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When it is possible that combatants are unaware of each other perception rolls are made to determine who sees who.
In this case the orcs should be given automatic success unless the players are traveling with some extreme tactic.

1)The players fail perception and the orcs are granted stealth until they make any action that would justify a new perception check vs stealth.

2)The orcs can use their surprise round when ever they like.
They can attempt to stealth into a position where they can accomplish their goals,
or if for what ever reason they cant seem to get the ability to close into melee
you can use these special initiative actions to give them better options in the first round on combat.

Most of these posts are correct in that any time they move out of cover or concealment,
they are not going to be able to use stealth under normal circumstances.

technically this wasted their surprise round since the players are aware of the threat. (automatic success on perception check)

The orcs should move to the edge of the cover/concealment.
Then when the players are in optimal range, they attack.
If they rolled good for initiative they charge in getting 2 rounds on the players flatfooted AC
If they rolled bad, they reset to the top initiative position and get 1 round on flatfooted AC.

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Well Paladin restricts your alignment to LG so if you want to play an actual paladin,
then you have to look at Asmodeus and determine how his ideals can be met by a lawful good character.

Quotes from the inner sea guide:
"Some say that when the world was forged, Asmodeus wrote the contract of creation, agreed to by the gods."
"Asmodeus believes strict discipline, unwavering obedience, and the strong ruling the weak."
"Of all the evil gods, the other deities find Asmodeus the easiest to bargain and deal with."

So this is good,
Asmodeus isn't cruel and he doesn't despise kindness.

Play a paladin from Cheliax who helps only those who will bow down to your ability to help them. (boot kissing etc)

Those who ask for help but do not give praise have too much pride, and need to be taught humility!

Your word is unbroken. You hold people to their word and bring them to justice upon ANY infringement not to your liking. Likewise, you hold yourself to your own word, and will not break it even under penalty of death.

You perspective isn't that Asmodeus is evil, he is just the rightful ruler of this world. And as such you pay him the homage he deserves, for you know one day, all will bow to him and his fair rule will govern all to peace.

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"a LG character who is trapped in a room and must kill 1 of 2 innocents in order to leave and save the world"

Paladin should diplomacy the two innocents into fighting to the death.
Paladin: "I need one of you to be worthy of me killing in order to save the world"
The paladin kills the one who committed murder and successfully leaves.

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As a skimmed other posts above, they are correct in that the most reliable way to locate an invisible creature is to wait for it to attack you. For that split second you know where it is, and if you are smart and held your action you can strike at it before it moves from its known location.
CRB Page 563: "... If an invisible creature strikes a character, the character struck knows the exact location of the creature that struck him ..." until it moves, and/or unless it has reach :D

They are also correct in that ...

As you stated, it is impossible to use stealth while attacking or running.
Also note stealth checks are made free with a move action.

This means you can still stealth after you attack if you still have a move action left.

More then you wanted to know: Other ways to locate Invisibles

"NOTICE a creature using stealth." There are some fun modifiers to come up with a DC, but the important part is you haven't located anyone, just know they are there.

This is clarified for us later.

Targeting a creature means you have to know their exact location.

We have a few more things to look up:
Invisible (Appendix2: conditions)
Blinded (Appendix2: conditions)
Invisibility (spell)
Invisibility (Appendix1: special abilities)

Invisible(Appendix2: conditions) (CRB Page 567)
Nothing relevant to locating.

Blinded(Appendix2: conditions) (CRB Page 565)
Not applicable, but can be if creatures are invisible because you are in complete darkness :D

Invisibility(spell) (CRB Page 301-302)
"... Ofcourse, the subject is not magically silenced, and certain other conditions can render the recipient detectable (such as swimming in water ... ) ..."
Detection is different from locating. The bonuses to stealth here are to not being DETECTED. The spell points out some ways that perhaps you could know their exact location. A light source on them, displacing water etc. And I would add/say that creating an aerial displacement could do the same, blanketing the area in ash, creating other clouds of visible aerial debris.

