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Merisiel gets more close an throws an acid's flask at the swarm.
rgd touch atk: 1d20 + 1 ⇒ (16) + 1 = 171d6 ⇒ 2

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fort save: 1d20 + 9 ⇒ (17) + 9 = 26
attack: 1d20 + 11 ⇒ (13) + 11 = 24
Toshiro attacks the swarm.
It can't take weapon damage I know OOC. I
'm assuming that hits
"My attacks don't work! How will we beat this dammed creature!"

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"Get out of it, FOOLISH MORTAL!" Insidion says, the last words not his own.
He retrieves another flask of acid and prepares to throw it once Toshiro is clear of it.
ranged touch, acid flask: 1d20 + 4 ⇒ (17) + 4 = 211d6 ⇒ 3

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"You have to use splash weapons!" Clair yells at Toshiro.
She prepares to throw her vial of alchemist's fire as soon as Toshiro's left the swarm.
Readied attack: alchemist's fire: 1d20 + 5 ⇒ (18) + 5 = 23 Fire damage: 1d6 ⇒ 4

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Once Galandaro gets close enough to throw the flask he hurls it at the swarm...
Alchie fire throw: 1d20 + 6 ⇒ (8) + 6 = 14....DMG: 1d6 ⇒ 3

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just realized that I miscalculated the touch flat footed AC, Insidion's flask hits in round 1
Merisiel throws another flask at the swarm, but misses this time. The bottle breaks when it hits the floor, covering the swarm and Toshiro in acid. really, they have touch AC18 Toshiro resists the strange feeling in his stomach and swings his weapon at the swarm. Some sprites die when the blade swings through the swarm. I let Toshiro make a 5-ft step out of the swarm so the others can throw their splash weapons, I hope that's fine As soon as Toshire steps out of the swarm three vials fly towards the swarm, to of them mit the target and melt away a good amount of sprites.
The swarm moves to the center of the group and suddenly starts to glow brightly.
Angry Glow ability, DC16 Fort if you are within 10 ft.
Round 3
Insidion
Galandaro
Clair
Merisiel
Toshiro -9HP
-----
Sprite Swarm -16HP

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Fort DC 16: 1d20 + 5 ⇒ (13) + 5 = 18
"What a hell...?!", Merisiel exclaimed as the swarm starts to glow brightly.
The rogue get away from the swarm and tells to her comrades: "I have no more weapons to fight these creatures".
Double move.

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Insidion waits until his companions have cleared the area, then throws another acid flask.
ranged touch, acid flask: 1d20 + 4 ⇒ (7) + 4 = 111d6 ⇒ 5
miss direction, if needed: 1d8 ⇒ 6

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Galandaro follows the thief to a safe location...
kicking myself for not having restocked alchi fire or acid flasks or anything for swarms...

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Fort: 1d20 + 5 ⇒ (15) + 5 = 20
Clair's unaffected by the swarm's angry glow and moves up north, away from the swarm and her allies. "Everyone, stay away from me!"
She taps into the negative emotions inside her and concentrates, channeling a wave of negative energy that harms every living creature within thirty feet.
Channel Negative Energy: 3d6 ⇒ (3, 3, 6) = 12
DC 16 Will for half damage.
My first time using channel versus a swarm! It's an area effect, like the splash weapons, so it should do 50% more damage.
Additional fire damage from previous round's alchemist's fire: 1d6 ⇒ 4

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While Galandaro, Merisiel, and Toshiro move away from the swarm Insidion throws a flask of acid at the swarm but misses. Some splashes hit the glowing mass of feys. Claire channels some energy against the swarm.
Will: 1d20 + 7 ⇒ (19) + 7 = 26
The swarm starts to move again, covering Clair in tiny feys.
Swarm damage: 2d6 ⇒ (1, 6) = 7 distraction, DC16 Fort
Round 4
Insidion
Galandaro
Clair
Merisiel
Toshiro -9HP
-----
Sprite Swarm -32HP

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With one last acid flask in his bandolier, Insidion pulls it out and hopes for a better result. However, it is as poorly thrown as the other two.
ranged touch, acid flask: 1d20 + 4 ⇒ (2) + 4 = 61d6 ⇒ 4
miss direction: 1d8 ⇒ 2

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Fort: 1d20 + 5 ⇒ (16) + 5 = 21
Clair steps out of the swarm with a multitude of tiny wounds on her arms and realizes the swarm will be on her again in no time. She again focuses on the negative energy within her and channels it outward in order to hurt the tiny fey.
Channel Negative Energy: 3d6 ⇒ (3, 5, 5) = 13
DC 16 Will for half damage.

