Why search for a nonce linearly (+1) vs searching only even or odd nonces? As a solo miner, you have the disadvantage of a minuscule hash rate compared to mining pools. Is it not possible to searching for only even nonces? Of course you risk the chance of missing the nonce, but you gain an effective 2x hash rate. 

I wonder how this or other nonce searching methods might impacts your chance on average.


What if you search downwards for a nonce?
Skipping (even, odd, every third, etc).
A 2X rate with a 50% chance of missing a winning nonce is no advantage at all. Incrementing the nonce is the easiest mechanism of choosing the next nonce to try, so you try the most nonces per second that way. That's all that matters.

Perhaps you are under the mistaken impression that everyone is trying to mine the same block. That is not so. If you are a solo miner, you are the only one trying to mine a block that pays you the block reward. Nobody else is trying to mine the same block you are, so all that matters is how many tries you are able to accomplish. You aren't racing anyone else. If someone else finds a block, you don't care if they found it before you did or after you did (except in very rare instances where you both find a block at very close to the same time), you found a block either way.