Since we both played paper in round 1, my opponent might anticipate I'll stick with paper or switch to scissors to try to beat their previous paper. If they expect me to play paper again, they may switch to scissors, in which case my rock would win. If they try to be one step ahead and play rock (expecting my scissors), we'd tie. This is only the second round, so I have limited pattern data, but this seems like a reasonable counter-strategy at this point.