Sacred Geometry


Rules Questions

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You could also do Ray of Frost + Heighten Spell + Rime Spell.


Pathfinder Companion Subscriber

I've just started playing a level 5 arcanist with both Sacred Geometry and Arithmancy in a Tears of the Bitter Manor campaign game.

As I worked out all the Arithmancy DC's for the spells in my spellbook beforehand, that feat is adding zero time to combats. I think Arithmancy is a very cool feat.

As for Sacred Geometry, I've not actually used it yet. I chose two +1 metamagic feats (cos I can only cast 2nd level spells right now, and I haven't cheesed Wayang spellhunter/Magical lineage onto one spell). Instead of boosting spells to buggery, I saw the feat as a way of adding versatility to the characters prepared spells. Obviously it's very possible to screw the game over using this feat, just as it's possible to screw the game up with other feats/combinations.
And with 5 ranks in Know (Engineering), I managed the primes when I did some practice rolls.

I would say it's highly unlikely that this feat will be allowed in PFS. If I was running a home game I would insist that all Arithmancy DC's were worked out ahead of time.

And I'd insist that any Sacred Geometry calculations were made without dragging the turn out. If you're casting as a full round action (and you will be below level 9) you state you're starting casting on your turn, and you have until your spell goes off to get the sums done. If you haven't got there in time, the spell fails. Although I do like the idea of your action delaying until you make the prime. Oh, and no calculators or programs for it. Just as you would let a disorganised player play a master summoner, you wouldn't want someone who's bad at math to be using this. Doesn't that go without saying?

It's a real shame that options for the game get banned from PFS play because there's an idiot out there who will abuse it. My only options for play are PFS play, so I'm bound by what's allowed there.


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I don't get the "no using calculators" that makes no sense. It (should) make the number crunching go faster which would make this better. And really you shouldn't be using this anyway, as it is phenomenally overpowered. Nothing makes it "better".


Anzyr wrote:
I don't get the "no using calculators" that makes no sense. It (should) make the number crunching go faster which would make this better. And really you shouldn't be using this anyway, as it is phenomenally overpowered. Nothing makes it "better".

I think there are two groups of thought regarding how the feat is executed.

One is deciding whether a prime constant can be reached at all, given the result of the dice. In this case, you should use calculators. Heck, you should make a program that takes the dice results as input, and the resulting formula as output. That'll speed it up even more.

The other group of thought is treating Sacred Geometry as an arithmetic mini-game of sorts. The player actually mentally doing arithmetic is a goal in and of itself. In this case, you should limit all electronics.

Of course, the feat is, as you say, phenomenally overpowered and nothing makes it "better". So I guess the point is moot.


Here is an idea for a rewrite for this feat.

It allows you to apply any metamagic feat, but this must be done at spell prep and it uses a slot of the effective level. If you don't get a prime constant the slot you were attempting to prep in is expended.

Spont casters can't use this feat.

There now the wizard has to go through a mini-game in-between sessions to get access to lots of meta-magic. The feat is still really really strong, but less broken.


Marcus Robert Hosler wrote:

Acid Splash + Heighten Spell + Dazing spell

No SR Will save or be dazed for X rounds. (Basically an unlimited save or die)

That's a pretty good one, much better than mine. It will be a minimum 7th level caster though.


This feat seems awesome, but I can see this holding up a game like nobody's business.

Liberty's Edge

I actually laughed out loud when I read the feat description. I want to buy whoever wrote it a beer.

If I were the GM, I would allow the player to roll ahead of time, at the end of their last turn, but when their turn comes up, if they're not ready with an answer, they pay the longer cast time, but don't get the free metamagic.

BY THE POWER OF MATH!


is this feat PFS legal?

Sovereign Court

Undone wrote:
is this feat PFS legal?

It's not. If you check the Additional Resources, you'll see that there are things in Occult Mysteries that are legal, but this feat isn't one of them.


