The sequences repeat themselves. You have to memorize it.
Are you sure? Because I started trying to track the moves after reading your post and this is what I got. rock, scissors, paper, paper, rock, scissors, paper, paper, paper, scissors, paper, rock, scissors, paper, rock, scissors, scissors, paper, paper, scissors, rock paper, scissors, rock, rock, rock, paper, paper, scissors, scissors, rock, rock, rock, scissors, rock, rock, rock, paper, paper, scissors, paper, paper, rock, scissors, scissors.
Some parts seem like they're going to start repeating like the three rocks followed by two scissors but then it restarts before the second scissors and then changes the pattern in the later part before moving onto an entirely new sequence.