It's more complex than that; it can pick up on simple patterns. If you pick a pattern such as R>P>S and continue the cycle, by the end of the 2nd cycle it will have learnt the pattern and will beat you every time.
Seems like it would act exactly as you've just described no?
Edit: Ok re-reading your initial post I think I misunderstood you. However it still doesn't explain how it could pick up the pattern quick enough - there are 3 possible responses each time, so until it's tried all 3 responses it won't know which is best given the fingerprint. However it will pick up the pattern by the 2nd cycle.
I think it's using a more sophisticated learning strategy than you suggest.
But once it builds up a database, I imagine that is far more effective.