I'm just waiting for someone to quote this feat while waving an "Arcanist is Broke!" flag.

Yeah, isn't every spell caster past like, level 10 with this thing?


Artemis Moonstar wrote:

I'm just waiting for someone to quote this feat while waving an "Arcanist is Broke!" flag.

Yeah, isn't every spell caster past like, level 10 with this thing?

I don't think it's gonna happen, myself. You only need Arcanist to wave the 'Arcanist is overpowered' flag. Anything else is gravy.


Artemis Moonstar wrote:

I'm just waiting for someone to quote this feat while waving an "Arcanist is Broke!" flag.

Yeah, isn't every spell caster past like, level 10 with this thing?

Already happened, a lot.


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When my players try to complain about why I only blanket allow PRD and Ultimate Psionics material, I point to sacred geometry. That feat is why I audit everything else.


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Marcus Robert Hosler wrote:
When my players try to complain about why I only blanket allow PRD and Ultimate Psionics material, I point to sacred geometry. That feat is why I audit everything else.

You warm my heart, my friend. I can only hope my upcoming work with Wilder is quality enough to find a home at your table.


Marcus Robert Hosler wrote:
When my players try to complain about why I only blanket allow PRD and Ultimate Psionics material, I point to sacred geometry. That feat is why I audit everything else.

I have this same rule.


master_marshmallow wrote:
Marcus Robert Hosler wrote:
When my players try to complain about why I only blanket allow PRD and Ultimate Psionics material, I point to sacred geometry. That feat is why I audit everything else.
I have this same rule.

At least you allow it in. I've seen others that just go "Nope." to everything outside the PRD, some even go as far as banning everything outside the core book because of things like the synthisist.


Darche Schneider wrote:
master_marshmallow wrote:
Marcus Robert Hosler wrote:
When my players try to complain about why I only blanket allow PRD and Ultimate Psionics material, I point to sacred geometry. That feat is why I audit everything else.
I have this same rule.
At least you allow it in. I've seen others that just go "Nope." to everything outside the PRD, some even go as far as banning everything outside the core book because of things like the synthisist.

Rule 1: If it's allowed in society it's allowed.

Rule 2: GM Veto for obnoxious OP stuff like creating a legion of undead.
Rule 3: See rule 2.


This has worked well for me so far...

Rule 0: I get to veto anything that starts breaking the game... At any point in time outside of combat.

Rule 1: Everything is allowed upon GM review.
-Note: I generally allow whatever, since many times my players need it.

Rule 2: Upon any significant power increase (new levels, for example), and in between sessions, GM has the right to audit your character, and enforce Rule 0.

Dark Archive

Artemis Moonstar wrote:

I'm just waiting for someone to quote this feat while waving an "Arcanist is Broke!" flag.

Yeah, isn't every spell caster past like, level 10 with this thing?

As it turns out, if you keep your knowledge (engineering) ranks maxed as you level up, you will pass the check for modifying a spell to the highest level you can cast 95% of the time starting at level 6. Once you reach 14 ranks you cannot fail (even with a roll of all 1s).


Marcus Robert Hosler wrote:
When my players try to complain about why I only blanket allow PRD and Ultimate Psionics material, I point to sacred geometry. That feat is why I audit everything else.

That doesn't seem to be a great argument as it doesn't really hold up to the obvious follow up question: "Ok, that's one awfully balanced feat. What are the others?"

Off the top of my head, the only other I can think of is Bewildering Koan. So two horribly unbalanced feats? Is that really enough to justify banning what could amount to another full-sized pathfinder book of material, instead of say, just going with it and picking out any bad eggs like the two previously mentioned as they come up?


chaoseffect wrote:
Marcus Robert Hosler wrote:
When my players try to complain about why I only blanket allow PRD and Ultimate Psionics material, I point to sacred geometry. That feat is why I audit everything else.

