In a certain game called Lucky Balls, a player is asked to pay a fee of $3 in order to play the game. A player is then asked to draw exactly 4 balls, without replacement, from an urn containing 3 red balls, 3 blue balls, 3 green balls, and 3 yellow balls. The player is then rewarded $2 for every yellow ball picked. How many dollars is a player expected to gain from this game?
Note: A negative value indicates a loss.