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D.R.A.I.C.H. Pick up the spell you want. 
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Corsair
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For hurried readers, the last chapter is the summary.

1. Why do I wish to select specific spells?
In the present edition, all Lores have been improved.
Nowadays, there is hardly any spell which is scrap.
As a result, you can safely assume that whichever spell you pick is going to be useful, and adjust your strategy on the battlefield according to the spells you’ve got.

But I want more predictability.
If I could select one or two specific spells, and be highly confident that I will get them, then I could build up my army taking that specific spell into account.
Example: all spells in Dark Lore are awesome. However, I may wish that my Level 4, who happens to be my general, get specifically spell #5 Soulstealer in order to gain more wounds. Is this possible?
Or could I be certain to get both #5 and # 6 Black Horror, and plan on that? Or at least one of these two spells?
Finally, I could select a specific Lore because spell #1 and #2 are excellent against Stunties while spell #3 and #4 are outstanding against Lizzies; when I face my opponent, am I going to get the spells appropriate to my opponent?


2. Spell selection.
P. 490. Your sorceresses have selected their Lores beforehand, at the same time as you create your army. Lores may no more be adapted to the opponent you happen to meet.

If you have several sorceresses, you select who gets his spells first.

Roll 1D6 per sorceress’ level. It indicates which spell the sorceress gets.
If you roll a spell twice, whether for the same sorceress or because another sorceress already has that spell, then you replace the duplicate spell with another spell of your choice in the same Lore, which is not taken yet.
After choosing replacements for duplicates, you can substitute one of the spell you rolled with either the signature spell (for BRB Lores – I call this spell Spell #0) or with Spell #1 (for Dark Magic), these spells being allowed to be taken several times.

As a consequence:
- Signature spell can be granted, just like Dark Lore #1.
- The higher the level, the more likely you get duplicates, therefore the more likely you can select the very one spell you dream of. Or possibly the two spells you really wished you had.
- If your two sorceresses take the same Lore, then the second one will have many more opportunities to roll duplicates, therefore your chances to get the specific spell you wish increase.

I will now examine what are the odds of getting a specific spell, according to the level of the sorceress.
If the odds are close to 100%, then it is reasonable to build up your army “knowing” that you’ll get this or that specific spell available.
Next, I’ll consider that two Sorceresses take the same Lore, in order to increase the odds that the highest level gets the one or two spell you want.

I’ll examine if it is reasonable for competitive friendly games, where you accept a moderate risk of failure, and for tournaments, where you’re supposed to play several games with the same list and you want to get the highest certainties you can get.

In order to fix ideas, I’ll always consider that you really want spell #6, and if you want two spells, they will be #6 and #5. Of course, the same result would be true for any other given spell selection.

Be aware that I am not a statistician, so the odds may be mistaken sometimes, especially the odds to get spell #5 and #6, which are very tricky.


3. Getting specific spells with one sorceress.
With a single sorceress using a Lore, chances to get Spell #6 are:
72,2%with a Level 3.
90,7%with a Level 4
98,5%with a Level 4 and her Tome of Furion.
I consider that a Level 4 is enough for a competitive friendly game, that is 1/11 games against your strategy.
For a competition, it is not enough and the ToF is mandatory. Too bad, this precludes the use of any other Arcane item. This is why a second Sorceress is to be considered, using the same Lore.

If either one of Spell #5 or #6 was acceptable, the odds become:
88,9% with a Level 3 (or Level 2+ToF), enough for a competitive friendly game
98,1% with a Level 4, fine for a tournament.

If I want to base my strategy on getting simultaneously #5 and #6, then the odds are:
83,3% with a Level 4, barely acceptable for a competitive friendly game
96,9% with a Level 4+ToF, fine for a tournament.


4. Two sorceresses, two Lores.
In tournament level games, only two Level 4 can grant you the availability of spell #6 or #5 in Lore X and the availability of spell # 4 or #3 in Lore Y, with a likelihood of 96.3%.
In competitive games, you could hope for getting spell # 6 and #5 in Lore X and spell #4 and #3 in Lore Y with your two Level 4, you’ll be on spot for 7 games out of 10!


