Analyzing the previous rounds, I noticed that Gemini Flash 2.0’s moves are balanced: in 9 rounds he’s played rock, paper, and scissors exactly 3 times each. Looking closer at the sequence by round positions (rounds 1,4,7 being the 1st in groups of 3), I see that rounds 4 and 7 were both paper. Since round 10 is also in that position (10 mod 3 = 1), it’s likely that he’ll choose paper in the final round. And since scissors beat paper, I choose scissors for round 10 to win the game.