Sorry about the confusion.... I went back as you were posting to put the whole thing in quotes...

The reference to shooting myself was the feeling I had after reading....NOT writing..

 

google "2 envelope paradox"



I ain't going down this time..... Muahahhahaha!

 

I couldn't visualise [sic] you spelling "normalised" with an "s".

 

IMO, the paradox has thrown away an important part of the original problem by not looking in the envelope - that being information. As soon as you stop opening the first envelope, you no longer have a 'logical' situation - you have an asinine mathematical proof (apologies to math dorks). You don't have infinite chances to switch; you have just one. And you know the value of the first envelope and, should you choose to switch, the second as well. Once you knew the two values, you couldn't possibly improve upon the higher value. [/engineerspeak]

 

SO the answer is....

 

I'm going with "it doesn't matter". Up front, you have a 50% chance of getting the "high" envelope. Opening your envelope gives you no further information - there's still no way to tell if it's high or low. So, switching doesn't give you a further advantage. Unlike the three envelope problem, you don't get any new information when a "door" (envelope) is opened so it's a moot point as to whether it's opened or not. This problem would stay the same whether or not the envelope was opened.

Of course, if you know that they normally offer more than what the envelope you opened holds, then I would switch if the amount seems rather low. But, that's a whole different story.

 

For what it's worth... if you're looking at a single isolated incident, then no it doesn't matter. If you're looking at the statistical value of it, then it does matter.


As I was thinking about this, I came to the conclusion that the 3 door scenario is actually a cleaner logic problem, primarily because the results are all or nothing*. The envelope problem brings with it the individual value quandry.


* Unless you're demented and see substantial value in winning a goat.

 

I wish I had a goat (and not for the reasons you might suggest ). I could avoid mowing my back yard, and make lots of goat cheese.

Plus, goat meat is excellent, especially in Southern Indian food.

 

Would you rather have a car?

 

Last night on the Tonight Show they had a segment at the L.A. County Fair where they were giving the microphone to various people and having them walk around as if they were news reporters. One gentleman - a forty-something plumber with spiked blond hair - decided to take us into the Big Red Barn to see the newborn baby goats: "they're so cute!"

"Here we are," he proclaimed as he walked inside, "baby goats!"

In the lower right corner of the television screen a text message popped up: they're sheep, not goats.