Two people, Andre and Erik, are going to play a game. They are going to take out their wallets, count the money in each wallet, and give all of the money to the person whose wallet contains the least. Assume for the sake of the problem that they do not know anything about the other person's cash habits.
Andre thinks about it and concludes that if he loses, he will lose all of the cash that he has, but if he wins (meaning that Erik had more), he will win Erik's money, which was even more than he would have lost. With equal chances of winning and losing, he decides that the advantage is his.
Likewise, Erik has the advantage. With equal chances of winning and losing, he would potentially win more than he would potentially lose, so the advantage in the game is his.
Can they both have the advantage?
This puzzle was found on http://www.brainteaser-world.com/, and is apparently attributed to Maurice Kraitchik.