Wed Aug 04, 2010 11:00 pm
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Corsair
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5. Getting specific spells in Dark Lore with a high sorceress and her Level 1 assistant.
Dark Lore has no signature spell, it is Spell #1 which is the default spell.
Suppose you wish your highest Level sorceress to get #6.
First, a Level 1 selects one spell. If she gets #6, she’ll transform it to #1.
Odds that the other sorceress gets #6 are:
90,7% with a Level 3, fine for a competitive friendly game
98,5% with a Level 4, fine for a tournament.

Odds that the other sorceress gets #5 or #6 are:
97,2% with a Level 3, fine for a tournament
100,0% with a Level 4, overkill!

Odds that the other sorceress gets #5 and #6 are:
84,7% with a Level 4, barely acceptable for a competitive friendly game.
100,0% with a Level 4+ToF. This is the way to achieve certainty to get 2 spells!


6. Getting specific spells in Dark Lore with a high sorceress and her Level 2 assistant.
Here, the danger is that the Level 2 rolled spells #1 and #6. Then she cannot anymore leave the #6 for the High Sorceress. However, it happens only 5,6% of the time, and the spell #6 is taken nevertheless (albeit more difficult to cast).
The odds that the High Sorceress get #6 are:
91,8% with a Level 3, fine for a competitive friendly game
94,4% with a Level 4, that is not acceptable for a tournament, because the odds were better with a Level 1!

The odds that the High Sorceress get #5 or #6 are 99.8 for a Level 3.

The odds that the High Sorceress get #5 and #6 are:
81,3% with a Level 3, barely acceptable for a competitive friendly game.
94,4% with a Level 4, quite acceptable for a tournament.


7. Getting specific spells in BRB Lores with a high sorceress and her Level 1 assistant.
This time, if the Level 1 rolls any spell but #6, she is doing the same job as her Dark Lore counterpart. The trouble is that if she rolls #6 that you wish the High Sorceress had, then she has to take the signature spell and her role is wasted.
The odds to get spell #6 for the High Sorceress are therefore lower than for Dark Lore:
86,1% with a Level 3, still OK for a competitive friendly game
96,9% with a Level 4, fine for a tournament
99,7% with a Level 4+ToF, probably overkill.

If you’re happy with either #5 and #6, then the Level 3 is probably enough with 95,8% chances.

The odds that the High Sorceress get #5 and #6 are:
84,5% with a Level 4, just good for a competitive friendly game.
99,5% with a Level 4+ToF, required for a tournament.


8. Getting specific spells in BRB Lores with a high sorceress and her Level 2 assistant.
Let’s increase the level of the assistant to Level 2. Here, she can still guarantee that she will not unduly get #6 which is reserved for the High Sorceress. Even if she rolls twice 6, she will be able to replace the duplicate spell with another spell of your choice, then switch the remaining #6 for #0. In case she rolls any 6, then her role becomes like the Dark Lore Level 1. The stats below combine all together (i.e. if she gets any 6 or not). Overall, as there is no risk to block spell #6, the stats are better than for Dark Lore.

The odds to get spell #6 for the High Sorceress are:
94,7% with a Level 3, excellent for a competitive friendly game.
99,4% with a Level 4, perfect for a tournament.

If you’re happy with either #5 and #6, then the Level 3 is enough with 99,2 % chances.

The odds that the High Sorceress get #5 and #6 are:
84,5% with a Level 4, just good for a competitive friendly game.
99,5% with a Level 4+ToF, required for a tournament.


Wed Aug 04, 2010 11:03 pm
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9. Getting specific spells with two Level 3.
There is one more possibility to get with certainty all 6 spells in a Lore: take two Level 3! The advantage is that whoever gets the wanted spell will cast it at the same Level.
A variant to consider seriously is to take a Level 3 and a Level 2 with ToF. Casting will just be slightly more difficult.

