The envelope problem, and a possible solution

[econophile]

there was a link to a decent explanation to the problem in the original thread. the set up of the problem is that one envelope has $N and the other envelope has $2N in it. the trick is that the value of N is unknown.

but the participant must have some belief about how likely different values of N are. this belief just describes how likely the participant thinks different values for the smaller envelope are. and if the player thinks some values are more likely than others (maybe he believes extremely high values are unlikely) then it is not true that after learning the contents of one envelope the other envelope has a 50/50 chance of being the big envelope.

for example, if you open the envelope and discover a large amount of money, you might think that it is probably the 2N envelope. if you open the envelope and discover a small amount of money, you might think it is probably the N evelope.

so, after opening the first envelope, switching will sometimes have +EV and sometimes -EV. but before you learn the contents of the first envelope, you are indifferent between switching and not switching.