WLLN
For a sequence of iid random variables, as the size of the sequence grows, its sample mean gets closer to the independent mean.
What does this imply? a small advantage will become apparent for sufficiently large amount of trials. At the casino maybe they have a 51% change of winning against any one individual player playing an optimum strategy. It doesn’t look like a good business but really this tiny edge makes them money in the long run over several customers. It’s like your metaphor with slopes: the steeper one will always catch up … eventually.
Now the casino may loose money in the short term, you may loose against someone not as skilled once or twice… and as humans this affects us, but if we are right about our beliefs, the player with the advantage will win in the long term. Keep your faith in the math.