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One of my current characters is pretty unique.
Void Wizard 1 / Eldritch Knight 6 / Arcane Archer 2
...hes a human and a legal build. Most players won't be able to recreate this if they tried.
The retraining rules say, "If retraining a class level means you no longer qualify for a feat, prestige class, or other ability you have, you can't use that feat, prestige class, or ability until you meet the qualifications again." Therefore, if you retrain out of the base class and that causes you to no longer meet the requirements of the prestige class, you no longer have access to the class features from that prestige class, and therefore can't use that prestige class to meet the requirements of anything (including itself).
I'm at a loss to see how your character works without violating that.

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There are no requirements that haven't been met in this build at any point during the retraining. I think you are probably looking for the martial weapons? I mentioned before that Arcane Archer grants those because its a weird and old prestige class and that's probably a holdover from some edition of D&D.
Trust me, at least some PFS GMs would slap you too :-)
I'm sure its only out of love because they care.

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I don't see how your build is legal.
You can't have two PrCs that only exist because of each other.
This was covered extensively in the Can retraining be used to make a character that could NOT be built from the ground up? thread.

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The problem with the build is here:
Retraining: Can I retrain out of my base classes and use my prestige class levels to meet the requirements for that prestige class?
No.
The retraining rules say, "If retraining a class level means you no longer qualify for a feat, prestige class, or other ability you have, you can't use that feat, prestige class, or ability until you meet the qualifications again." Therefore, if you retrain out of the base class and that causes you to no longer meet the requirements of the prestige class, you no longer have access to the class features from that prestige class, and therefore can't use that prestige class to meet the requirements of anything (including itself).
The issue though is that since you do not have the necessary qualification for eldritch knight (lacking martial proficiency from base classes), you do not access any features from that prestige class, which means you lack the necessary BAB for arcane archer. Yeah, arcane archer would rectify that issue if you could reach it, but cannot since your eldritch knight levels do not allow you to qualify for the requirements of anything, as the FAQ states.

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Lormyr, you seem to have missed the first half of the sentence you bolded. The "can't use a PrC to meet requirements of anything" is conditional on if retraining out of a base class caused you to no longer meet that PrC's requirements. It is not a blanket "PrCs can never serve as prereqs ever", which seems to be how you took it. Rather, it is "PrCs that you don't currently qualify for can't serve as prereqs".
@Nefreet - I skimmed the thread you linked, and carefully read every post by the Design Team, and I found nothing supporting your claim that "You can't have two PrCs that only exist because of each other." I found a clear declaration that you can't use a PrC to qualify for THAT PrC, and that you can't ever retrain a level of anything into a level of PrC, but the build in question isn't running afoul of either of those.
I don't see anything illegal about the build (so far).

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At the indicated levels, an eldritch knight gains new spells per day as if he had also gained a level in an arcane spellcasting class he belonged to before adding the prestige class.
Actually you guys are missing an important point. The second he retrains his level of wizard to magus his levels of EK are no longer legal, as the base class he progressed the spell casting is no longer valid. Under this argument, his levels of EK are doing NOTHING (not giving BAB, or anything else). Thus, the levels of AA are also invalid as he doesn't meet the requisite BAB, this is the above argument about "PrCs can't be used to qualify for each other exclusively".
Even if this WAS legal, his levels of EK and AA would be doing very little, as when he level he progressed the Magus spell casting, and he no longer has said class. I suppose in this case he could retrain the EK levels into EK levels to replace the relevant class feature with one that would do something now, but this would be ignoring the above argument about when he retrains he no longer meets prereqs.