That doesn't seem to be a great argument as it doesn't really hold up to the obvious follow up question: "Ok, that's one awfully balanced feat. What are the others?"

Off the top of my head, the only other I can think of is Bewildering Koan. So two horribly unbalanced feats? Is that really enough to justify banning what could amount to another full-sized pathfinder book of material, instead of say, just going with it and picking out any bad eggs like the two previously mentioned as they come up?

Oh he isn't banning it, like I had thought before too.

He does allow the stuff outside, but only after he's reviewed it.

Honestly though I'd review all of it. Even the PRD stuff, so no one is getting all techy on ya.


Ah, that's a reasonable stance then. Feel free to pretend I never posted.

Sovereign Court

I too don't allow anything until I've reviewed it. I'll usually say yes, especially if it's also allowed in PFS or if it's from a decent 3PP. But I just don't want any powers at my table that I don't even know about. I think it's a GM's responsibility to understand the rules and abilities the players are using.

Grand Lodge

Pathfinder Rulebook Subscriber

I'm pretty much open to anything, so long as your turns stays short and sweet. Sacred geometry isn't that so nope.


The concept build I have is focused on sacred geometry as a way to ignore the repetitive meta-magic reduction feats, classes, and traits. One spell I love to use this with is explosive runes, but only with the ruling that damaging a rune counts as a failed attempt to disarm the magical trap.


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Ravingdork wrote:
Nathanael Love wrote:
Lemmy wrote:

A completely overpowered feat that greatly slows down gameplay... I haven't seen something this badly designed in... well... a long, long time.

Who created this abomination? And who approved it?

People keep asking this question, but the authors of the book it is in are right at the bottom of the page. . . we know who approved it. . .

Yes, we do...

Authors • Jason Bulmahn, Crystal Frasier, Jim Groves, Brandon Hodge, James Jacobs, Erik Mona, F. Wesley Schneider, and Jerome Virnich

Creative Director • James Jacobs
Editor-in-Chief • F. Wesley Schneider
Managing Editor • James L. Sutter
Lead Developer • Mark Moreland
Senior Developer • Rob McCreary
Developers • Logan Bonner, John Compton, Adam Daigle, Mark Moreland, and Patrick Renie
Associate Editors • Judy Bauer and Christopher Carey
Editors • Justin Juan, Lyz Liddell, Ryan Macklin, and Matthew Simmons
Lead Designer • Jason Bulmahn
Designers • Stephen Radney-MacFarland and Sean K Reynolds

...but what to do about it? It's not like we do the whole torches and pitchforks thing anymore.

Artanthos wrote:
swoosh wrote:

http://www.d20pfsrd.com/feats/general-feats/sacred-geometry

Just.. wat? Such a weird (and amazing) feat.

My PFS wizard is so taking this feat at 9th level.
I would be VERY surprised if this was ever approved for Society play.

.

HURRAY FOR PUBLIC SCHOOL !!

.


And the point you were trying to make was...


Grand Magus wrote:
Ravingdork wrote:
Nathanael Love wrote:
Lemmy wrote:

A completely overpowered feat that greatly slows down gameplay... I haven't seen something this badly designed in... well... a long, long time.

Who created this abomination? And who approved it?

People keep asking this question, but the authors of the book it is in are right at the bottom of the page. . . we know who approved it. . .

Yes, we do...

Authors • Jason Bulmahn, Crystal Frasier, Jim Groves, Brandon Hodge, James Jacobs, Erik Mona, F. Wesley Schneider, and Jerome Virnich

Creative Director • James Jacobs
Editor-in-Chief • F. Wesley Schneider
Managing Editor • James L. Sutter
Lead Developer • Mark Moreland
Senior Developer • Rob McCreary
Developers • Logan Bonner, John Compton, Adam Daigle, Mark Moreland, and Patrick Renie
Associate Editors • Judy Bauer and Christopher Carey
Editors • Justin Juan, Lyz Liddell, Ryan Macklin, and Matthew Simmons
Lead Designer • Jason Bulmahn
Designers • Stephen Radney-MacFarland and Sean K Reynolds

...but what to do about it? It's not like we do the whole torches and pitchforks thing anymore.

