In either case (solo vs pool), the luck factor would be the same, amirite?
Is this statement accurate "I am just as likely to find a block solo mining, as I am in a pool." ?
I understand that the pool rewards everyone trying contributing by sharing out the reward block. And that you could probably go for years solo mining and not see any return. But its equally possible, though improbable, that you could find / solve a block in your first five minutes.
I'll try to explain in a simple manner. Imagine, there's a massive field divided into small parts. When a pool mines, all the pool's miners dig holes in each of the parts. Each person gets it's own part while the pool operator tells you which parts to dig next. The miners dig and dig until one of them finds a block (in this example buried underground). Everyone who contributed to digging in that field gets a certain amount of the block depending the amount of holes they dug (shares). Though some pools have various methods but they all loosely situate around this method. However, if you are mining solo, you are in a different but still massive field, but you are the only one digging. See the difference?