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I agree with Jiggy on the stipulation that I don't know what "The Shard" is.
This build seems legal by the letter of the rules if not the spirit of them.
I'm not going to weigh in on the legality of the issue, but the Shard in question is (minor Shattered Star spoilers):

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PRD wrote:At the indicated levels, an eldritch knight gains new spells per day as if he had also gained a level in an arcane spellcasting class he belonged to before adding the prestige class.Actually you guys are missing an important point. The second he retrains his level of wizard to magus his levels of EK are no longer legal, as the base class he progressed the spell casting is no longer valid. Under this argument, his levels of EK are doing NOTHING (not giving BAB, or anything else). Thus, the levels of AA are also invalid as he doesn't meet the requisite BAB, this is the above argument about "PrCs can't be used to qualify for each other exclusively".
Even if this WAS legal, his levels of EK and AA would be doing very little, as when he level he progressed the Magus spell casting, and he no longer has said class. I suppose in this case he could retrain the EK levels into EK levels to replace the relevant class feature with one that would do something now, but this would be ignoring the above argument about when he retrains he no longer meets prereqs.
The line you cite does seem to indicate that he can't retroactively decide that his EK levels are advancing wizard casting instead of magus casting.
However, that doesn't make his EK levels illegal; it merely makes them unhelpful, in the same way that a 1st-level aasimar fighter qualifies to enter EK but would gain no benefit from the EK's spellcasting advancement due to their being nothing to advance. Same with a non-spellcaster entering Dragon Disciple via an SLA. They can absolutely do it, they just miss out on a major class feature.So, the aforementioned Wiz/EK/AA is legal, but a lot less effective than the player probably thinks. (Unless there's another wrinkle we haven't heard about yet?)

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When you retrain a class level, you lose all the benefits of the highest level you have in that class. You immediately select a different class, add a level in that class, and gain all the benefits of that new class level.
If you are suggesting I'm losing spell casting (a benefit of magus)I would argue it falls under all the benefits of my new wizard level as covered by the retraining rules.

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Quote:When you retrain a class level, you lose all the benefits of the highest level you have in that class. You immediately select a different class, add a level in that class, and gain all the benefits of that new class level.If you are suggesting I'm losing spell casting (a benefit of magus)I would argue it falls under all the benefits of my new wizard level as covered by the retraining rules.
Not sure I'm following you here. You say "it" falls under "all the benefits of my new wizard level". What is "it"?

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Spell casting progression.. is it.
I lost magus spell casting. I added a wizard level. Spell casting progression for prestige classes advances the base class. I would argue casting spells falls under:
gain all the benefits of that new class level.
Edit: Even if some people disagree that spell casting doesn't 'benefit' me or isn't included in 'all' somehow retraining the class feature 'spells per day' fixes this situation.

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Also Exguardi pointed out to me that anyone looking to recreate this build can make a version that doesn't require a shard.
Scryer Wizard 1 / Magus 1 / EK 5 / Arcane Archer 1
When you gain your arcane archer level retrain the magus level to wizard which gained a bab at level 2. Even avoids the above conversation for ease of use! Drawback: you can't choose your school and just have to be the best one, poor you.

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Spell casting progression.. is it.
I lost magus spell casting. I added a wizard level. Spell casting progression for prestige classes advances the base class. I would argue casting spells falls under:
Quote:gain all the benefits of that new class level.Edit: Even if some people disagree that spell casting doesn't 'benefit' me or isn't included in 'all' somehow retraining the class feature 'spells per day' fixes this situation.
A selection for a class feature of one class is not a benefit of a different class. The ability to be advanced by EK levels is not a function of being a wizard, it's a selection made as part of the EK class.
As for retraining the "spells per day" class feature: not every class feature can be retrained. There's an explicit list in the retraining rules stating what class features can be retrained for each class.

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I just wrote up a summoner myself. Not, like, some wacky blood summoner of doom and fluffy bunnies. Just a summoner. And no weird spell choices or anything, really. Kinda neat, you know, haste as a 2nd-level spell, a big green eidolon...fun!
As I do love Golarion's Harrow cards, I just rebuilt an older first level character as a Varisian Story Summoner. His eidolon is a storykin using Disguise and a mundane scarf / hat combo to pass herself off as human; she focuses on being a skill monkey. It's a waste of three good evolution points but taking Skilled three times and allocating class skills appropriately gives a +3 class skill bonus and a +8 racial bonus to skills like Perception, Sleight of Hand, and Disable Device (alas, magical traps elude her).
In combat he will use and abuse the standard action Summon Monster (X) SLA that so few summoners use along with either his Harrow deck (random monster alignment and templates with DR and SR) or his Summon Good Monster feat (certain monsters have the Diehard feat... a pony may not hit hard, but it makes a devil of a meat shield).