I do see the distinction you're trying to make between "affect" and "indicate". But I think ultimately it's not very significant in this context. A few members do seem to admit that past spins don't "affect" future spins, but then go on to assert that they can "indicate" them. If you understand the meaning of statistical independence:
P(A|B) = P(A)
Then there really isn't much room for manoeuvre; there really isn't some clause or loophole in the definition which means that although past spins don't "affect" future spins, they really actually sorta kinda do if you squint a little bit and don't think too carefully.
I would like tell you that I have been a physicist by education. I don't say this to gain authority. I'm telling you this in order to convince you that I'm fully aware of the equations and the science you are referring to.
The thing however is a bit more complicated than this, if you care to look under the surface.
First of all, I will make a distinction that I have made before. Mathematics is a theoretical science, while physics for example is an empirical science.
To put it simply:
- Math depends on some main theoretically constructed, undisputed axioms.
- Physics depends on physical observation and testing and nothing is set in stone. (though it also uses math for calculations)
Now there is a strange thing with probability. It is between math and physics. The genesis of probability was a purely empirical one. In fact gambling played a major role in the development of probability. Then (as even today in physics) the mathematicians took over.
But we should never forget that probability is in its heart an empirical science, not a theoretical one. So any equation is not set in stone. It is true until disproved. Because there are no stones (axioms) in physics. Just to understand how deep and complicated this new science is I will mention (if you not already know) that scientists can not even agree in the interpretation of what probability is. Therefore there is not even a universally accepted definition of probability.
There are different interpretations
of the true meaning of probability, all supported with valid arguments.
Does this mean that past spins "affect" or indicate future spins?
I just want to shake a bit your (false) sense of security, based on mathematical equations. Just leave a door open. Hey! Scientists can not even agree what probability is :-)
I have written a post about why math can be an obstacle in roulette research
. It is a short and - I hope - interesting, reading.
And to put it more simply, in absolutely physical terms, is darn hard to prove that roulette spin outcomes are independent. If not for anything else, because the throwing point is dependent on the previous spin. But this is not my main argument.