Thanks for the mention @arallmuus. I will try answering OP's query with another perspective to make things more clear:
Hey blxn,
I understand your confusion. It is difficult to imagine how can a software be fair and at the same time provide edge to the casino, right? To understand how the system works, let's take an example:
Suppose you and me are playing a game. We would pick a number between 1 and 100 and if the number is between 1 and 52, I win and if the number is between 53 and 100, you win. Now it maybe possible that the number turns out to be 77 in first attempt so you will win. But say, we play this game 10K times, who do you think will have edge in the long run? In long run, I will win more rounds because my winning chances are 52% while you only got 48% chance!!
So let's translate the above explained game into casino terms:
House Edge: Since I have 52% chance to win the bets in long run, this is called house edge.
Provably Fair: Since the number is picked randomly, this is called Fairness.
How it works technically?In every Casino game, we try to draw a number between 0 and 1 as randomly as possible. Then we multiply the drawn number with the total number of possibilities. The resulting number is then rounded off and the nth number in the sequence is the result. This is how fairness is maintained digitally. Confusing, eh? Let me give an example:
In a traditional roulette game, there are 38 possible scenarios. We first try to pick a number between 0 and 1 as randomly as possible. Let say we got 0.6225. Then we multiply the number with 38.
38 * 0.6225 = 25.175.
Now we round off 25.175 to upper integer i.e. 26. So the result of the roulette wheel of the round should be 26.