To be in the net and deserve to talk about it I am SURE there is a filthy little trick involved.
Yet Another Math Problem
by AlmostAtheist 47 Replies latest jw friends
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AK - Jeff
Dave - Dammit, now I will be trying to work out probabilities all weeklong in my work.
Jeff
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Gerard
Yep, switching is better. When you first choose, the odds of any box being the cash box are 1/3. When I show you one of the empty ones, I increase the possibility of the box I *didn't* show you to 1/2. Your box, chosen prior to my revelation, still only has a 1/3 chance. So switching is better.
I disagree. You are getting into 'cumulative'distribution" and theory that does not apply to this reality.
It does not matter if we started with 3 boxes, or 300. The FACT is that at this point you have only 2 boxes to chose from. In our world called Reality, there is a factual 50% chance and the cumulative theory that each box may represent from past choices taken, is a useless concept in a factual 1:2 choice.
Don't believe me? Lets say we both walk out of the room and an unrelated third person comes in to chose one box of the two. The money is in one of them. His chances are 50%.
Why? Because the physical world is not concerned with cummulative chance theory. It is however, an entertaining theoretical game for teachers to torture students.
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AlmostAtheist
>>Don't believe me? Lets say we both walk out of the room and an unrelated third person comes in to chose one box of the two. The money is in one of them. His chances are 50%.
Well, this is why the answer is non-intuitive. :-)
I was wrong when I said the stuff about "1/2". The actual odds of winning the cash when you switch is 2 out of 3. The odds of winning without a switch is 1 out of 3.
Your unrelated third person is still subject to this. He would be asked to either stick with the first choice, or switch. Then he will be subject to these possibilities:
* The player originally picked empty box A. I open empty box B.
* The player originally picked empty box B. I open empty box A.
* The player originally picked the box with the cash. I open either empty box.In the first two cases, the player switches and gets the cash. In the third case, switching makes him lose the cash. So his odds are 2/3 in favor of winning if he switches. (Shamelessly stolen from http://en.wikipedia.org/wiki/Monty_Hall_problem)
Unless of course the 3rd person is Juni: she'll win regardless -- she's lucky!
Dave
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Gerard
Your unrelated third person is still subject to this. He would be asked to either stick with the first choice, or switch. Then he will be subject to these possibilities:
* The player originally picked empty box A. I open empty box B.
* The player originally picked empty box B. I open empty box A.
* The player originally picked the box with the cash. I open either empty box.In the first two cases, the player switches and gets the cash. In the third case, switching makes him lose the cash. So his odds are 2/3 in favor of winning if he switches. (Shamelessly stolen from http://en.wikipedia.org/wiki/Monty_Hall_problem )
Unless of course the 3rd person is Juni: she'll win regardless -- she's lucky!
Dave
My point is that this theory is defective because it relates to past cause-effect events, a concept that mingles with philosophy.
How many "cummulative choices" are acummulated in ancient objects and situations??? One can not beguin to compute the theoretical possibilities and complexities....never mind compute random events, yet some believe that it is possible, that there is ZERO randomnes in the unioverse and one can "calculate" , predict and manage the the future with exactness. Some people use this concept erroneously and afirm that the past cannot be ignored when assessing cummulative probabilities. The bottom line is that the past of an object has no bearing on its present time and choice being subjected to.
Cumulative probabilities are subjective, irrelevant and useless on each particular and individual choice, regardless of how they got there.
The debate resides in that mathematically, this is correct, but tries to substitute reality with ambiguous cause-effect power. So, scientifically, that it is correct but FALSE.
Realize it is a thought GAME, mathematicaly correct but factually ambiguous and most important: the cumulative game is absolutely unable to affect the FACTUAL 1:2 choice at the end, or each past choices for that matter.
Imagine:
Father: In which hand I hid the coin? You have 50/50 chances, my dear son....
Son: Wrong!!!! When was the coin minted? In which year? How many coins were produced in that batch? How many batches? How were they distributed? What is the poluplation of America? Of Ohio? How many people carry coins vs. dumping them on asthays? Pocket carriers vs. purses? How many get destroyed? How many get swallowed? How?When?Who? Where?
Assume you gather and compute all cumulative variables of the coin in question and its cumulative chances. Can a mathematician tell me with a strainght face that the boy's chance of getting the coin from his father's hand is not 50%.
See how effective this mathematicaly correct theory is in reality? That is because it is not absolute but it is a paradox.
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Leolaia
Don't believe me? Lets say we both walk out of the room and an unrelated third person comes in to chose one box of the two. The money is in one of them. His chances are 50%.
But the situation of the "unrelated third person" is not the same as yours. That's the point. The odds are better than chance that, before he walked into the room, you already forced Dave to reveal the other empty box because you had already picked an empty box. You picked a box at random (with only a 1:3 chance of being right), and similarly the "unrelated third person" would pick a box at random (with only a 1:2 chance of being right), but your second choice is not the same as the "unrelated third person" because your action two out of three times influenced Dave to eliminate the second box. He had no choice, for he could not reveal the box with the money in it and he had to reveal one of the boxes. Because that box has then been eliminated, and because you know that one of the boxes must contain the money, you know that there is a 2:3 chance that your box is the empty box. In other words, you have superior information than the "unrelated third person" because your initial choice secured in your hands a box that more likely than not made Dave eliminate the other empty box. You are gaining an advantage from Dave's own knowledge of which box contains the money. Now, if the option was for you to be blindfolded and select the boxes all over again after the third box was eliminated, then that would be 50/50 odds because you wouldn't know which box was the one that with 2:3 odds made Dave eliminate the other empty box.
One can not beguin to compute the theoretical possibilities and complexities....never mind compute random events, yet some believe that it is possible, that there is ZERO randomnes in the unioverse and one can "calculate" , predict and manage the the future with exactness.
It is probably true to some extent that, in the human world, there are all sorts of biases and subtle social and psychological influences that affect the probabilities in the real world. The "thought experiment" is one that has ideal conditions. But if you contend that there is a non-significant statistical difference between the two situations, I think that is where you would be wrong. Or if you mean that the import of the prior choice is of no more consequence than the proportion of coins minted/distributed/swallowed/etc. to a simple coin flip (wherein every single coin has a heads and a tails), then I think you've missed the point...
Here is an applet where you can try it out for yourself:
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Terry
What should you do? Keep your original decision? Switch? Or does it matter one way or the other?
Switch!
The first choice is a one in three chance 1/3
The second choice is two to one.
You actually have a 2/3rds chance of winning if you switch to the other door, and only a 1/3rd chance if you stay with your original pick.
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Terry
A grasp of counter-intuition can be the basis of good spirituality. This is why the "Hanged-Man" card in the Tarot deck is so representative of that part of the journey of life. Pascal's wager is based on a simlar concept
Are you back on the Ganja?
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Leolaia
After the first 100 trials for each:
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Narkissos
The trick imho is that probability applies to big numbers. On a single choice the odds are actually equal (leaving psychology aside, which is not the point of the problem).
You can approximately predict the result for 100 throwing of dice, but you can never predict the result for the next (marginal) one.
