Observing the opponent's moves, a three‐round grouping pattern emerges:
• Rounds 1–3: [rock, paper, scissors]
• Rounds 4–6: [rock, scissors, paper]
• Rounds 7–9: [paper, scissors, rock]
Notably, the first move in groups 1 and 2 is rock, and group 3’s third move is rock. If the opponent repeats the cycle, then round 10 (beginning a new group) is likely to be rock. To beat rock, my optimal move is paper. With this win I secure the overall game, so I choose paper for round 10.