There is a problem proposed by Maurice Kraitchik that is supposedly unsolved(according to this VSauce2 video):
Take two people and compare the amount of money that is in their wallets. The person who has less gets all of it. If X is person 1's money and Y is person 2's, person 1 has a possible gain of X + Y and possible Loss of -X, making the average gain Y.
But these two values are not the same, aren't they? The first one(X + Y) is the money Person 1 ends up with, while the second one(-X) is their loss. When you just compare the gains/losses(aka relative to X) the paradox goes away:
Person 1's gain: Y; Person 1's loss: -X
Where did I go wrong(or am I right)?