Why does the math in pathfinder "break down" at higher levels?


Pathfinder First Edition General Discussion

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Alzrius wrote:

This is a misconception. AD&D 2E did have a limit on how many levels characters could earn; it was just a "soft limit" at first, rather than a hard one.

I say "soft limit" to indicate that rather than having an express prohibition, the AD&D 2E PHB simply didn't present the information necessary for gaining levels beyond 20th.

I disagree with your assessment.

The AD&D 2e DMG states; "Theoretically, there is no upper limit to character class levels (although there are racial limitations."

There are other places in the book too which mention characters going beyond 20th level - in fact, basically everything is covered, except for spells:

Each class (except druid) had a clear point at which gaining a level took exactly the same number of experience points - such as a fighter of 9th level or higher needing 250,000 XP to level, every level, or a wizard of 11th level or higher needing 375,000 XP for each level.

Each class gains only a flat amount of HP after 9 or 10 levels, so you always know how many HP to add.

The books had a chart that list the improvement rate of THAC0 specifically so that you can calculate for levels 21+ - since they don't need to tell you the rate for any other reason because they also included a table that did the math for you up to level 20.

Saving throws had maximum values, which the PHB shows you the level at which you reach them - and for Wizards & Rogues that is 21+

The book tells you everything you actually need to know in order to see that you can level to your heart's content - they just expected that you weren't going to go past 20 because A) it took a ridiculously long time to gain levels after about 10th level, and B) Most characters didn't get much in the way of "new" stuff to do at those levels... something which, it seems, bored enough people badly enough that every edition of D&D (or D&D-like) games since then has been trying to fill each and every level with something "special".

Saying that there wasn't "express prohibition" of gaining levels beyond 20th is true - there was actually express permission, even though it didn't take the form of a "+X Experience/level" statement which was only ever pointing out the obvious in the first place.


I seem to have lost my copy, but if I remember correctly the high level campaigns book published near the end of 2nd Edition had rules for going beyond 20th level. True Dweomers were the first attempt at epic level spellcasting rules.


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I still hate seeing people so vehemently opposed to high level play because "the rules break down". Yes, there are more options and abilities at higher levels, but isn't that expressly the point? You get levels to get more abilities to do more things. If those "more things" include teleporting away from every fight, what do you ever get done? How is that even adventurous? It boggles the mind and boils the blood.

I can see how specialized builds can be pushy. I can see how high level wizards might have upper hands when dealing with problems. But it's not like this makes everything a cakewalk. See how good that teleport out of all danger strategy goes for you and your companions when you get snuck doses of poisons. Or your spellbook has suddenly been filled with explosive runes. I know it seems unfair to explicitly go after weaknesses of characters, but it's not like people wouldn't have heard of your characters by that point.

There is a bit of an obscure guideline about high level characters and NPCs. The spell description for Legend Lore says something along the lines of every character with at least 11 class levels is legendary. It's more a rule of thumb than anything else, but if your characters are legends in their own times, they won't have the same adventures as "kick the door down and look for trouble."

What other people said in this thread hit the nail on the head. You've got to challenge the players where they live. Take away running and porting, or even scrying and frying, by giving consequences in story for such actions. This is a role-playing game, after all.

Sorry for the wall of text, but I get heated when people keep saying they don't do high level play because it doesn't work. It works fine if you get a good storyteller and run the right numbers, but it's only very rarely that anyone I know is willing to try and step up to the challenge. And that is very frustrating as a player, I'll have you know.


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aceDiamond wrote:
I still hate seeing people so vehemently opposed to high level play because "the rules break down". Yes, there are more options and abilities at higher levels, but isn't that expressly the point?

No, the point is to have fun. Many people feel that rocket tag isn't fun. The high-level game effectively privileges offense over defense for everyone except Schroedinger's wizard. You either win instantly or lose inevitably.

If that's the style of play you like, enjoy it. But be aware that not everyone will agree.


But it doesn't always have to be rocket tag. How does it always seem to come down to such a thing? I remember some encounters of high level being easier than others, but how often do your encounters become rocket tag?

In fact, I remember a guide to DMing that spells out how to avoid this, mostly via manipulation of CR and placing more grunt enemies to even action economies. In my personal experience with high level DMing, you'd be surprised how effective just outnumbering PCs by one creature, albeit where every enemy has a CR lower than the average party level, is over throwing one super-powered boss creature at them.