Invisibility(Appendix1: special abilities) (CRB Page 563-564)
" ... creatures can be heard. smelled, or felt. ..."
" ... A creature can generally notice the presence of an active invisible creature within 30 feet with a DC 20 perception check"
" ... It's practically impossible(+20DC) to pinpoint an invisible creatures location with a perception check. ..."

Modifiers from the chart I think are a little screwy. But we will use common sense to work through this.

To copy it as its written in my CRB

Invisible creature is.................Perception (DC modifiers)
In combat or speaking.....................-20
Moving at half speed.........................-5
Moving at full speed........................-10
Running or Charging.......................-20
Not Moving......................-40 (should be +40?)
Using Stealth....................Stealth check +20
Some distance away.............+1 per 10 feet
Behind an obstacle(door).................+5
Behind an obstacle(stone wall)......+15

It should be fairly obvious that "In combat or speaking" should be a penalty as well as the Moving at half, full or running. Not moving should NOT be a penalty so we have to consider if this is +40 to the DC. I would argue that although it is a HUGE bonus, it makes sense since not moving in this case refers to ANY movement, and not just move actions.

Locating an invisible creature happens in two ways an at two levels of success.
1) know something is there.
2) know where it actually is.

The DC is going to vary slightly depending on how well you understand how to build a perception check, but don't worry about this to much. The point to make is, that the DC is +20 for being invisible. If they beat THAT dc by 20, then they also know the creatures exact location.(until it moves)

creature is walking 20 feet from you.
To hear the sound of a creature walking is base DC 10. This creature is invisible so DC is 30(10+20). Invisible bonus is reduced according to the above chart conditions in this case walking is -5 so DC is 25(10+20-5) 20 feet away is +2 so DC is 27 (10+20-5+2)

one might argue that the distance modifier is doubled since it is on both charts, but then you would also double behind a door, and that makes no sense. (Of course you shouldn't really get the +20 invisible bonus behind the door either, but it's just a rule, and we have to allow it to be imperfect)

So DC 27 to know it is walking near you. But DC 47 to know its exact location.
(There are other correct solutions using modifiers differently. just use your judgement and then stick with it as a house rule.)

Stealth just changes the base DC. You still add 20 for being invisible and still add 20 more to locate.

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A good trick for players who "can't play paladins" is to have them write up a long back story. They can talk with the GM about the actual character moments, saved village from X, found lost artifact of Y, etc.
Once they have 10-15 GM approved moments, they have to write up a good 5 pages or so of history. This should help them remember who the character is, and try and meet the characters goals stubbornly, rather then give into the players desire to be rich and alive.

Also you are lucky to have good examples at the table. You could try to openly praise these kinds of actions in the attempt to classically condition your players. :P

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Starting on page 549 of core rule book.

Here we have some lovely rules to "do it yourself" item creation. Not really power you want to give your players lightly, but none the less the rules exist and I find some of the formulas less then clear, in particular the multipliers when stacking item abilities.

Now to be clear before we get started I am looking for rules lawyer and am not concerned with what is fair/O.P.

From what I can tell, there are two broad mechanics when dealing with multipliers.

1)Whether or not the items uses an official hero slot. (Head, neck, etc.)

2)How many abilities an item has. (Fireball 1/day and burning hands 3/day)

Pertinent rules Directly from page 549 and the Table on page 550.

"Multiple Similar Abilities: For items with multiple similar abilities that don't take up space on a character's body, use the following formula: Calculate the price of the single most costly ability, then add 75% of the next most costly ability, plus 1/2 the value of any other abilities."

"Multiple Different Abilities: Abilities such as an attack roll bonus or saving throw bonus and a spell-like function are not similar and their values are simply added together to determine the cost. For items that take up space on a character's body, each additional power not only has no discount but instead has a 50% increase in price."

On Table 15-29: Estimating magic item gold piece values

No space limitation: multiply entire cost by 2

Multiple different abilities: Multiply lower item cost by 1.5

6 possibilities.

