New miner here - trying solo

[chasran01]

Greetings folks!

I've got my ASICs (L3++) and giving things a shot as of late. LTC mining that is.
I'm curious, however, to know if it is possible to find a block solo, really at any time, as I understand the longer and more work your miners do over time, increase the chances... But even though my has rate shows ~30% chance around the 30 day mark(according to the calculator), I could strike a block sooner, if lucky enough, right?

I've heard of some folks hitting 3-4 blocks in a month... that's possible?
To my understanding, yes the hash rate counts, but isn't it the miner that completes the block the one that claims it? Obviously, the more you put into a network, the more "luck" one would have, but a small hash miner could still swoop in and snag it?

Just curious, as some sites have % pool luck and personal luck tags, and I'm just mining away, letting these do their thing. Like fishing essentially... Just cast these out and wait.

With that said, however, do I lose the built up stats if I switch solo pools here and there, or is it easier to just stick it out here with PH and see what luck comes my way? Thanks so much and I'm looking forward to my new hobby!