So long as the conditions (minimum payout, etc) are met, the reward is mined directly to miners.
[/quote]

Ok I have more noob questions , is that payment system automatic that when some earning line cross pool will send coins to that adress what miner using? And what is that 120 confirmation, after that pool get that reward and tx fees? I dont still 100% get that CPPSRB payment system. Let's think about situation that pool had a bad luck like last 10 blocks and then miners join the pool after that so is that new miner going to pay shares didnt get paid last blocks? And If pool have good luck so are miners getting paid more than usually or does pool save those extra for future that could pay when is not so good luck? Hopefully you understand my thoughts

I have been mining in Eligius last three blocks, I guess I came here with good luck
483.5%
183.0%
111.2%

EDIT:

Have been mining here since 11.7 (3.75days) and been part of mining power for 4 rewarded blocks.

273.4%
483.5%
183.0%
111.2% (part of that)

So average luck should be ~262%.
My stat page shows:
Estimated Total:    0.02675039 BTC   100.00%.

0.00824840 (calculated daily amount for 7ths with 100% luck)*3.75 (my time in eligius) = 0.0309BTC
So if that stat page is rigth for my earnings it is only 86% what it should be for 7ths with 100% for that period. Pool luck has been 262% average at this time and my actual hashrate in Eligius pool about 7.3ths. So  there was no benefit for good pool luck for me?