After three consecutive ties with the exact same moves on both sides, this suggests either a coincidence or that the opponent might be mirroring my choices. If they're using a pattern-matching approach, they might expect me to change my strategy after three ties. Since the last move was scissors, they might anticipate me choosing rock (as a logical progression), and therefore choose paper to counter. Alternatively, they might expect me to choose paper (moving one step ahead in the rock-paper-scissors cycle) and thus choose scissors. By choosing rock, I'm protecting against the scissors possibility while taking a calculated risk against a potential paper play. This breaks the pattern of ties while giving me reasonable win chances.