Artanthos wrote:
swoosh wrote:

http://www.d20pfsrd.com/feats/general-feats/sacred-geometry

Just.. wat? Such a weird (and amazing) feat.

My PFS wizard is so taking this feat at 9th level.
I would be VERY surprised if this was ever approved for Society play.

.

HURRAY FOR PUBLIC SCHOOL !!

.

Lol. If I'm catching your meaning right... Sad but true. Lol.


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It's nice how a mathematician playing a 7 int sorcerer can make great use of the feat but the less mathematically inclined painter playing the 22 int wizard is SOL.

Such awesome role playing opportunities!


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Unless there are some clever optimizations possible to significantly reduce its complexity class (I suspect not), the calculations required to use this feat have a computational complexity of O(n!). That is, the size of the search space of the problem grows with the factorial of the number of dice you need to roll, which must equal your ranks in Knowledge (engineering).

Analysis:

The feat calls for n number of dice to be rolled (where n is your ranks in KE), the results then being combined in some way using only the four basic binary arithmetic operators, '+', '-', '*', and '/', and the result must match one of three prime numbers. Any such arithmetic expression can be modeled by a binary expression tree, which is a full binary tree wherein the internal nodes are the operators and the leaves are the operands (i.e. the numbers which came up on the dice). Unfortunately, I can't really illustrate it here because this messageboard apparently lacks anything like a 'pre' or 'code' bbcode tag, and it's probably confusing without illustration. Wikipedia's page on the subject fortunately includes diagrams which should make it clear: binary expression tree

To solve the problem presented by the feat we need to find one such binary expression tree, which evaluates to one of the three prime constants, out of all the possible structurally distinct binary expression trees which could be constructed using the four binary arithmetic operators available to us (for the internal nodes) and the numbers which came up on the dice (for the leaf nodes).

How many such trees are there?

Let SDT(n) be the number of structurally distinct full binary trees with n leaves; note this is independent of assigning any particular operators or dice results to the nodes of any tree (yet).

To find SDT(n), this page has a nice easy-to-use lookup table for, and a good explanation of how to find, the number of structurally distinct binary trees, however it includes all structurally distinct binary trees (not just the full ones) and works by a count of all the nodes (vertices), not just the number of leaves. Fortunately it's easy to convert to what we need here, since the internal nodes for all of our full trees are themselves binary trees with n-1 nodes. Therefore, SDT(n) can be found simply by finding the row in the table on that page for n-1 number of vertices, and then looking at its rightmost column. For example, if n=10, according to that table SDT(10)=98 structurally distinct trees. SDT(n) grows exponentially with n, so we're already at O(c^n)|c>1 (exponential complexity).

Let m be the number of operator nodes in any of our binary expression trees; this must always be n-1, so m=n-1.

The number of possible arrangements of operators in any given tree structure must be 4^m, since any of the 4 operators could be used at any particular operator node. This means we're up to SDT(n) * 4^m for our search space (still exponential complexity), but we haven't populated the leaves with dice results yet.

For each of those SDT(n) * 4^m trees, we have to try populating the leaves with every permutation of our n dice results, so that brings us up to SDT(n) * 4^m * n! trees in our search space.

This brings us up to O(n!), factorial complexity.

What does this mean in terms of the actual numbers:

With 5 ranks in Knowledge (engineering), SDT(5)=3, 4^4=256, 5!=120, so our search space is 3*256*120=92160 different configurations.

With 10 ranks in Knowledge (engineering), SDT(10)=98, 4^9=262144, 10!=3628800, so our search space is 98*262144*3628800, which is greater than 93 trillion different configurations.