It's not that it is necessarily broken, just misunderstood and difficult to do well.


Nipin wrote:
Lemmy wrote:
Nipin wrote:
I liked when this thread was about high level math and not high level spellcasting.
To be fair, spell casting is the main reason high level math breaks down...
I disagree, the math breaks down due to scaling of modifiers outpacing the growth of typical target values (DC, AC, etc.) which make it non-trivial to challenge high level players without either guaranteeing failure for some of the group or guaranteeing success for others. In many cases this is not an issue (e.g., only your scout needs to be able to sneak past the sentry), but in common cases it causes concerns (e.g., everyone needs to be able to hit the dragon). This is the commonly held belief. Certain buffing spells do impact this issue, but the discussion has gone off-topic and is now focused on the narrative impact of spellcasters (which also significantly impacts high level play, but was not the original topic of discussion).

Yeah, you're right on that one. I was thinking mostly of save DCs, since failing a save usually means the character is out of the game, but I forgot about attack/AC disparity and the fact that spells are not the only SoL effects.

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aceDiamond wrote:

But it doesn't always have to be rocket tag. How does it always seem to come down to such a thing? I remember some encounters of high level being easier than others, but how often do your encounters become rocket tag?

In fact, I remember a guide to DMing that spells out how to avoid this, mostly via manipulation of CR and placing more grunt enemies to even action economies. In my personal experience with high level DMing, you'd be surprised how effective just outnumbering PCs by one creature, albeit where every enemy has a CR lower than the average party level, is over throwing one super-powered boss creature at them.

It's not that it is necessarily broken, just misunderstood and difficult to do well.

It doesn’t for us. And, I don't think it really does IRL table-top games, just in theory.


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DrDeth wrote:
It doesn’t for us. And, I don't think it really does IRL table-top games, just in theory.

Good point! People whose experience with the game differs from yours actually don't exist. They are just ghosts on the internet.

Pretty spooky, if you ask me.


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Vivianne Laflamme wrote:
DrDeth wrote:
It doesn’t for us. And, I don't think it really does IRL table-top games, just in theory.

Good point! People whose experience with the game differs from yours actually don't exist. They are just ghosts on the internet.

Pretty spooky, if you ask me.

They said I was crazy! That these people on the internet weren't real! BUT I KNEW! I KNEW! THEY'RE THE ONES WHO ARE CRAZY!


Don't call me crazy. I'll kill you and your whole family if you call me crazy!!

Shadow Lodge

You don't get to disagree with DrDeth unless your name is on the credits sheet for the first edition of Chainmail.


Kthulhu wrote:
You don't get to disagree with DrDeth unless your name is on the credits sheet for the first edition of Chainmail.

I hope you're joking

Owner - House of Books and Games LLC

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My discovery from years of high-level play was that combat was boring. We didn't play at high levels to have high-CR fights, we played at high levels to have high-CR stories, and to do crazy things that just wouldn't be possible for mortals.

By the time we were done with the campaign this spring, the players were pretty much all experts at their characters. But that was okay - that's the point. They all knew what their character could do, what the other characters could do, and who should step in when.

What we found is the math is only broken if you're not having fun. And that had less to do with the modifiers and CRs and encounters than how well the encounters fit the storyline and how cinematic they were, regardless of how difficult the encounters were regardless of whether they were actual combat encounters or not.

Now, it was a crazy amount of work as GM, but I would never say it wasn't worth it. However, my view is you should never never ever run a high-level campaign without (a) an actual plot and (b) being prepared to adjudicate all sorts of whacked out unbelievable stuff.

After all, there's no epic fiction out there about a bunch of murder hobos wandering the countryside - it's all about continent-spanning quests, intrigue, and the like. Along with a few insane battles along the way :)


Considering how many folks on the forum won't even hesitate to criticize some Gygax's positions on roleplaying, I think there are no sacred cows here. A bad argument is a bad argument, no matter who makes it.


Lemmy wrote:
DM_Blake wrote:

They're supposed to be binary. It's the only thing that makes them viable.

I remember the good old days, way back when Hold Person gave you one save. You make it, you're good, but if you fail, you're paralyzed for a bunch of rounds. Period. People actually cast Hold Person in those days. I used it when I played a caster. Other players used it. DMs would have their NPC casters use it.

