A game favorable to both players?

A math teacher is having lunch with two students, Bob and Alice.

Teacher : Let's play a game. Put your wallets on the table. We'll count the money in each. Whoever has the smallest amount wins all the money in the other wallet.

Bob : If I have more than Alice, she'll win just what I have.
But if she has more, I'll win more than I have.
So I'll win more than I can lose.
The game must be in my favor.

Alice : If I have more than Bob, he'll win just what I have.
But if he has more, I'll win more than I have.
The game is in my favor.

How can a game be favorable to both players?
Does this paradox arise because each player wrongly assumes his chances of winning or losing are equal?