The Level 3 will have 88,8% chances to get #6, and even if she doesn’t, then the Level 2 has the certainty to get it, or a quasi certainty without ToF (98.5%), with just 1 less to cast.

If you want both #5 and #6, then select the spells first with Level 2 + ToF, then Level 3 will have the certainty to get the missing ones (or 96,9% if there was no ToF).


10. Summary for competitive friendly games.
If you want either spell #5 or #6, then take a Level 3 (88,9%).
If you desperately need spell #6 on your High Sorceress, take a Level 4 (90,7%), or a Level 3 assisted by a Level 1 or 2 (86,1% to 94,7%)
If you need simultaneously spells #5 and #6 on your High Sorceress, take a Level 4 (83,3%), knowing that an assistant Level 1 brings not much more certainty.


11. Summary for tournaments.
If you want either spell #5 or #6, then take a Level 4 (98,1%).
If you desperately need spell #6 on your High Sorceress, take a Level 4 assisted with a Level 1 (Dark Lore - 98,5%) or Level 2 (other Lores - 99,4%).
If you need simultaneously spells #5 and #6 on your High Sorceress, only a Level 4 + ToF grants a high enough likelihood (96,9%) but Level 4 + Level 2 is nice enough for Dark Lore (94,4% - for some reason, I have the feeling that I may have goofed this specific stat).


12. Conclusion.
It is now feasible to plan to get a specific spell (even two specific spells) when you create your army.
Let’s take advantage of this!

Hope it helps.
Comments welcome, as usual.

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Wed Aug 04, 2010 11:05 pm
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Calisson - absolutely magnificent work as ever & always old boy! Very very impressive and extremely useful/insightful - particularly for tournament play! I shall be perhaps using these stats for the upcoming UK throne of skulls in Oct where I intend to take a coterie of sorceresses!! :twisted:

- Beanz

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Thu Aug 05, 2010 12:19 am
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thanks man. very neat ;)

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Thu Aug 05, 2010 6:55 am
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Well done & good read.
One small remark.
For the steupt of Lv4 and Lv1 it could be eithered handled that way that the Lv1 is used to enhance the chances that the Lv4 gets the right spell. Or the other way around, the Lv1 is used as a throw-away caster going allways for the No.6 spell (or other big one) and going for IF (incl. misscasts).
In this set up Lv4 goes first to ensure that the Lv1 has a roughly 85% chance to get the required spell.


Thu Aug 05, 2010 7:39 am
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One small comment/correction:

Calisson wrote:
8. Getting specific spells in BRB Lores with a high sorceress and her Level 2 assistant.
Let’s increase the level of the assistant to Level 2. Here, she can still guarantee that she will not unduly get #6 which is reserved for the High Sorceress.


This is wrong. You cannot guarantee, that your Supreme Sorceress can get spell #6, if you first roll on Dark Magic with a Level 2.

If she rolls #1 and #6, you are out of luck. No way to change it.

Bye
Thanee


Thu Aug 05, 2010 7:48 am
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Thanee wrote:
One small comment/correction:

Calisson wrote:
8. Getting specific spells in BRB Lores with a high sorceress and her Level 2 assistant.
Let’s increase the level of the assistant to Level 2. Here, she can still guarantee that she will not unduly get #6 which is reserved for the High Sorceress.


This is wrong. You cannot guarantee, that your Supreme Sorceress can get spell #6, if you first roll on Dark Magic with a Level 2.

If she rolls #1 and #6, you are out of luck. No way to change it.
This is why I separated Dark Magic (chapter 6) and other Lores (chapter 8 ).
With other Lores, you can: if you roll 1-6, then you keep #1 and change #6 to #0 (signature).
With the Big Rulebook Lores (Metal/Fire/Shadow/Death), the low level sorceress will always be able to discard, showing high respect, the spell that the High Sorceress wishes to preserve for herself.