But then someone came along and made an edition where Hold Person allows a save every round. Now, if it affects the target at all, it probably only paralyzes him for a round or two. Maybe you waste your spell slot and your entire round just paralyzing one enemy for one round - you trade your round to neutralize his round. If you're lucky.

I often think that if you are a target of a spell, even if you make your save, it still affect you somewhat, like you cannot now perform a full round action as a result of shrugging off the magical effect, or it stunned you just enough so you cannot make a full attack, or etc.


mkenner wrote:
I seem to have lost my copy, but if I remember correctly the high level campaigns book published near the end of 2nd Edition had rules for going beyond 20th level. True Dweomers were the first attempt at epic level spellcasting rules.

More accurately, that book presented rules for never going beyond 30th level - the core books could take you to any level you wanted to.

Of course, that book also added some pretty interesting things, like a "fighter skill' which is both the origin of Whirlwind Attack, and for D&D 4e's "powers" since it plays just like a target: one enemy; str vs. ac; 1[W]+str damage, Special: if you reduce an opponent to 0 hit points with this attack, deal 1d8 damage +1d8 damage per 5 levels above 10th to all enemies within 5 feet of equal or lesser size and AC to the target slain power.


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Scavion wrote:
Kthulhu wrote:
You don't get to disagree with DrDeth unless your name is on the credits sheet for the first edition of Chainmail.
I hope you're joking

He’s kidding. I was a Developer back in the OD&D days, so I can say I was a bit of a expert on that period, and sure, that means I have played for a long time. But my Pathfinder experiences are no more in depth and my Pathfinder gamemastery opinion is no more valid than any other poster-player here.

Still, I have seen almost no “rocket tag” games IRL. YMMV.

Does anywhere here play a table game game where Rocket Tag is a standard thing?


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DrDeth wrote:

Does anywhere here play a table game game where Rocket Tag is a standard thing?

No, because we stop playing when the game gets to the rocket tag stage, as it almost inevitably seems to when the levels get high. Actually, we probably play at lower than average levels because the rocket tag for us starts at about level 12 or so, sometimes lower.

Grand Lodge

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gbonehead wrote:
What we found is the math is only broken if you're not having fun.

True enough. My own playthrough of levels 21+ in 3.5 was just fine. We were all fighter-types, we had epic combats, and enjoyed ourselves.


DrDeth wrote:
Does anywhere here play a table game game where Rocket Tag is a standard thing?

At higher levels, yeah.


Pathfinder Rulebook Subscriber

That does not describe most, or even many, of the combats run in my 1-20 campaign. There was a wizard and a cleric present at all times, for a good bit of the campaign, a sorcerer.


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At higher levels, rocket tag is a consequence of offense outstripping defense*. Basically martials should be killing anything they can successfully land a full attack on, while caster should be completely killing/rendering useless/or inflicting lethal damage with a combination of two spells at this level. You can not play this way, but this sort of scenario is what the rules actually develop as the best strategy. I mean sure you can not shoot the medic first in a game, or not focus fire in a game, but that's just intentionally being sub-optimal and forcing people to be sub-optimal sucks.

*unless your a full caster, then defenses approach but never quite reach impenetrable to non-full casters.


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Orfamay Quest wrote:
DrDeth wrote:

Does anywhere here play a table game game where Rocket Tag is a standard thing?

No, because we stop playing when the game gets to the rocket tag stage, as it almost inevitably seems to when the levels get high. Actually, we probably play at lower than average levels because the rocket tag for us starts at about level 12 or so, sometimes lower.

That does seem to be how it goes. Most of the campaigns I've been in or run closed out around levels 12-14. Granted, nobody ever ouright said "Pathfinder's math breaks down at high levels, let's quit," but the fact that so many of my Pathfinder games ended right around the point that people say the math is shaky does seem telling.


Pathfinder Rulebook Subscriber
Anzyr wrote:

At higher levels, rocket tag is a consequence of offense outstripping defense*. Basically martials should be killing anything they can successfully land a full attack on, while caster should be completely killing/rendering useless/or inflicting lethal damage with a combination of two spells at this level. You can not play this way, but this sort of scenario is what the rules actually develop as the best strategy. I mean sure you can not shoot the medic first in a game, or not focus fire in a game, but that's just intentionally being sub-optimal and forcing people to be sub-optimal sucks.

