Although I don't understand exactly how you're playing the system, from what you've said about "elimination" I'm guessing the logic goes something like this (I'm using the even chances to keep it simple, but the principle is the same for any bet):

For two red/black outcomes, the only possible alternatives are

RR

RB

BR

BB

You arrive at the table and see the last number is 16. This immediately allows you eliminate half of the possibilities, so you are left with BR or BB. But this elimination doesn't give you any advantage, because the next outcome is still just as likely to be R as B. And similarly if you're playing dozens. Eliminating lines from the block will always leave some in which the next bet is equally likely to be a low, middle or high dozen, so it's just as much of guess as if you hadn't eliminated any lines in the first place. This must always be so, because outcomes are independent.