With 15 ranks in Knowledge (engineering), SDT(15)=4850, 4^14=268435456, and 15! is over 1.3 trillion, so that works out to over 1.7 septillion (i.e. 1.7*10^24) different configurations in our search space.

The feat is fundamentally broken, but not because it's overpowered.


Without even trying to dig into the math, that analysis is fundamentally flawed because you're not looking to exhaust the search space. There is not only one solution, nor do you have to find all the solutions. You only need one.

Others have posted fairly simple and elegant approaches to finding those solutions. It's not really difficult, but will definitely slow down play.


thejeff wrote:
Without even trying to dig into the math, that analysis is fundamentally flawed because you're not looking to exhaust the search space. There is not only one solution, nor do you have to find all the solutions. You only need one.

One out of X, where X is a ridiculously large search space. The computational complexity of the direct brute force approach is O(n!); that is precisely what my post demonstrated.

thejeff wrote:
Others have posted fairly simple and elegant approaches to finding those solutions. It's not really difficult, but will definitely slow down play.

Links? The only "solution" I've come across fairly consistently produces incorrect results.

EDIT: n/m, found a way to reduce the search space significantly.


AxiomOfAnarchy wrote:
thejeff wrote:
Without even trying to dig into the math, that analysis is fundamentally flawed because you're not looking to exhaust the search space. There is not only one solution, nor do you have to find all the solutions. You only need one.

One out of X, where X is a ridiculously large search space. The computational complexity of the direct brute force approach is O(n!); that is precisely what my post demonstrated.

thejeff wrote:
Others have posted fairly simple and elegant approaches to finding those solutions. It's not really difficult, but will definitely slow down play.
Links? The only "solution" I've come across fairly consistently produces incorrect results.

But it's not one out of X. The number of combinations is ridiculously large, but so is the number of combinations that solve the problem. And you only need one of those combinations.

I'm not sure what problem your math is actually trying to solve. What you don't allow for is how many working combination there are. That essentially divides your search space, since you only need to brute force until you find the first one.

In reality, you don't need to brute force of course. I'm not sure how I'd write a program to solve it, but it really is a few minutes of work at worst to actually solve any given example.

As suggested earlier in thread: multiply a couple dice together until you're near one of the targets. Add or subtract to reach the target. Pair the rest of the dice together so they come to 1 or 0, then multiply and add.

Let's say you roll 15 dice trying to cast an effective level 9 spell. The prime numbers are 101, 103, 107.

15d6 ⇒ (4, 5, 2, 3, 3, 5, 1, 4, 2, 1, 5, 4, 5, 3, 3) = 50

Edit: Solved for the wrong thing
So 5*4*5 = 100, leaving me with 2,3,3,1,4,2,1,5,4,5,3,3, then you just subtract or divide out pairs.
(5*4*5 +2-2+3-3)*1*4/4+5-5+3-3+1 = 101

That took about 4 minutes, but it's actually easier to match dice together than to keep track while typing it out. (And there's a cat demanding attention.)

I don't know about formal mathematical solutions to the problem, but it's pretty trivial to do by hand.


There is a couple of things I learned..

Gotta bunch of extra numbers? Can you subtract them to make 0?

Because 0 x anything = 0. So once you can consistently get a preset grouping of numbers, you can almost always throw out the rest with 0.

1x1 = 1. 1xX=X. Which is a few more ways you can math out a few numbers as well.

I've got a chatroom based game that the GM is often fairly slow in, so I took the feat myself with my arcanist. Just cause.


Darche Schneider wrote:

There is a couple of things I learned..

Gotta bunch of extra numbers? Can you subtract them to make 0?

Because 0 x anything = 0. So once you can consistently get a preset grouping of numbers, you can almost always throw out the rest with 0.

1x1 = 1. 1xX=X. Which is a few more ways you can math out a few numbers as well.

That's even easier and I don't know why I didn't think of it. And that means it really does get much easier as you get more dice.

