Quote:
Originally posted by rsl12
or to make it more clear...
You pick up cup A and don't look inside. Now you know that you have the cup that contains either $2X or $X. Should you switch? The answer is clearly that it doesn't matter, because the other cup either contains $X or $2X! And even if you were to look inside cup A and see it contained $1, this should not change the logic one bit.
|
I agree with the original logic completely. You are looking at it wrong...the problem assumes the values based on a known. You are getting it wrong: There isn't X and 2X: Cup A contains X, and then in Cup B there is either 2X or .5X. Statistically, it is a good idea to risk .5X for an even chance of gaining 1X.
The paradoxical nature of this problem is the unrepeateable way in which it is set up, and repeatability is the only thing that statistics can help with.
You are looking at it as if someone is holding a nickel in one hand and a dime in the other, and you are offered a choice between the two. That is not how the problem is set up...both quantities are unknown.
To repeat the problem over and over, you would have to set it up that you are repeatedly given a dollar. Each time you are given a dollar, you are offered the chance to trade it for either two dollars or fifty cents, based on a coin flip, or keep it. If you were offered this choice 100 times, you would either have 100 dollars if you kept it, or (50*2+50*.5) 125 dollars if you swapped each time.
Make sense? It isn't a paradox at all, your brain is just having a hard time resetting the problem properly.