I see your point, guess I simply don't understand the protocol then. I was sure that you get a "cryptographic target key" and then you try all options starting from 0 to the maximum bit field size (which is?).
Also you mention something about solo mining, I'm currently using Bitcoin client and I see it do 4208 khash/s. I don't know if it uses my GPU, I have AMD Radeon HD 6800 how can I verify I'm using the GPU?
mining is like throwing a bunch of coins, if they all land heads, you win. saving the coins from you failed attempts do not help toward your future attempts.