Gambling is all about random number generation, and provably fair scheme provides guarantees that casino doesn't cheat, but we also know that humans are horrible random number generators - we are very easily predictable.
There are many online demonstrations available, I'll just drop one here:
http://www.cs.stir.ac.uk/~kms/schools/rps/index.phpAfter 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.Exactly! And that's only a single example out of many ways of overplaying robots. I used to play with bots on newly appeared poker sites, and won over 0.1 BTC that way(unfortunately, it looks like there are no such sites around anymore). It takes several hours(with small bets) to understand their algorithm, and then you can make larger bets and win most of the time. And even in the Rock, Paper, Scissors game, as you said, the algorithm can be abused.
Regarding dice, you can play with the same server seed as many times as you want, so I don't see how AI can provide a provably fair dice site with an additional edge.