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Topic: A Simple Challenge (Read 1543 times) |
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Hermit
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A Simple Challenge
« on: 2008-04-11 06:16:41 » |
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You are presented with three boxes. In one is a gold brick. The other two contain turds. The boxes are identical and closed sufficiently well not to allow you to sniff out the answer. You will be keeping the contents of the box you choose, once you have made a final choice.
You are asked to select a box. Any box.
You do so.
The boxmeister then opens one of the remaining boxes and shows you a redolent turd.
After giving you an opportunity to fill your sight - and nose - with its full steaming glory, you are asked to decide if you wish to stand by the choice you made previously or if you would rather choose the other box.
Assuming that you really, really would prefer a gold brick to a steaming turd, what should you do?
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With or without religion, you would have good people doing good things and evil people doing evil things. But for good people to do evil things, that takes religion. - Steven Weinberg, 1999
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David Lucifer
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Enlighten me.
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Re:A Simple Challenge
« Reply #1 on: 2008-04-11 15:10:51 » |
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This is one of my favourite puzzles because even after writing a computer simulation that proved my intuitions were wrong I had trouble believing it! 
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Walter Watts
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Just when I thought I was out-they pull me back in
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Re:A Simple Challenge
« Reply #2 on: 2008-04-11 17:11:33 » |
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Quote from: Hermit on 2008-04-11 06:16:41
You are presented with three boxes. In one is a gold brick. The other two contain turds. The boxes are identical and closed sufficiently well not to allow you to sniff out the answer. You will be keeping the contents of the box you choose, once you have made a final choice.
You are asked to select a box. Any box.
You do so.
The boxmeister then opens one of the remaining boxes and shows you a redolent turd.
After giving you an opportunity to fill your sight - and nose - with its full steaming glory, you are asked to decide if you wish to stand by the choice you made previously or if you would rather choose the other boc.
Assuming that you really, really would prefer a gold brick to a steaming turd, what should you do?
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It might seem intuitive to stand by the choice you made, as you seemingly now have a 50-50 chance of the gold brick being in the box you chose.
However, all the intuition in the world won't change the fact that by sticking with your original box you’ll win only if your original choice was correct, which happens only 1 in 3 times on average.
On the other, and winning hand, if you choose the other box, you’ll win whenever your original choice was wrong, which happens 2 out of 3 times.
Walter
Mind blowing!
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Walter Watts
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No one gets to see the Wizard! Not nobody! Not no how!
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Hermit
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Re:A Simple Challenge
« Reply #3 on: 2008-04-11 17:47:56 » |
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Smiles broadly. I had a particular reason for asking.
And Behind Door No. 1, a Fatal Flaw
Source: New York
Authors: John Tierney
Dated: April 8, 2008
The Monty Hall Problem has struck again, and this time it’s not merely embarrassing mathematicians. If the calculations of a Yale economist are correct, there’s a sneaky logical fallacy in some of the most famous experiments in psychology.
The economist, M. Keith Chen, has challenged research into cognitive dissonance, including the 1956 experiment that first identified a remarkable ability of people to rationalize their choices. Dr. Chen says that choice rationalization could still turn out to be a real phenomenon, but he maintains that there’s a fatal flaw in the classic 1956 experiment and hundreds of similar ones. He says researchers have fallen for a version of what mathematicians call the Monty Hall Problem, in honor of the host of the old television show, “Let’s Make a Deal.”
Here’s how Monty’s deal works, in the math problem, anyway. (On the real show it was a bit messier.) He shows you three closed doors, with a car behind one and a goat behind each of the others. If you open the one with the car, you win it. You start by picking a door, but before it’s opened Monty will always open another door to reveal a goat. Then he’ll let you open either remaining door.
Suppose you start by picking Door 1, and Monty opens Door 3 to reveal a goat. Now what should you do? Stick with Door 1 or switch to Door 2?
Before I tell you the answer, I have a request. No matter how convinced you are of my idiocy, do not immediately fire off an angry letter. In 1991, when some mathematicians got publicly tripped up by this problem, I investigated it by playing the game with Monty Hall himself at his home in Beverly Hills, but even that evidence wasn’t enough to prevent a deluge of letters demanding a correction.
Before you write, at least try a few rounds of the game, which you can do by playing an online version of the game. Play enough rounds and the best strategy will become clear: You should switch doors.
