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Seeing the halfling unsteady on her feet, Orenjii moves toward her and closes some of the arrow wounds.
Cure Moderate Wounds: 2d8 + 4 ⇒ (6, 8) + 4 = 18
"I have been informed that it is not yet your time to depart this world."

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Oooh ow ... Thanks, I don't really like being turned into a pin cushion
She goes into 'hide and go sneak mode'
stealth: 1d20 + 21 ⇒ (3) + 21 = 24
draws her crossbow and moves carefully along the wall

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"Fall back, heals up, take cover!" Arxoias goes after the yellow goblin. Move action move, ready action to shoot if enemy shows up
Musket vs Touch: 1d20 + 9 + 1 ⇒ (7) + 9 + 1 = 17Deadly Aim: 1d12 + 10 + 1 ⇒ (12) + 10 + 1 = 23

GM Mike...R |

Rani creeps along the wall, glancing around the corner she spot one of the goblins. The cave wall between her and the goblin provides enough cover to hopefully avoid notice, although there are no obvious options for hiding if the goblins decide to come back around the corner.
Arxoias follows the goblin which attacked Orenjii. Heading to the southern exit from the cave with the glowing crystals she finds herself in a short section of tunnel. To the south she can see what appears to be another cave, this one full of dull brown mushrooms. To the west is a tunnel which slopes gently downwards. There is no sign of the goblin.
ROUND 1/2:
Arxoias
Goblin (yellow)
Goblin (orange)
Goblin (red)
Rani -24
Orenjii -13
Renart
(Bold may act)

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Renart will slip into a state of peak athleticism (controlled rage) and advance on the (red) goblin, hurling a javelin at them, before closing with them.
Javelin: 1d20 + 12 ⇒ (20) + 12 = 321d6 + 2 ⇒ (6) + 2 = 8
confirm: 1d20 + 12 ⇒ (5) + 12 = 171d6 + 2 ⇒ (6) + 2 = 8
Mr. Badger will follow, cornering the goblin.

GM Mike...R |

Renart will slip into a state of peak athleticism (controlled rage) and advance on the (red) goblin, hurling a javelin at them, before closing with them.
[dice=Javelin]1d20 + 12; 1d6 + 2
[dice=confirm]1d20 + 12; 1d6 + 2Mr. Badger will follow, cornering the goblin.
Just to double check, what are Renart and Mr. Badger's movement speeds? It looks like Renart moved 45 feet as a move action and Mr. Badger double moved 55 feet, so wanted to check that was correct.

GM Mike...R |

To keep things moving along, I'll move on to the next round.
The second of the two goblins who had retreated around the corner after attacking Rani (orange) spots Renart looking to engage his ally and moves behind the kitsune while drawing his dogslicer. His companion (red) follows suit, drawing his own dogslicer, and then both goblins attack...
Goblin (orange) attack vs Renart + flank: 1d20 + 8 + 2 ⇒ (16) + 8 + 2 = 26
Goblin (red) attack vs Renart + flank: 1d20 + 8 + 2 ⇒ (18) + 8 + 2 = 28
Goblin (orange) Damage vs Renart (including 3d6 sneak damage): 1d4 + 3d6 ⇒ (3) + (1, 3, 5) = 12
Goblin (red) Damage vs Renart (including 3d6 sneak damage): 1d4 + 3d6 ⇒ (1) + (6, 6, 1) = 14
The yellow goblin is also probably up to something, but it's not clear to anyone exactly where she has gone.
ROUND 2/3:
Arxoias
Goblin (yellow)
Goblin (orange)
Goblin (red) -8
Rani -24
Orenjii -13
Renart -26
(Bold may act)

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Arxoias moves to the other side of the cave entrace and sees the yellow goblin. She opens fire.
Musket vs touch: 1d20 + 9 + 1 ⇒ (16) + 9 + 1 = 26Deadly Aim PBS: 1d12 + 10 + 1 ⇒ (6) + 10 + 1 = 17

