In being fixated with the concept that every spin is completely independent. The math guys ignore the differing probabilities of various groups of numbers.Every spin is not independent.
A fact that gamblers can exploit to their advantage !
All phenomena in this universe are in fact interdependent on a subatomic level. These math guys here, as you call them, are primarily dealing with pure math, whereas some other deal with applied math.
The difference is obvious and crucial when it comes to a deeper understanding of a chaotic pattern generator like roulette. For example, the branch of mathematics known as number theory,
was once considered one of the most useless, but now plays a vital part in computer encryption systems .
You could also think about how applied math relates to other subjects and to the real world.
Applied math tries to model, predict and explain things in the real world: for example, one area of applied mathematics is fluid mechanics, which analyses how fluids are affected by forces. Meteorology and prediction of storm fronts is another example of applied maths which very much might be compared to probability theory.
Pure math, on the other hand, is separate from the physical world. It solves problems, finds facts and answers questions that don’t depend on the world around us, but on the rules of mathematics itself. It has no actual value for the avid roulette player.