This answer goes against our intuition that, with two unopened doors left, the odds are 50-50 that the car is behind one of them. But when you stick with Door 1, you’ll win only if your original choice was correct, which happens only 1 in 3 times on average. If you switch, you’ll win whenever your original choice was wrong, which happens 2 out of 3 times.
Now, for anyone still reading instead of playing the Monty Hall game, let me try to explain what this has to do with cognitive dissonance.
For half a century, experimenters have been using what’s called the free-choice paradigm to test our tendency to rationalize decisions. This tendency has been reported hundreds of times and detected even in animals. Last year I wrote a column about an experiment at Yale involving monkeys and M&Ms.
The Yale psychologists first measured monkeys’ preferences by observing how quickly each monkey sought out different colors of M&Ms. After identifying three colors preferred about equally by a monkey — say, red, blue and green — the researchers gave the monkey a choice between two of them.
If the monkey chose, say, red over blue, it was next given a choice between blue and green. Nearly two-thirds of the time it rejected blue in favor of green, which seemed to jibe with the theory of choice rationalization: Once we reject something, we tell ourselves we never liked it anyway (and thereby spare ourselves the painfully dissonant thought that we made the wrong choice).
But Dr. Chen says that the monkey’s distaste for blue can be completely explained with statistics alone. He says the psychologists wrongly assumed that the monkey began by valuing all three colors equally.
Its relative preferences might have been so slight that they were indiscernible during the preliminary phase of the experiment, Dr. Chen says, but there must have been some tiny differences among its tastes for red, blue and green — some hierarchy of preferences.
If so, then the monkey’s choice of red over blue wasn’t arbitrary. Like Monty Hall’s choice of which door to open to reveal a goat, the monkey’s choice of red over blue discloses information that changes the odds. If you work out the permutations (see illustration), you find that when a monkey favors red over blue, there’s a two-thirds chance that it also started off with a preference for green over blue — which would explain why the monkeys chose green two-thirds of the time in the Yale experiment, Dr. Chen says.
Does his critique make sense? Some psychologists who have seen his working paper answer with a qualified yes. “I worked out the math myself and was surprised to find that he was absolutely right,” says Daniel Gilbert, a psychologist at Harvard. “He has essentially applied the Monty Hall Problem to an experimental procedure in psychology, and the result is both instructive and counter-intuitive.”
Dr. Gilbert, however, says that he has yet to be persuaded that this same flaw exists in all experiments using the free-choice paradigm, and he remains confident that the overall theory of cognitive dissonance is solid. That view is shared by Laurie R. Santos, one of the Yale psychologists who did the monkey experiment.
“Keith nicely points out an important problem with the baseline that we’ve used in our first study of cognitive dissonance, but it doesn’t apply to several new methods we’ve used that reveal the same level of dissonance in both monkeys and children,” Dr. Santos says. “I doubt that his critique will be all that influential for the field of cognitive dissonance more broadly.”
Dr. Chen remains convinced it’s a broad problem. He acknowledges that other forms of cognitive-dissonance effects have been demonstrated in different kinds of experiments, but he says the hundreds of choice-rationalization experiments since 1956 are flawed.
Even when the experimenters use more elaborate methods of measuring preferences — like asking a subject to rate items on a scale before choosing between two similarly-ranked items — Dr. Chen says the results are still suspect because researchers haven’t recognized that the choice during the experiment changes the odds. (For more of Dr. Chen’s explanation, see TierneyLab.)
“I don’t know that there’s clean evidence that merely being asked to choose between two objects will make you devalue what you didn’t choose,” Dr. Chen says. “I wouldn’t be completely surprised if this effect exists, but I’ve never seen it measured correctly. The whole literature suffers from this basic problem of acting as if Monty’s choice means nothing.”
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With or without religion, you would have good people doing good things and evil people doing evil things. But for good people to do evil things, that takes religion. - Steven Weinberg, 1999
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Blunderov
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"We think in generalities, we live in details"
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Re:A Simple Challenge
« Reply #4 on: 2008-04-11 17:49:28 » |
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[Blunderov] Brilliant solution from Walter. Me, I was plodding along with the notion that a turd is unlikely to weigh as much as a gold brick and that the solution was obviously to select the heavier box. I suppose it was stipulated that the boxes were identical. I suppose that means mass too. Heavy shit.
