There are many online demonstrations available, I'll just drop one here: http://www.cs.stir.ac.uk/~kms/schools/rps/index.php
After a small number of games, computer becomes quite good at consistently beating you at the game.
So, theoretically a casino can observe how you place your bets, then predict your next bets and make their own bets (they always go first) accordingly. The flaw here is if this algorithm is implemented too naively, it can be abused by players by making big amounts of predictable low-value bets, and then making a big opposite bet.
We definitely know that. I think a friend did a test on my before and asked me to guess a few numbers from something to something (I forgotten!) and he showed me that I picked the same number, or the same pattern of numbers,,, over and over. And I did not even realize it.
Casinos definitely watch players, and they see if you like to take big risks and low chances, they will let you do it!