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.
