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The Covenants book has an extremely confusing line, filled with parentheses and commas describing the maximum level for a purchased summa.

3 x Level + Quality (Level limit: 8; Quality limit: 11 + 3 x (8 – level), or 22, whichever is lower)

In a strict reading, would a Level 5, Quality 20 summa be acceptable here? Is there an efficient local optima that provides the maximum level and quality for build-points spent?

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Yes, by a strict reading of the math in the excerpt, Level 5, Quality 20 is within the limits in the brackets.

To get the upper Quality limit of 22, you can't make Level higher than 4. At Level 8, the maximum Quality is 11. Between Level 5 and 8 each level you go up reduces the maximum Quality by 3.

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Since there are not that many combinations, running the numbers we get table:

Level   Max. Quality           Cost @ Max. quality
-----   --------------------   -------------------
1       22   11+3*(8-1) > 22   25   3*1+22
2       22   11+3*(8-2) > 22   28   3*2+22
3       22   11+3*(8-3) > 22   31   3*3+22
4       22   11+3*(8-4) > 22   34   3*4+22
5       20   11+3*(8-5) < 22   35   3*5+20
6       17   11+3*(8-6) < 22   35   3*6+17
7       14   11+3*(8-7) < 22   35   3*7+14
8       11   11+3*(8-8) < 22   35   3*8+11

As Simon says, your suggested summa would be perfectly acceptable.

What we also see though is that it would actually have been simpler to just say

  • 3 x Level + Quality (Level limit: 8; Quality limit: 22; Cost limit 35)

Optimum is an entirely different question though. That depends on how optimised the mages in the covenant are for learning from summa, their starting arts, how high they realistically want their arts to get before having to find new books and what the vis availability in the campaign is likely to be, amongst many others.

In most campaigns I've played in, right back to 2nd edition, players have been more than happy to sacrifice almost anything to get a good library, and then spent significant time in game making their libraries better!

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