There are tips also that you could beat the casino legally with black jack. It just need to study those mathematically calculations on the decision making to be made.
There are not. Provided the casino isn't using a weird set of non-standard rules that somehow give them a negative house edge (such as the dealer only hits up to 15 instead of up to the standard 17), then even if you play mathematically perfectly you should still expect to lose money. You can bring the house edge down a minimum, but it will never be zero and it will never be in your favor.
The only way to beat the house edge is via card counting, which is impossible online or if the casino uses continuous shuffle machines.
so maybe there's an edge or something for them.
There's always an edge. The majority of the house edge in blackjack comes from the fact that if both the player and the house bust, the house still takes your money. It is then adjusted depending on the particular ruleset the casino is using. The biggest change is had when changing the blackjack payout from 3:2 to 6:5, which increases the house edge by over 1%. Other rules regarding splitting, doubling down, surrendering, etc. all affect the house edge too.