As it pertains to roulette, the VDW(Van de Waerden) says that in every 9 spins you will ALWAYS and I mean ALWAYS (discounting the zero for now) have an Arithmetic Progression.
Isn´t that because it´s about a specific number of colours contained in a specific number of spins? Add blue and yellow to the red and black and there goes the arithmetic progression, or you´ll have to a) increase the number of spins; or b) change the rules. It´s not a "property of random" as I see it.