*unless your a full caster, then defenses approach but never quite reach impenetrable to non-full casters.

We had epic battles against Gargantuan blue dragons, running battles with liches, and descents into heavily fortified demiplane fortresses, so I guess we were doing it wrong.


RJGrady wrote:
Anzyr wrote:

At higher levels, rocket tag is a consequence of offense outstripping defense*. Basically martials should be killing anything they can successfully land a full attack on, while caster should be completely killing/rendering useless/or inflicting lethal damage with a combination of two spells at this level. You can not play this way, but this sort of scenario is what the rules actually develop as the best strategy. I mean sure you can not shoot the medic first in a game, or not focus fire in a game, but that's just intentionally being sub-optimal and forcing people to be sub-optimal sucks.

*unless your a full caster, then defenses approach but never quite reach impenetrable to non-full casters.

We had epic battles against Gargantuan blue dragons, running battles with liches, and descents into heavily fortified demiplane fortresses, so I guess we were doing it wrong.

Did you try just shooting the medic first? You can't really do it wrong per se, you can just make sub-optimal decisions. There's nothing wrong with that, but I don't think the math should require you to make sub-optimal decisions for the game to not devolve into rocket tag.

Out of curiousity, which of the above things was your group incapable of? Did your martial not deal enough damage? Did your caster lack instant kills/lockdown/aoe damage? Or was your DM fudging things?

Grand Lodge

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Anzyr wrote:
There's nothing wrong with that, but I don't think the math should require you to make sub-optimal decisions for the game to not devolve into rocket tag.

Eh, I'm not here to make optimal decisions. I'm here to have fun.

If things look grim, then I pull out the optimal stuff.


RJGrady wrote:
Anzyr wrote:

At higher levels, rocket tag is a consequence of offense outstripping defense*. Basically martials should be killing anything they can successfully land a full attack on, while caster should be completely killing/rendering useless/or inflicting lethal damage with a combination of two spells at this level. You can not play this way, but this sort of scenario is what the rules actually develop as the best strategy. I mean sure you can not shoot the medic first in a game, or not focus fire in a game, but that's just intentionally being sub-optimal and forcing people to be sub-optimal sucks.

*unless your a full caster, then defenses approach but never quite reach impenetrable to non-full casters.

We had epic battles against Gargantuan blue dragons, running battles with liches, and descents into heavily fortified demiplane fortresses, so I guess we were doing it wrong.

Nowhere did he imply that your particular games were "wrong." A lot of what he said was true.

High end Martials absolutely obliterate enemies they can land their full attacks on uninhibited. They can also be very easily cancelled out.

Casters can render enemies useless whether they save or not. SR is relatively meaningless. Their damage capabilities range from meh to WMD levels.

Parties tend to focus fire one enemy then the next. Enemies should do the same as well, but that would kill folks really quickly. Ergo you end up with a lot of hand waving on the tactics of enemies. Whenever an enemy switches targets from an injured one to a less injured one for whatever reason is making a less intelligent move. This is pretty common.

"I'm going to stop hitting the Cleric and start hitting the Fighter because he hit me a little bit harder, but then the Cleric is going to literally send me to hell for all eternity."


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Ya, I mean you can have fun playing lots of game sub-optimally (I mean sure you should always play metaknight...), but at no point should the system require it.


Pathfinder Rulebook Subscriber
Anzyr wrote:


Out of curiousity, which of the above things was your group incapable of? Did your martial not deal enough damage? Did your caster lack instant kills/lockdown/aoe damage? Or was your DM fudging things?

I was the DM. Not a single die roll was fudged in the entire campaign. I'm not a purposeful "killer DM" but I am pretty mean; I killed a few PCs over the course of the campaign, some of them quite permanently. I had monsters CDG PCs, I made use of invisibility, heal, and so forth. And my experience was the opposite of "rocket tag." It was more like chess; fatal strategy enacted through moments of decision, occasionally relying on attrition. I played the bad guys in what I considered a reasonable fashion.

There was no conceivable way for the martial to do enough damage to kill the dragon in two rounds. I think the blue dragon, specifically, was eventually felled by Power Word Kill on the second attempt, after it had been whittled down. Surprisingly, there were no PC fatalities during that battle.

There were a couple of quick battles, like when the party ambushed the succubus sorcerer, but on the whole, as the campaign progressed, battles become something of a time suck. I was much more worried about that than "rocket tag." I think the blue dragon was thirty something rounds played out in just under three hours.


