Independence or not, somehow all independent trials find a way to be close enough to equilibrium after enough trials. In fact, the more independent the trials are, the more likely to seek their rightful place as far as their probability is concerned.

That is y it never fails to observe this:

At the bottom of the daily count in a casino like Wiesbaden, the number of B/R, O/E, H/L, dozens, columns, although not in perfect equilibrium, they are close enough to confirm and reconfirm their rightful place within their probability. And that's about 300-500 spins.

You will never are going to see 200 B and 100 R, Or doz.1 150, doz.2 100 and doz.3 50.

The question is y?

If this is an undisputable fact, ( which it is), then y the independent nature of trials, doesn't overpower their tendency to seek out equilibrium? (except in very short runs).

And y a system can't be built, around the premise that independent trials seek out their rightful place within their assigned probability?

Instead, system opponents employ the "independence excuse" to prove that all system will fail.

When it is so obvious that independence is good for systems.