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Fritz
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Re:A Simple Challenge
« Reply #5 on: 2008-04-12 21:07:25 » |
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You're all evil (in a good way :-) ) for making an old man's brain hurt on a Saturday night.
Thank You ... I think
Fritz
PS: and with all the snow gone, I have subsequently surveyed the wintering grounds of our fearless canine companion and found only turds and no gold bars littered about the yard ... what are the 'odds'.
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Where there is the necessary technical skill to move mountains, there is no need for the faith that moves mountains -anon-
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Hermit
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Re:A Simple Challenge
« Reply #6 on: 2008-04-13 06:29:00 » |
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The good news is that turds do not hang around for long in spring. The bad news is that they do release methane as they decompose - and mass for mass, methane is 72 times worse of a greenhouse gas than CO2. Nonetheless, having got that bit of science in so as to avoid board spamming, a recommendation.
Here is a recommendation for Fritz
It is intended to spare him the shitz
I hope he will love it to bitz.
-=-
Spring is sprung the turds are here,
I'd clean them up, but I don't care,
Even if they taint the air.
Its fertilizer - good for grass,
So I think I'll sit here on my - backside,
Exercise my brain; and drink some beer,
Lest I come all over queer,
Cleanup can happen - some other year.
Let me hint at the answer to your question
There was once an inn, a rambling, collapsing, thatched roof, old inn, The Even Steven, which squatted on some overgrown and under traveled country road. Late one dark and stormy night, a traveling man, a gambling man, came into the inn for shelter.
He sat in the pub, nursing his sorrows and after introductions had been made, talked with the publican, Mr Stephen Even, who had some sorrows himself. He complained incessantly as to how business was terrible, travelers were scarce, and his three gorgeous daughters were lonely and gave him no peace.
Eventually the traveler went up to his room, and no sooner than he had he closed the door but somebody knocked at it. He opened it, and there was a stunning blond, totally nude, but bearing a steaming cup of cocoa. She explained that she was Jane, the publican's oldest daughter, and had brought up some cocoa to help him sleep; and while she was there, was there anything else he would like? He thanked her politely, tipped her nicely, and bid her goodnight. Poor Jane left in tears.
A moment later, and there came another knock on the door. This time an even more stunning brunette. She too wore nothing but a smile, and explained to him that she was Jenny, the publican's middle daughter, come to turn his bed down. She came into the room, turned down the bed, fluffed the pillows and asked if, seeing as she was there, there was anything else that he might like to take? Again, the traveler declined, thanked her politely, tipped her nicely, and bade her goodnight. Jenny too departed in tears.
Moments later, a third knock. This time a ravishingly sweet redhead stood there. It was easy to see that she was a true red head, as she bore the badge prominently, baring all before her, not to mention behind her..She explained that she was Jasmine, the publican's youngest daughter, and had worried that he might be cold, so had brought up a hot water bottle. She slipped into his bed and pushed the hot water bottle to the bottom, and then looked up at him and asked if there was anything else he would like. His response was that all he wanted was to be able to sleep in peace. Nonetheless, he thanked her, tipped her, but despite this, Jasmine also made a soggy farewell.
The weary traveler had just climbed into bed when there was a thundering knocking and hammering at the door. He got up and opened it, and there was Stephen. Furious! How could his guest treat his daughters so? Was there something wrong with them? Was the traveler blind? Did he require an engraved invitation? Or was it the traveler would prefer a boy or a goat?
His guest apologized for upsetting the girls, but said, "Mr Even, I told you in the pub, I'm a gambling man!"
"So?" asked Mr Even.
"Well," replied the traveler. "I'm very sorry sir, your daughters are quite delightful, but being a gambling man, I only lay odds."
And now you know :-P
Copyright: Hermit 2008
License: Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.
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With or without religion, you would have good people doing good things and evil people doing evil things. But for good people to do evil things, that takes religion. - Steven Weinberg, 1999
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Fritz
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Re:A Simple Challenge
« Reply #7 on: 2008-04-21 13:10:10 » |
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[herimt]
Quote:
Nice one ... the poetry has captured my spring cleanup intentions (Single malt Lowlands Scotch thought )...clearly I'm not at ODDs, rather in good humour ... :-)
Cheers
Fritz
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Where there is the necessary technical skill to move mountains, there is no need for the faith that moves mountains -anon-
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