Um... even very poorly built martials (and I mean purely getting normal STR buffs and taking power attack and using 2 handed weapon, nothing fancy), should be tearing through dragons. I mean an Ancient Blue Dragon has a base AC of 37 (realistically it will have an AC of 45~ish). Even the above poorly built martial should be hitting the dragon on a 5 at minimum by level 14 (making the dragon a CR+4) and thus hitting most of their iterative attacks. I genuinely I have no idea how it possible that your martial couldn't kill the dragon in one round let alone two short of lacking WBL or a catastrophically unoptimized build. Could you please elaborate, because the situation you described is numerically highly unlikely

Grand Lodge

Anzyr wrote:
...but at no point should the system require it.

I don't find that it does.


At high levels, rocket tag is a consequence of the system (as described above). If you don't want it to be rocket tag the system absolutely requires you to make sub-optimal decisions and choices. Now if your just saying that the system doesn't require it if you accept rocket tag at high levels, then that's fine, but I'm confused what you are getting at TriOmegaZero.

Grand Lodge

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Anzyr wrote:
I'm confused what you are getting at TriOmegaZero.

I'm simply saying that the system doesn't enforce rocket tag. Player choice does.


If you mean the players choosing to play the system in any way other then rather sub-optimally as the system not enforcing rocket tag, then sure I guess.

But if your players are making basic optimization choices, then the system will lead to rocket tag. That isn't the players fault, its the system. Don't hate the player man, hate the game.

Grand Lodge

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Anzyr wrote:
But if your players are making basic optimization choices

I don't find that those lead to rocket tag. You need to be a little more advanced than that.


Is "Invest in STR, a 2 handed magic weapon, and power attack" really that high up the optimization chain? I mean I'll admit my perspective might be skewed here, but pumping STR on those martials types seems like something players have been doing in well... pretty much every game ever across multiple mediums.

Grand Lodge

Anzyr wrote:
Is "Invest in STR, a 2 handed magic weapon, and power attack" really that high up the optimization chain?

I don't find that turns the game into rocket tag in the higher levels.

Grand Lodge RPG Superstar 2012 Top 32

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TriOmegaZero wrote:
Anzyr wrote:
Is "Invest in STR, a 2 handed magic weapon, and power attack" really that high up the optimization chain?
I don't find that turns the game into rocket tag in the higher levels.

Just for the sake of discussion...

The above example with the blue dragon involves power word kill, meaning a party of at least 18th level.

That means the fighter probably had:
+18 BAB
+11 STR (18 to start, +4 level, +6 belt, +4 inherent)
+2 Weapon Focus/GWF
+4 Weapon Training
+3 Weapon
-5 Power Attack
--------------------------
+33 to hit, and that's pretty conservative I think. First attack hits on a 4, second on a 9, third on a 14, fourth on a 19.

Damage is:
+16 STR
+2 Weapon Spec
+4 Weapon Training
+3 Weapon
+15 Power Attack
------------------------
+40 damage per hit, average 47 if it's a greatsword.

So with average rolls, you're hitting twice a round for about 100 damage. You need 7 hits to kill the dragon. That means the first hit of round 4 drops him, but a couple of lucky hits could reduce it to round 3 or even round 2 with a crit in there.

That's without so much as a haste spell to help you out, no gloves of dueling, no accounting for a 15-20 threat range, etc.

That's just the fighter. If anyone else is dealing damage at all, or providing buffs or whatever, we're looking at 2 rounds or less.

Is that "rocket tag"? I dunno; I'm not sure what qualifies.

But it's very different from the stated 30-rounds-to-a-PWK. PWK means the dragon had as much as 100 HP left, so he'd only taken 250 damage in 30 rounds. That's 8.33 damage per round.

That is 8.33 damage per round. From the entire party.

I don't know what the verdict is on "rocket tag", but I think it's safe to say that RJGrady's game is not the norm.


Thank you very much for that break down Jiggy (+1), it pretty much highlights exactly what I was talking about. And to me that Fighter is just a basic no-frills fighter. Not really optimized, but certainly not sub-optimal, but definitely something even a new player with virtually no experience could put together without a lot of thought. And even that is going to make quick work of an ancient Blue Dragon.

