The "fingerprint" is used to search a "history" of games against other humans. Based on the move that most commonly follows that "fingerprint" the computer selects the winning move. I'm assuming the "history" comes from within the game itself which is probably played by lots of people like you who want to test it with one of the two possible cycles (RPS or RSP). I suspect that the reason it picks up on the cycle so quickly is because all the curious tinkerers have biased the data it uses to make moves.