Based on the previous rounds, the opponent tends to win with rock (rounds 3, 6, and 8 when they chose rock to win) and tie with paper in other rounds (rounds 2, 4, 5, and 7). Given that round 9 is odd-numbered and the opponent appears to favor rock in rounds where they aim for a win, I predict that they might choose rock again. Since paper beats rock, I choose paper for this round.