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Perception: 1d20 + 13 ⇒ (6) + 13 = 19
"What a hell...!"
Merisiel looks horrified in the table's direction, then turns to the others:
"Hey, look. It seems... a human arm", she points to the human arm severed just below the elbow lying under one of the library tables.
"It wears a ring. And probably its owner had a longbow", the rogue points to the composite longbow close to the arm-on-the-table.

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Insidion kicks a few of the tiny, shriveled fey out of his way as he moves to look at the ring. However, with all the chaos of magic in the room, he can't tell what it does.
spellcraft to ID ring: 1d20 + 4 ⇒ (5) + 4 = 9
"There's another room to the north," he says. "We should DISMEMBER OUR FOES!" another voice finishes.

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Clair walks over and inspects both the composite bow and the ring, and shares whatever she learns.
Spellcraft, Bow: 1d20 + 3 ⇒ (19) + 3 = 22
Spellcraft, Ring: 1d20 + 3 ⇒ (17) + 3 = 20

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Insidion nods and follows Toshiro.
How about we check the passage to the west first, then the north, then the east?

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Galandaro looks over the bow and tests the pull...determining he does not have sufficient strength to use it he offers it to someone else.
"Was anyone seriously hurt from that swarm fight?" he inquires.

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Since there are no threats in this area any more, I can do it quick :)
room to the west
This library contains tomes pertaining to Hell and its infuriatingly complex legal system as well as codices on the Abyss and Abaddon. Several of the books in this room are burned beyond recognition, while others are weeping blood into slowly evaporating pools. A palpable presence of dread and desperation fills the entire chamber.
room to the north
While much of the sealed wing is in considerable disrepair, this library seems largely untouched by the battle that had come before. Bookcases that rise from floor to ceiling line the walls of this spacious library, and the table in the middle of the room is strewn with open books and crumpled notes referencing lists of books and page numbers. These jottings look fairly recent.
All of the books in this vast collection detail the myriad planes. Some of the books here also detail the enigmatic Dimension of Dreams and the creatures that reside within.
rooms to the east
The myriad books in this collection contain fantastical titles such as Journey to the Heart of Mnemovore, Prisoners of the Crux, Seekers of Jandalay, and Visions of Herald’s Fall. These titles and more analyze known demiplanes, pocket dimensions, and other interstitial dimensions such as the First World and the Plane of Time.
This other library feels unusually claustrophobic, with its looming shelves rising higher than the room is wide. Books are scattered across the floor, though none of them appear damaged. Rather, this library looks like it was hastily searched. Most of the books in this small library reference features, traits, and inhabitants of the Astral Plane. A handful of tomes reference an esoteric plane hidden within the Astral Plane known as the Akashic Record.
It's research time again :)

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It's research time again :)
Which skill check?
"I can stay with it, if nobody oppose", Merisiel told to Galandaro about the bow.

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So, I think it will be Knowledge (arcana) again, checks made by @Galandro with the aid of @Insidion.

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listed below are any relevant skills Galandaro has for the research sans any other bonuses...not quite sure which apply
Perception: 1d20 + 9 ⇒ (1) + 9 = 10
Planes: 1d20 + 9 ⇒ (3) + 9 = 12
Arcana: 1d20 + 11 ⇒ (19) + 11 = 30
Linguistics: 1d20 + 8 ⇒ (1) + 8 = 9

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listed below are any relevant skills Galandaro has for the research sans any other bonuses...not quite sure which apply
[dice=Perception]1d20+9
[dice=Planes]1d20+9
[dice=Arcana]1d20+11
[dice=Linguistics]1d20+8
@Galandro, as long as you have 5 ranks in Knowledge (Arcana), I suggest you to make around 5 checks of it, then roll 5d12, separately, only to move forward.