1)Slotted item with 1 ability.
Strait forward. No multipliers.

2)Slotted item with more then one ability (abilities are "Similar")
Rule1 only applies to unslotted items.
Rule4 states it is x1.5 for each ability beyond the most expensive
So only rule 4 applies. EZ

3)Slotted item with more then one ability (abilities are "Different")
Rule2 states each additional power is x1.5
Rule4 also states x1.5
I think its a little presumptuous to say rule 2 and 4 refer to the same rule.
So the first ability is normal price and additional abilities are x2.25

4)Unslotted item with 1 ability
Strait forward. x2 as per Rule3

5)Unslotted item with more then one ability (abilities are "Similar")
Rule1 states it gets a discount for its cheaper abilities
Rule3 states it is x2
If we add these rules together we get: X2 for the most expensive ability, x1.5 for the second most expensive ability, and normal price for further abilities. Fair enough.

6)Unslotted item with more then one ability (abilities are "Different")
Rule2 states no change(because it is unslotted)
Rule3 states it is x2
Rule4 states it is x1.5 for each ability beyond the most expensive
If we add these rules together we get x2 for the most expensive ability and x3 for all other abilities.

My questions!

1) Is rule 2 a more detailed version of rule 4?
One confusion is whether or not rule 2 and rule 4 are the same rule. They certainly seem similar, nearly identical, but rule two leaves unslotted items exempt. I can accept them as the same rule with community feedback and even more so with a paizo employee ruling. The only hard part to swallow is that slotless items are not penalized for multiple abilities...perhaps because of the default x2 cost?
Anyway a ruling on this effects possibility 3 and 6.

2) Are things like weapons, scrolls, and wands considered unslotted?
By the math they are clearly not unslotted as they don't cost x2. They also don't take up a hand slot since gauntlets can be used with a sword. It seems an implied wield slot exists for each hand. Just some simple nitpicking, but may as well ask while we are on the subject of being rules geeks.

3) What are the other benefits of unslotted items other then the obvious that it doesn't take up a slot? Would it be possible to activate a command word unslotted item from your backpack? would an unslotted gem of +2 int work from your backpack? To make things easier assume the item has to be attuned to the wielder(doesn't function until with the user for 24 hours, even though this drawback doesn't apply to wands and other "wielded" slot items.)

4) Which abilities are considered "Similar" and which are "Different?"
A detail of all the categories would be very helpful

5) What's an example of an item that requires a skill to use?
Can i just say this sword requires knowledge nature to use its magic missile spell and apply a 10% discount? Probably not, so what are a few examples? Try not to dismiss the question by simply stating the 10% rule is meant to help you value an item and isn't used as a crafting discount. This I know.

6) How do you apply the discount modifiers?
Racial restriction 30% Class restriction 30% skill restriction 10% if added they sum 70% reduction to create a special race item. Or if I do them one at a item, it reverse compounds 30% then 51%(for both 30's) then 55.9%(for 30,30 and 10% respectively)

Thank you very much if you made it this far! Your input will help me greatly as a GM who wants to create clear crafting rules for my advanced players, as well as allow for me to create some unique loot that will put sparkle back into the eyes of players who have done more then enough pathfinder "baal runs". (D2 ref.)

As a bonus for getting this far I will leave you with this thought,
consider it motivation.

A belt(slotted item) that adds +6 to all SIX of your stats costs 6x6x1000 (36,000) + 36,000 X 1.5 (54,000)x 5 (five other stats)
36 + 54 + 54 + 54 + 54 + 54 = 306,000 gold

an UNSLOTTED item that adds +6 to all SIX of your stats costs
6x6x1000 (36,000) x2(first ability) 72,000 + 36,000 X 1.5 (second ability) 54,000 + 36,000 X4 (4 more stats)
72 + 54 + 36 + 36 + 36 + 36 = 270,000 gold

:/ Save more then 10% by UNSLOTTING an item?

that's where my doubt began...

Godspeed to the brave community who help!