It's noted in The Cradle and the Crescent that to initiate a ungifted student into Solomonic Summoning and all five Solomonic arts is vis-consuming, time-consuming and Might-consuming.
Reading through the Rules and trying to generate the totals required, they're not kidding about the vis consuming.
Let's assume a a teacher who's experienced, but not absolute top level. Their relevant stats are:
- Sihr 30
- Solomonic travel 30
- Com + Bargain 10
- Int + Magic Lore 10
- Presence 2
- Penetration 5
For Sahirs using initiation rather than opening the Arts, they can gain a major virtue / gain a major virtue and a minor flaw / gain a major virtue and a major flaw.
This requires an Opening total of 30/25/15, direct expenditure of 15/12/7 pawns of vis, and for a spirit to have their Might score reduced by 15/12/7 points.
The teacher's opening total is calculated as (Int + Magic Lore + Solomonic Travel + Summoning Strength + Aura)/2. The book says to assume Aura for labwork sahirs is 0, so this is equal to (10 + 30 + Summoning Strength + 0)/2 = 20 + Summoning Strength/2.
So the teacher needs a Summoning Strength of 20/10/0 to reach the required lab total.
In addition to this, the teacher needs to get the spirit to agree to perform the initiation. The Bargain Ease Factor will be 18 (base) - 3 (single task) + 6 (lasts a season) + 3 x Might Score reduction (=15/12/7) +- other modifiers = 66/57/42 +-other modifiers. The main modifiers are to accept duties (-6 per heavy duty, -3 per small duty), and having offered extra vis (up to a maximum of his Sihr). There are going to be limits to how much a jinn wants done (and the sahir can feasibly do), so let's assume the sahir accepts one heavy and one small duty, for a resulting reduction in the ease factor of 9, leading to an ease factor of 57/48/33. We'll come back to vis later.
The Sahir's Bargain total is Comm + Bargain + Summoning Strength + die. Let's assume a die roll of 3 (as this can be made up with confidence if necessary, and we don't want to risk wasting our massive vis spend). Then we've got 10 + Summoning Strength + 3 = 13 + Summoning Strength. To meet the Bargain EF, we therefore need a Summoning Strength for this purpose of 44/35/20.
We can summon a spirit using either a summoning naranj, or Sihr (or some other summoning art, but let's ignore that). I don't think it matters much for our purposes which we use, although a naranj is quicker and easier to penetrate on.
Our summoning total is Pres + Sihr + Aura + die, against an ease factor of the jinni's Might. The book isn't specific about the aura to use here, so let's use 0 again (although it seems reasonable you might have travelled to somewhere with a better aura for this part). We will assume a die of 3 again.
Our Summoning Total is therefore 2 + 30 + 0 + 3 =35. For an ungifted sahir, the Might of the spirit summoned must be at least equal to the lab total, i.e. 30/25/15. A gifted sahir could use a lower Might spirit, although there will be a floor equal to the Might Score reduction required (+1? Is this right? It feels like there should be a limit on the proportion of a spirit's might it will spend, but I can't see anything written for sahir). We will assume the Sahir can muster sufficient penetration to summon the spirit - this shouldn't be too hard with a naranj, as they come with a x6 penetration multiplier. The Summoning Strength is Summoning Total - Might, i.e. 5/10/20 for an ungifted sahir, and 19/22/27 for a gifted sahir. Summoning the spirit costs at base the magnitude of the spirit's might, i.e. 6/5/3 pawns for a ungifted sahir, and 4/3/2 pawns for a gifted sahir.
This is sufficient for the case of an initiation with a major flaw, but not otherwise. Fortunately, we can raise the summoning strength at a rate of 2/pawn of vis. We have a deficit to make up of 39/25/0 for an ungifted sahir, or 25/13/0 for a gifted sahir, so this requires 20/13/0 or 13/7/0 extra pawns of vis.
The total cost in vis to initiate one major Solomonic virtue is therefore (15+6+20)/(12+5+13)/(7+3+0) = 41/30/10 for a ungifted sahir, or (15+4+13)/(12+3+7)/(7+2+0) = 32/22/9 pawns for a gifted sahir, all of which have to be of the right art. This is technically doable, assuming the vis limits are calculated separately for the Summoning roll and the actual Opening (so you have a limit of 30/30, rather than 30 total), but it seems a lot for anything other than the "with Major Flaw" initiation, especially since you'll usually want both a Summoning and a Solomonic art initiated.
Have I got this right? Is there a way to make this significantly easier(/cheaper) that I'm missing? (Obviously boosting your Pre+Sihr or Comm + Bargain will help a bit, and you can use a Khuddam bond to boost a Summoning naranj slightly, but those both feel like nibbling at the edges rather than making a fundamental change).