What newcomers to p2pool usually don't immediately grasp is there are two types of shares in p2pool.
Thanks for the explantion but I did know that. I was explaining that my miners were seeing accepted shares so my local pool was accepting them to demonstrate I didn't think there was a problem with the miner. I was asking if I can still get the same payout over a longer period of time, or if something was broken and I needed to fix something. I'm going multiple blocks found by p2pool before even a single share is found by me, doesn't that mean I may as well have had my miner turned off during that period? So I know the mechanics of p2pool but I'm a bit fuzzy on the statistics science involved, and if over a longer period of time can it even out even if you have little hash rate compared to everyone Can I somehow get the same payouts as I do on normal pools, if I wait long enough?
This kind of kills the appeal of smaller miners, though I don't know what is more, all the smaller miners (under 1TH) added up vs entities that command larger hashrates. If its only the bigger miners that matter in the 51% threat, then I guess its just a matter of convincing them. I fell for the rhetoric on /r/bitcoin on reddit, about saying everyone should switch to p2pool, but I didn't they were only talking to > 1TH people only.
The mechanics are that every share you find is added to the share chain. That share will pay out for 8640 found shares and it drops off the payout list. One share every 30 seconds, 2 a minute, 120 an hour, 2880 a day, 8640 per three days.
The expected time to share is just an educated guess by the software. Based on your hash rate, you have a very high probability of finding a share every 12.6 hours. Does that mean it's going to happen like clockwork? Not at all. I had an S1 go for over a day before finding a share. Once you find that share, though, every block the p2pool network finds within the 3 day window you'll be paid. Even if your miner is shut down.
With lower hash rate, you'll notice the variance quite a lot. Firstly, you'll see it just to get a share on the chain. Then you'll see it from the p2pool network finding blocks. When you mine on the larger pools, you see less variance because they're solving blocks faster. You also get smaller rewards per block because your contributions count less.
So... if you're more comfortable getting a slow, steady payout, go with one of the larger pools. If you don't mind the variance, stick with p2pool.