Analyzing the previous rounds, I noticed the opponent used a repeating cycle: rounds 1-6 were rock, paper, scissors in order. In rounds 7 and 8 the pattern shifted—if they were following the original cycle, round 7 should have been rock but they played paper, and round 8 should have been paper but they played scissors. It appears they are choosing the move that beats what the standard cycle would have been. Following that logic, in round 9 the expected cycle move would be scissors, so to beat scissors they should choose rock. To counter an opponent playing rock, I choose paper.