21 Mar '09 23:22>
THE DIFFERENCE
The difference in picking the second envelop to begin with, and switching after we open the first is this.
With the latter we have information we did not have before, specifically a dollar amount which limits our possibilities to two equally likely cases.
PARADOX #1 - Common Sense =VS= The Math
It is counter to our common sense that this would make a difference, but the math works out differently than we naturally expect from a common sense perspective. This is the paradox.
It shouldn't matter but it does, similar in vein to (albeit in a distinctly different manner from) the Monty Hall problem.
PARADOX #2 - Is the amount really important?
Or perhaps the paradox is in the fact that regardless of what we actually find, it is better to switch. In this respect, the fact we know the amount is important, but the actual amount is not.
TESTING THE ANSWER
The difficulty of testing the actual returns via a series of random trials is that the original terms of the trial is unbounded, making it impossible to select the random numbers required to test it.
The difference in picking the second envelop to begin with, and switching after we open the first is this.
With the latter we have information we did not have before, specifically a dollar amount which limits our possibilities to two equally likely cases.
PARADOX #1 - Common Sense =VS= The Math
It is counter to our common sense that this would make a difference, but the math works out differently than we naturally expect from a common sense perspective. This is the paradox.
It shouldn't matter but it does, similar in vein to (albeit in a distinctly different manner from) the Monty Hall problem.
PARADOX #2 - Is the amount really important?
Or perhaps the paradox is in the fact that regardless of what we actually find, it is better to switch. In this respect, the fact we know the amount is important, but the actual amount is not.
TESTING THE ANSWER
The difficulty of testing the actual returns via a series of random trials is that the original terms of the trial is unbounded, making it impossible to select the random numbers required to test it.