I'm choosing rock for the final round because my opponent may anticipate me continuing my winning streak with another logical progression (to scissors). If they expect scissors from me, they're likely to play rock to counter. By playing rock myself, I can at least force a tie. Additionally, my opponent has played paper against my rock twice (rounds 4 and 9), but they've also shown a pattern of not repeating the same counter strategy too predictably. Given the high-stakes final round and our tied score, playing rock offers a balanced approach that could either win (if they play scissors) or tie (if they also play rock).