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Thu Aug 05, 2010 7:57 am
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Fluff aside the statistics of a lev 1 firing off a #6 spell get a TOUCH scarier when you realise WHAT they need to roll instead of a level 4 rolling it lol

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Thu Aug 05, 2010 7:08 pm
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Very, very nice summary.
Thanks for it Callison!

-Farodin

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Thu Aug 05, 2010 8:08 pm
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Calisson wrote:
This is why I separated Dark Magic (chapter 6) and other Lores (chapter 8 ).


Ah, you are right, of course... must have missed 6. somehow. :)

Bye
Thanee


Thu Aug 05, 2010 8:48 pm
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Though some times you may want that lowly lv1 to get the lv6 spell so you can cast it off with IF because it is vital.

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Fri Aug 06, 2010 2:34 am
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You need lots of dice to get a vital IF off with a reasonable certainty.
If no IF, then the dispell scroll will destroy your tactics.
Even a Druchii sorceress cannot achieve a 2/3 probability for an IF.

Probability of IF according to the number of dice thrown:
Code:
Dice   IF
 1    0,0%
 2    2,8%
 3    7,4%
 4   13,2%
 5   19,6%
 6   26,3%
-----------
 7   33,0%
 8   39,5%
 9   45,7%
10   51,5%
11   56,9%
12   61,9%

This is in complement of the excellent sheet made by Furgil, which stops at throwing 6 PD

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Fri Aug 06, 2010 8:08 am
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I cannot replicate your math correctly for spell generation of a lone level four trying to obtain the #6 spell, for me I only get roughly 84.1% to obtain it while your math seems a lot more optimistic.

Care to show the math behind it a little more so I can see where I go wrong.


Fri Nov 16, 2012 7:28 am
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I think the easiest way is to calculate the inverse. For example, a level 4 with ToF trying to roll 5 spells without a double and without 6 can be calculated like: 5x4x3x2x1 (possible permutations for 5 different outcomes) / 6^5 (all possible permutations)
= 1.54%
So the inverse is 98.45%.

When you can roll x out of 6 spells, this becomes: 1 - P(5, x) / 6^x.
So:
5 spells -> 98.45%
4 spells -> 90.74%
3 spells -> 72.22%
2 spells -> 44.44%
1 spell -> 16.67%

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Fri Nov 16, 2012 9:19 am
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Now, I recall: this is exactly how I did.
Mathammer threads are made just for that: to help people who don't have math skills to the same degree.

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Fri Nov 16, 2012 2:06 pm
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Calisson wrote:
Now, I recall: this is exactly how I did.
Mathammer threads are made just for that: to help people who don't have math skills to the same degree.


Redid the math for it, and got it to match your numbers this time. Did a mistake when excluding 6's from tuples in my math which made me end up with 84.1% instead of 90.74%.


Fri Nov 16, 2012 2:21 pm
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So next you're ready to write your own Mathammer article! ;)

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Fri Nov 16, 2012 2:24 pm
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On this topic but in another vein, for wizards that aren't loremasters but get to roll 6 times for spells. Does swapping for signature spell happen before or after you do any replacing for duplicates?


Fri Nov 16, 2012 2:25 pm
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It makes no difference.

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Fri Nov 16, 2012 2:28 pm
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Calisson wrote:
It makes no difference.


Well if you roll 1,1,2,3,4,5 and are aiming for #6 order of operations matter! :P


Fri Nov 16, 2012 2:30 pm
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You are free to pick the order as I understand the rules. So if you roll a double 1, you are permitted to pick #6 and then replace your second #1 by the signature. So yes, even if you roll a the same spell two or three times, you can still end up without that spell.

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Fri Nov 16, 2012 3:30 pm
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You roll all the dice at once for any given wizard.

The order matters only if you have two wizards.
In that case, you roll for the first wizard, pick up spells, solve doubles, swap any spell for the basic spell - and once spells are definitively stabilized for your wizard, you proceed on to the next wizard, for which you roll all dice at once and so on.

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Fri Nov 16, 2012 4:54 pm
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