That's not necessarily the way it works. No matter which nonce you try, in the end you're goingto have a similar mining success at the same speed.

Imagine buying lottery tickets, and the tickets only having one number to match. Let's say you start buying a ticket each second. No matter how you select these tickets you're going to have the same chance, whether 1, 2,3,4,5..., 2,4,6,8,... 1,2,3,5,8,13,... assuming the same speed.

No number is inherently "more random" or "better".