They played 9 games. Below is one way possible outcome
Player A won three games. At that point Player B is now down three cents, but wins the next six games for a total net win of 3 pennies. So Player A wins three games and Player B wins three pennies:
Game 1 winner: A
Game 2 winner: A
Game 3 winner: A
Game 4 winner: B
Game 5 winner: B
Game 6 winner: B
Game 7 winner: B
Game 8 winner: B
Game 9 winner: B
They played 9 games. Below is one way possible outcome
Player A won three games. At that point Player B is now down three cents, but wins the next six games for a total net win of 3 pennies. So Player A wins three games and Player B wins three pennies:
Game 1 winner: A
Game 2 winner: A
Game 3 winner: A
Game 4 winner: B
Game 5 winner: B
Game 6 winner: B
Game 7 winner: B
Game 8 winner: B
Game 9 winner: B