Ball Picking Contest

Question

Balls stand in a line, and two players, Player One and Player Two, take them in alternating turns, Player One going first. Each player's score is 0 when play begins. Whoever is to move removes the first ball, or the first two balls, of what is left of the line. Every ball carries an integer value, possibly negative, which is added to the score of the player who takes it. A taken ball leaves the game for good. Each side is out to finish with the biggest profit it can get for itself. Play continues until the line runs out. ...