy it for 10cents, the person I try to sell it to for 9 will anticipate that the person they try to sell it to for 8 cents will anticipate that.... the person they try to sell it to for 2 cents will realise that they will never be able to sell it to anyone for 1 cent, so will not buy it for 2 cents, so in an odd sort of way, if everyone in the chain is smart and has foresight and logic, nobody would ever buy the bottle off you once you are done with it, so you should never buy the bottle at anything other than a ludicrously high price. But there are thick people everywhere to be taken advantage of)
Imp in bottle, you can always sell for a hlf cent, quarter cent ad infinitum, as a written agreement if the coin doesn't actually exist. shares are valued at fractions of a cent...
and what would as ludicrously high price be for something that will grant your every wish?
the first person would buy it for as mush as they could afford and then just get the money back so it's not like there's a dilemma you face when coming up with a price like, "hmm, I could buy this for as much as a pound but would it be worth it?"
also, with the Newcombe paradox, do you know his thoughts about your moves, in otherwords are you aware that:
"- IF he thinks you will take both, then in advance, he will have put nothing in Box B. If he thinks you will only take Box B, then in advance he will have put a million pounds in Box B."?
This is a little like a dollar auction. I auction a dollar as normal, the only catch is that the second highest bidder also has to pay, but gets nothing.
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