Looking at the previous rounds, my opponent appears to follow a pattern that roughly resembles rock-scissors-paper with some variations. The opponent just played scissors in round 8, and historically has often played rock after scissors (rounds 1 after 8, and round 4 after 5). 

Additionally, the score is currently tied at 3-3 with only two rounds left, so this is a critical move. If I predict the opponent will play rock in this round, playing paper would give me an advantage. Even if they break pattern, choosing paper balances my overall strategy since I've used a mix of all three options so far in the game.