In essence.. The guys pointing huge amounts of hashing power to the pool make my chance of getting that one solving hash even bigger. "It's the pool and it's size what matters." From this you can calculate your "luck factor."
Unless I'm misreading what you mean you're wrong. All that matters is your own hashrate because you're SOLO mining. Just because you do it through a pool doesn't change a thing compared to running bitcoind yourself and mining on that (edit: except that ckpool takes 0.5% if you do solve a block).
EDIT: Every share you solve has a chance of being a block solver. How many shares you can solve depends solely on your own hashrate and the difficulty, not on the total hashrate of the pool.
Hmm.. But a large pool will "cloud" many shares and distribute them. So you can factor your own hashrate against the pool as opposed to the overall hashrate. That way increasing your "luck factor." The overall hash "cloud" and your single instance in that will not weigh against a large pool with a shared hashrate. That's what I mean. Shares are being solved equally over the Net, but a large pool will "suck in" a significant portion of shares, thus mining in this pool wil change your overall "luck factor" as opposed to "going it alone on the Net." It's about "time" and "volume." Am I wrong?
The way I understand it every miner here is independent of each other. You are solo mining here no different than if you were doing it yourself on your own pool. The difference is most people dont know how or have the time to set up their own pool, so you pay CK a small share to use his pool, only if you find a block.
Another way of looking at it is this. Mining solo or in a pool with a given hashrate over the very long term will result in the exact same amount of bitcoins being mined. The only thing a (regular) pool does for you is making payouts much more regular since the block rewards are shared between miners and the bigger the pool hashrate the more regular it becomes. Because the block reward isn't shared on ckpool you are solo mining and it doesn't matter how big the total hashrate is.
Hope I explained it, if not then I'm sure Con or Kano will come along and do a better job. Thing to remember is that only your own hashrate and the difficulty matter and nothing else.