Partigyle: Please Check My Math
I'm planning my first partigyle next month. It will be a doppelbock/alt. I've run the calculations through and they work out on paper, but this is one of those things that I have been working on so long that I can't quite see the forest for the trees any more. I want to make sure that my math is solid.
The base recipe is follows: 18 lb Munich 10 2 lb Pilsner 1/2 lb Melanoidin 1/4 lb Carafa III I plan on making 5.25 gallons of Doppelbock and 3.25 gallons of alt. Assuming 70% efficiency, that gives me 523 gravity points to work with. I will extract approximately six gallons of wort each with both the first and second runnings. I plan on taking two gallons from the second runnings and adding them to the doppelbock; then I will do a very long boil to get down to the proper final volume. The alt will get a regular 60 minute boil. I'm getting a OG of 1.068 for the doppelbock and 1.051 for the alt. But just looking at that, the math does not seem right. Please someone confirm this for me! 
I've recently been reading into Partigyle so I'll take a stab at it. Assuming your numbers of 523 points extracted over two 6 gallon runnings (12 total) is correct, I get about the same as you. Per Mosher (Radical Brewing) I will assume that the first runnings contain roughly half the sugars and the second and third runnings contain 1/3 and 1/6 respectively. In your case, we're just adding the 2nd and 3rd together as one.
523 points total = 261.5 per batch Each batch contains 6 gallons = 43.58 points per gallon Add 2 gallons to first batch = add 87.16 points Total points, volume of batch 1 = 348.66 @ 8 gallons Subtract 2 gallons from batch 2 = remove 87.16 points Total points, volume of batch 2 = 174.34 points @ 4 gallons Postboil volume Batch 1 of 5.25 gallons (348.66/5.25) = 1.0664 Postboil volume Batch 2 of 3.25 gallons (174.34/3.25) = 1.0536 I hope I didn't flub anything up there! Good Luck! 
On second thought, after review some info on conversion efficiency based on mash thickness found here (http://braukaiser.com/wiki/index.php...ion_efficiency) I think we may be significantly off based on your mash thickness.
If you are doughingin with about 8.5 gallons of water to yield you 6 gallons of first runnings, then that would give you about 1.65 QT/LB. According to this, you'd be getting more around 1.075 @ 6 gallons for your first runnings. That would not leave you much sugars for a 6 gallon batch sparge. Sorry, someone with more experience will have to chime in here! 
Partigyle is pretty cool, it will be a fun brew day. My initial reaction is that the gravities you plan for the two beers are too close together. This will require some blending of first and second runnings for both beers, which I did once and it was a PITA.
My advice is to focus on hitting the numbers deadon on the first beer. Then let the second beer just be what it is based on the volume of wort you have. You can then adjust hopping based on the intended ibu:gravity ratio. But with some planning, you should be able to get pretty close. As far as figuring out the mash numbers, do you have a brew log that you can look back into previous mashes? Specifically, it would be good to know: water:grist ratio volume of 1st runnings gravity of 1st runnings With this info you can figure out your conversion efficiency (based entirely on crush unless your pH and/or temp are way off) based on the braukaiser link above. This will let you calculate the volume and gravity of your first runnings based on total lb of grain and mash thickness. From there, apply the rest of your efficiency calcs to tell you the gravity and volume of your second runnings. You might consider doing 3 runnings to get a little more effiency but also to allow for blending back in. You will need at least 2 buckets or other vessels besides your boil kettle unless you have a HLT. 
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http://www.brewingtechniques.com/lib....2/mosher.html 
OLDBREW, I saw that article the other day and did find it informative. However, it is also the article that misled me slighty, because I didn't connect the dots about the volumes he was using (or hence, the grist ratios). It seems to me his numbers and charts are only accurate as long as your first runnings are 1/3 of your total running, assuming you double batch sparge.
"For a onethird/twothirds split, I have found that approximately half of the extract from the malt ends up in first third of the mash runoff, and the other half ends up in the last twothirds. Because the volume of the first portion is half that of the second portion and has the same amount of sugars, it will be roughly twice as strong." So, as long as your sparge volume is twothirds of the total volume, you are good using this. But if you mash thin, you could end up needing to sparge a large amount, possibly leading to oversparging or exceeding the volume of your mash tun. 
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I've used those tables before, on the 50/50 split, my system worked a bit differently. I got about 50% in the first run and 25% for the second beer. I now work up my partigyles in this fashion and get pretty close. They are good approximations, but those efficiencies depend more on you. Also, you can mix and match in your running's to get where you want if need be.

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I made a fancy spreadsheet showing all this, if that will help. 
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