Quick correction - you are not working on the same block for over 24 hours.  The pool just hasn't solved a block in that timeframe.

According to my calculations, my expected earnings for the time period of 6/29 - 7/28 was about 1.9837BTC
My actual earnings in that same time period: 2.3968BTC

So, no, I'm not seeing a 50% reduction in income.

A rail in this context is really the distribution of power and over current protection in a PSU.  Literally, a single rail means there is effectively 1 copper trace that handles all of the power requirements to all connectors (PCI-e, ATX, Molex, etc).  Therefore, in a single rail system, the entirety of the power and amperage is drawn through that one rail.  Now, while this may not be beneficial when powering a CPU - you might want to have separate rails to ensure your PSU shuts down should one particular component be causing problems - it is really effective for mining applications.  You want all of the amperage/power down that 12V path to your PCI-e connectors.

Truth be told, most modern power supplies (i.e. those made after like 2009 or so) can effectively manage the power distribution across multiple rails; however, what's the point in this application?  You're only dealing with the 12V PCI-e connectors, so there's no need to have multiple rails controlling the 12V, 5V, 3V, etc.

You have a 630W PSU and you're asking if it's OK to pull 680W through it.  Let me ask you a question.  I'm going to give you a gallon jug and I want you to put 1.5 gallons of water into it.  What happens when the gallon jug gets filled and you still have half a gallon to go?  Here's another fun analogy for you.  A balloon will hold 10 in³ of air.  Put in 20.  What happens?

The short answer is don't do it.  While the PSU *might* be able to actually handle the load, you're just asking for trouble.  The components are rated for a given load.  When you go over that rating, you get lots of extra heat that the components were never designed to handle.  This leads to nasty things like fires.

You have 5 rPis with miners.  I'm not entirely sure what that means... does each rPi have a USB stick miner attached to it, something like this:


At any rate, all you need to do is point your mining software to the machine hosting the bitcoin core.  For example, on my local network, I have an rPi that controls 5 Antminer U2.  I run cgminer on that rPi.  I setup my "pool" to be my local bitcoin core.  In other words:
You get USER and PASSWORD from your bitcoin.conf file.  That file should look something like this:

Try using this: http://retrocalc.net
You can put in your start date, your end date and your hash rate, and it will tell you the expected earnings in BTC for that time frame.  For example, I put in 1.8Th/s with a start date of April 1, and end date of today and it calculates 11.146BTC.

Good luck with your legal action.

Most would recommend using at least an 80+ rated, single rail PSU with at least 500W deliverable to that rail.  Obviously at least 2 PCI-e connectors are necessary.  As for the PSUs I use for mine?  I have an EVGA 1300 G2 that drives 3, and a Corsair HX1050 that drives 2.

OP is up and running...

Things can certainly look daunting if you've never done it before, but that's why there are a ton of guides out there to help you.  Here's a good one: https://bitcointalk.org/index.php?topic=702653.0

Skills you need to have:

1) Ability to plug things in
2) Knowledge of how to use a web browser
3) Creating a Bitcoin wallet address

Yes, I'm simplifying that on purpose to show you that when you boil it all down, that's all you really need to do.  Here are the items you will need:

1) S3
2) PSU rated at least 500W with minimum 2 PCI-e connectors.  Don't cheap out here - get a good name brand.  If you're feeling adventurous, you can opt for the Dell server PSUs with breakout boards and adapter cables.
3) A paperclip, or you can purchase a jumper adapter
4) A router with some available network ports
5) Network cable
6) A computer with a web browser
7) An internet connection

Dogie's guide will walk you through the setup process.

Actually, you are.  After you create your order, go to your account page on Bitmain and click the orders link, then click the "edit" link for your order.  You can choose your carrier there.

I won't go with "nothing".  My answer is, "whatever is profitable enough to invest in ASIC design and development".  So, if X11, or BobsMagicHashingFormula becomes the next big thing, then somebody will develop an ASIC for it.  If there's money to be made, somebody's going to make it .

You need to do the PSU paperclip trick.  Check out Corsair's website here: http://www.corsair.com/en-us/rm-series-rm750-80-plus-gold-certified-power-supply and look at the "FAQ & Support", then "PSU Paperclip test".

That should get you up and running.

And when you're running it on a different pool, it will hash at 2.8TH/s?  Unfortunately I just am not knowledgable enough with the KNC hardware to provide you with any kind of root cause analysis.  My suspicions are that if it hashes at 2.8TH/s on other pools, but only 2.35TH/s on p2pool, then it suffers the same problem as the S2 does.  If that's the case, then either one of the cgminer developers, or KNC themselves would have to provide an updated version of cgminer for the unit that is compatible with p2pool.