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[dice=knowledge arcana aid]1d20+8
And I suggest @Insidion to make 5 "aid another" checks for @Galandro. :)

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aid k:arcana: 1d20 + 8 ⇒ (2) + 8 = 10
aid k:arcana: 1d20 + 8 ⇒ (11) + 8 = 19
aid k:arcana: 1d20 + 8 ⇒ (18) + 8 = 26
aid k:arcana: 1d20 + 8 ⇒ (2) + 8 = 10
aid k:arcana: 1d20 + 8 ⇒ (8) + 8 = 16

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Arcana: 1d20 + 11 ⇒ (1) + 11 = 12
Arcana: 1d20 + 11 ⇒ (1) + 11 = 12
Arcana: 1d20 + 11 ⇒ (11) + 11 = 22
Arcana: 1d20 + 11 ⇒ (18) + 11 = 29
Arcana: 1d20 + 11 ⇒ (2) + 11 = 13
5d12 ⇒ (4, 1, 10, 11, 1) = 27
tis a tad confusing through PbP, thanks to Sir Peter for the explanation aid

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tis a tad confusing through PbP, thanks to Sir Peter for the explanation aid
I'm here to help, buddy. :)

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I need to roll some more rolls for Galandaro, complexity is 20, the rolled 12s and 13 are too low to find something useful (even with two Aas)
Arcana: 1d20 + 11 + 4 ⇒ (20) + 11 + 4 = 35
Arcana: 1d20 + 11 + 4 ⇒ (11) + 11 + 4 = 26
Arcana: 1d20 + 11 + 4 ⇒ (9) + 11 + 4 = 24
Arcana: 1d20 + 8 + 4 ⇒ (2) + 8 + 4 = 14
Arcana: 1d20 + 8 + 4 ⇒ (5) + 8 + 4 = 17
Arcana: 1d20 + 8 + 4 ⇒ (16) + 8 + 4 = 28
Days 1-3:
Someone here was researching the Dimension of Dreams. Pages have been torn from some books, only to be used as bookmarks in others. Notes on the torn pages reference literature contained in the Lower Planes Archive elsewhere in the sealed wing. According to the registry, one book on the Dimension of Dreams is missing: the Libram of Forgotten Dreams. This book purportedly contains dozens of rituals pertaining to that realm.
Day 4:
The researcher veered away from the Dimension of Dreams and toward seemingly random books on Abaddon, the Abyss, and Hell. She has underlined unrelated passages and circled chapter numbers.
the bonus you get for this is already calculated in the other rolls
Day 5-6:
The nameless researcher’s investigation eventually became haphazard and inexplicable, though with patience it becomes clear that she was attempting to decipher some sort of encoded message — some of which earlier patrons of this library left in the margins of books. The entire decoded message indicates the location of a hidden passage in area "Astral References" and the location of the trigger mechanism concealed inside one of the bookcases.

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Clair jumps up from the chair she had settled in. "Let's go!"
She marches straight for the "Astral References" and inspects the area surrounding the passage and trigger mechanism for traps.
Perception: 1d20 + 2 ⇒ (2) + 2 = 4
"It's all safe, I guess. Kind of. Probably. I think. Most likely."

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"I have a headache from all this research conducted. I have not done this much reading since passing my tests ages ago."

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"Finally!" Insidion says after more days of boring research.
"Let's see what's inside! We will finally REND THEM LIMB FROM LIMB!"
The dragon disciple casts mirror image before entering.
mirror image: 1d4 + 2 ⇒ (2) + 2 = 4

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"Let the traps with me, boys"
Merisiel tries to look for any hidden trap at the door...
Perception: 1d20 + 13 ⇒ (20) + 13 = 33 +3 if it has a trap, total of 36!
OMG! Well, if it has a trap...
Disable Device: 1d20 + 17 ⇒ (6) + 17 = 23
Once she makes sure that the path is safe, the rogue enters cautiously in the "Astral References" area.
"Follow me", she whispers to the others.
Stealth: 1d20 + 15 ⇒ (4) + 15 = 19