RPG Superstar 2012 Top 16

And the dragon just sticks around in one place to eat full attacks from the fighter when it can Greater Vital Strike for OMFGHM? damage, and fly to any other position in the room?

Because, like, Pounce is so easy to get in PF. And TOZ already said they don't play with pure cheese.

I'd be expecting that Blue Dragon to have a barkskin or variant up, mage armor, and probably a shield of faith or similar. AC probably in the high 40's, if it has any brains at all. And all from level 1-2 slots.

==Aelryinth

Grand Lodge

Jiggy wrote:
But it's very different from the stated 30-rounds-to-a-PWK.

My table certainly wouldn't take that long either.


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Aelryinth wrote:

And the dragon just sticks around in one place to eat full attacks from the fighter when it can Greater Vital Strike for OMFGHM? damage, and fly to any other position in the room?

Because, like, Pounce is so easy to get in PF. And TOZ already said they don't play with pure cheese.

I'd be expecting that Blue Dragon to have a barkskin or variant up, mage armor, and probably a shield of faith or similar. AC probably in the high 40's, if it has any brains at all. And all from level 1-2 slots.

==Aelryinth

Yes, but if the dragon is doing all that then the Fighter should really be getting +5 magic weapon, haste, and say enlarge person. And no the dragon shouldn't be just sitting there taking hits *BUT* it should simiarly be killing PCs in 1-2 full round actions. Hence why the game becomes Rocket Tag, rather then Rocket Hide and Seek, or Rocket Four Square, or the dread Rocket Kickball.


Aelryinth wrote:

And the dragon just sticks around in one place to eat full attacks from the fighter when it can Greater Vital Strike for OMFGHM? damage, and fly to any other position in the room?

Because, like, Pounce is so easy to get in PF. And TOZ already said they don't play with pure cheese.

I'd be expecting that Blue Dragon to have a barkskin or variant up, mage armor, and probably a shield of faith or similar. AC probably in the high 40's, if it has any brains at all. And all from level 1-2 slots.

==Aelryinth

Cool. That doesn't change the fact that as written, a unoptimized fighter can still mince it's meat. The build jiggy posted doesn't take into account critical hits nor the multitude of other options that fighter has.

Also the MAIN point of his calculation was that the party was only doing about 8 damage a round. Which is pitiful. Even the Fighter can pop out his bow and do considerably more than that.

RPG Superstar 2012 Top 16

Dragons can use cleric spells as sorc spells, right? So, entirely possible to rebuild its spell list to be more optimal, and to include healing magic...i.e. Heal spells.

30 rounds tells me there was a lot more then just a dragon there, however. I imagine there were a bunch of minions and Summoned things around.

==Aelryinth


Aelryinth wrote:

Dragons can use cleric spells as sorc spells, right? So, entirely possible to rebuild its spell list to be more optimal, and to include healing magic...i.e. Heal spells.

==Aelryinth

I don't believe so. Atleast the entry I have in front of me doesn't say that.


Scavion wrote:
Aelryinth wrote:

Dragons can use cleric spells as sorc spells, right? So, entirely possible to rebuild its spell list to be more optimal, and to include healing magic...i.e. Heal spells.

==Aelryinth

I don't believe so. Atleast the entry I have in front of me doesn't say that.

Silver and gold dragons can. Off the top of my head, I'm not sure about other colors. I'm pretty sure none of the chromatic ones can, but I can't say for certain.


Vivianne Laflamme wrote:
Scavion wrote:
Aelryinth wrote:

Dragons can use cleric spells as sorc spells, right? So, entirely possible to rebuild its spell list to be more optimal, and to include healing magic...i.e. Heal spells.

==Aelryinth

I don't believe so. Atleast the entry I have in front of me doesn't say that.
Silver and gold dragons can. Off the top of my head, I'm not sure about other colors. I'm pretty sure none of the chromatic ones can, but I can't say for certain.

Where is this stated?


They could in 3.5, but I don't believe that was carried over to PF. A cursory examination of their entries seems to agree that the limited cleric casting some (and only some) dragons got in 3.5 was not carried over.

Liberty's Edge

Pathfinder Adventure Path, Rulebook, Starfinder Roleplaying Game Subscriber

See the PRD HERE; specifically, the asterisk footnote at the bottom of the Special Abilities table.

PRD wrote:
A silver dragon can cast cleric spells as arcane spells.

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