Hmmm... I wonder if they suffer the same problem the S2 from Bitmain did... S2 consistently reported / hashed at 10-15% lower on p2pool than on other pools.  Kano was working on a new cgminer build for a while, but not sure if he ever completed it.  I know KNC uses an older version of cgminer that they forked and customized with their own drivers.

Anyone else with the Neptunes on p2pool care to chime in here?

Oh, I see.  I guess I got a "lucky" May batch unit then... when I first got it, I never saw anything over 1.3, but with the restriction lifted for the 110V power, and the 1.5.2 firmware, mine now hashes at just about 1.4 (usually cycles between 1.39 and 1.41).

The biggest problem with this is as windpath points out, in addition to moving difficulty target and share weights.  All things being equal, you can easily calculate what the "ideal" value per share is.  P2pool pays out a block-finder's reward of 0.5% to the miner who found the block, and the remaining block reward to everyone else.  It pays 8640 shares as follows:

1 share (the miner who found the block) gets 0.125BTC which is 25*0.005
8639 shares split the remaining 24.875BTC, which is 0.00287938BTC per share

If the difficulty remained constant (which it does not), you could calculate how many shares you should have on the chain in the payout window (8640 shares, or about 3 days) knowing your hash rate:

Take the number of shares, multiply it by the reward per share and you've got your answer.  That answer, though, is really kind of irrelevant, since it doesn't take into account the variables.

Or, look at the "payout if block found now" stat, which will tell you exactly how many BTC you'll get should a block be found.

I suppose another way to get a gauge on how you're doing is to look at the current pool's hash rate vs your hash rate.  Then, take the blocks expected per day to give you an average expected daily payout.  Example you have 1TH/s and pool has 1000TH/s:

Not surprisingly, the number I ended up with is exactly what you'd expect any online calculator to give you for expected daily earnings with 1TH/s at current difficulty.  I could have simplified it considerably just by doing this:

Expected per-block earnings are then just:

So... at the end of all of that...

Look at the value given by "expected payout if block found now" and compare that to the "current block value" multiplied by "your hash rate" / "pool hash rate".

If your expected payout is bigger than the "current block value" multiplied by "your hash rate" / "pool hash rate" then you're doing better than expected (i.e. you've been lucky).  If your expected payout is smaller, you've been unlucky.

EDIT:
Most every p2pool front end will display your hash rate in a graph.  Take a look at windpath's node and you'll even see graphs of hash rate by mining address.

As for your hash rate always showing lower on p2pool... what's your hardware?

Especially shipped to the UK.  Hopefully the OP can find someone local willing to sell because it would cost me about the offer price just to ship to him.  Urgent means you pay 1BTC and I send it overnight to you

Hey OP... first, nice looking site, and offering up the S3 at non-inflated prices is refreshing to see.

Speaking of the S3, you might want to edit the description.  The S3 is 340W at the wall for 441GH/s... not the 366 you have listed.

No.  Opening port 9332 just exposes your node to the outside world, so other miners could potentially connect and mine on it.  If by "helping the shares" you mean, "having a lower percentage of orphans" then you're best served by ensuring the nodes you connect to have low ping times.  Opening port 9333 will allow for connections to the p2pool network's peers - i.e. nodes can connect inbound to you.  If you're having problems with "dead" shares, ensure your miners are configured optimally, and that you have solid internal network connections.

Quick explanation for you:

Orphaned shares - you found a share and broadcast your copy of the share chain.  Unfortunately, somebody else's copy of the share chain was broadcast and accepted prior to yours.
Dead shares - you found a share, but it is not added to the chain or broadcast because by the time you found that share, the share chain had already been updated.

Are you on US power (120V) or other?  Also, what are your voltage settings?  I have one of the May batch SP10s running in my home, and after tweaking the settings, it hashes at 1.4TH/s, pulling about 1200W from the wall.

The initially announced specs were 5.4TH/s, which Spondoolies-Tech later upped to 6TH/s (+- 10%).  I'm guessing actual implementation is showing 4.5-5TH/s... but we won't know actuals until Spondoolies-Tech announces the results of their testing.

At this point everybody is waiting for an update from Spondoolies-Tech regarding the new specs of the SP30 along with new pricing.  So far, the last update from them was "be patient, we're testing and will release results soon."