So 15d6 ⇒ (4, 6, 3, 1, 1, 1, 5, 3, 6, 4, 1, 6, 5, 4, 3) = 53

101 = (5*5*4 + 1) + 1-1*( 6 + 3 + 3 + 6 + 4 + 1 + 6 + 4 + 3)

103 = (5*5*4 + 3) + 1-1*( 6 + 1 + 3 + 6 + 4 + 1 + 6 + 4 + 3)

107 = (5*5*4 + 6 + 1) + 1-1*( 3 + 3 + 6 + 4 + 1 + 6 + 4 + 3)


Step 1: Give this feat to your grade school math teacher.
Step 2: ???
Step 3: Laugh

Shadow Lodge

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I finally got around to reading this abomination. WTF is wrong with you, Paizo?


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DnD encouraged me to learn math as a kid.

I can see a use for this feat. Most of them involve sneaky ways to encourage a kid (or yourself) to get better at math.

- A kid might try it because you told them "man, no one can do this!" just to prove you wrong
- A kid might try it because "it was the most powerful of powerful wizards ever"
- A kid might try it, because if they could you would buy them pizza afterwards, and they get a super-powerful wizard on top of it

...etc.

Result: Kid learns better math concepts, and gets immediate benefit


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Play a wizard. Do maths. Win Pathfinder. Paizo's apparent design specs summed up in one feat.


I used this feat for the first time last night. We decided that in interest of brevity we would put a timer on it. (about 3 min). I was able to get a level 6 answer with 10d6 in about 2.5. Then I'd realized that It should have been level 7. And so I recalculated and was able to get level 7 as well.

That was with very little practice. Given enough time, I should be able to make the correct solution more quickly. I agree, RAW its overpowered and broken. But I think there has to be a way to keep the flavor while making it not automatic and speeding things up.

Maybe geometric Yahtzee lol.


hewhocaves wrote:

I used this feat for the first time last night. We decided that in interest of brevity we would put a timer on it. (about 3 min). I was able to get a level 6 answer with 10d6 in about 2.5. Then I'd realized that It should have been level 7. And so I recalculated and was able to get level 7 as well.

That was with very little practice. Given enough time, I should be able to make the correct solution more quickly. I agree, RAW its overpowered and broken. But I think there has to be a way to keep the flavor while making it not automatic and speeding things up.

Maybe geometric Yahtzee lol.

Whoever invented this feat needs a picture of his face posted in the office with the words "This man is not permitted to design feats. If seen doing so call the police." attached all over the office.


If your GM allows it, there is a calculator on Android that does a pretty good job of quickly finding solutions to sacred geometry.


I don't think it would be so bad if Quicken Spell wasn't allowed with it. If it makes the spell take a full-round action to cast, wouldn't that mean the spell doesn't take effect until the start of the caster's next turn - giving them the time in between their turns to roll and calculate (and thus failing when it returns to their turn)? Or am I misreading how full-round casting works?

Liberty's Edge

Full-Round casting means the spell goes off on the turn you start casting it.

1 Round casting means you take a full-round action on your current turn and it goes off at the beginning of your next turn.

Prepared casters take a full-round action.

Spontaneous casters take 1 round to cast it.

These are, of course, ignoring quicken (and assuming the original speed of the spell was a standard action).

Scarab Sages

I was interested in this until I found out the 2 metamagic feats you get aren't actually gotten so if you take Quicken and Empower you can't then empower a spell normally so I lost interest.


Why would you ever use metamagic normally once you had Sacred Geometry?


And remember, just like in math class your DM may want you to write all of your work down on paper just to make sure you aren't cheating to get free metamagic applied to your spells.


TheMonocleRogue wrote:
And remember, just like in math class your DM may want you to write all of your work down on paper just to make sure you aren't cheating to get free metamagic applied to your spells.

You can just show him the dice groupings and explain it.

Once you've got the trick down it's pretty quick.

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