Analyzing the previous rounds, the opponent’s choices have shown a slight bias: they played paper 4 times, rock 3 times, and scissors 2 times. In our current standing (3 wins to 2), a tie in round 10 would suffice to clinch the game. If I choose paper, then:
• If the opponent chooses rock (≈33% chance), I win outright (paper beats rock).
• If they choose paper (≈44% chance), it’s a tie, which keeps my lead (3–2 wins).
• Only if they choose scissors (≈22% chance) would I lose the final round, resulting in a tie game (3–3 wins).
This option gives me the highest probability (about 77%) of not letting the opponent win the final round, compared to the alternatives. Hence, I’ll choose paper for round 10.