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Oh, that make sense. Sometimes I do miss GM layer...
Noted that Arxoias has direct line of sight to the northern part of that room around "yellow goblin placeholder", so unless the goblin has special ability that let him steath without concealment and cover, it can't use stealth in that part of the room.
Perception: 1d20 + 11 ⇒ (12) + 11 = 23

GM Mike...R |

Arxoias looks into the cave to the west, but doesn't quite spot the goblin, who had hidden herself behind a pile of fallen rocks. Spotting the changeling peering into the cave the goblin takes a shot at Aroxias with her bow and then steps backwards...
Goblin (yellow) attack vs Arxoias: 1d20 + 9 ⇒ (1) + 9 = 10
Sadly for the goblin, in her excitement at catching Arxoias unaware, her attack goes wide. The shot from Aroxias in return is much more accurate, badly wounding the goblin.
As the goblin would have shot at Arxoias when she reached the entrance to the cave to the west, I'm happy for Aroxias to move somewhere else after reaching that point as she would now know where the goblin is.
Rani's shot at the other goblin from her hiding spot also finds its mark, although due to the gobin's uncanny ability to dodge out of the way, she isn't able to do the normal amount of damage she would expect when attacking from stealth (i.e. the goblin has uncanny dodge, so sadly takes no sneak attack despite attacking from hiding).
ROUND 2/3:
Goblin (yellow) -17
Arxoias
Goblin (orange) -1
Goblin (red) -8
Rani -24
Orenjii -13
Renart -26
(Bold may act)

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Renart will tumble through yellow and ready to wrestle them, while Mr. Badger steps to flank them, rages, and will attempt to savage them.
Acrobatics: 1d20 + 13 ⇒ (14) + 13 = 27
Grapple: 1d20 + 14 + 4 ⇒ (6) + 14 + 4 = 24
Bite: 1d20 + 9 + 2 ⇒ (2) + 9 + 2 = 131d6 + 5 ⇒ (5) + 5 = 10
Claw: 1d20 + 9 + 2 ⇒ (9) + 9 + 2 = 201d6 + 5 ⇒ (2) + 5 = 7
Claw: 1d20 + 9 + 2 ⇒ (8) + 9 + 2 = 191d6 + 5 ⇒ (4) + 5 = 9

GM Mike...R |

Based on the description I assume Renart's attack is on orange rather than yellow (yellow is in the other cave) and that Mr. Badger would need to step between the two goblins in order to provide the flank and attack?
Renart manages to slip out from between the two goblins despite the less than ideal conditions (+5 to the DC due to the water on the floor and +2 due to needing to avoid the other goblin). He then gets behind one of them, successfully grabbing hold of the goblin while Mr. Badger lands two claw strikes against the poor creature.
ROUND 2/3:
Goblin (yellow) -17
Arxoias
Goblin (orange) -17 (grappled)
Goblin (red) -8
Rani -24
Orenjii -13
Renart -26 (grappled)
(Bold may act)

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The android strides toward the fight, staring at the orange-clad goblin and making it more difficult for it to escape.
evil eye: -2 to skill checks for 7 rounds, reduced to 1 round on a DC 16 Will save.

GM Mike...R |

Goblin (orange) will save vs Evil Eye: 1d20 + 2 ⇒ (10) + 2 = 12
The goblin being grappled by Renart attempts to extricate himself from his current predicament, although this endeavor is hindered by his inability to resist the malign power of Orenjii's hex...
Goblin (orange) escape artist vs grapple (inc Evil Eye): 1d20 + 13 - 2 ⇒ (13) + 13 - 2 = 24 @Renart: Would be be correct in thinking that Renart put the controlled rage bonus into strength so his CMD is currently 25?
Meanwhile his companion (red) strikes at Mr. Badger before dropping his bow and drawing a second dogslicer...
Goblin (red) attack vs Mr. Badger + flank: 1d20 + 10 + 2 ⇒ (10) + 10 + 2 = 22 @Renart: What is Mr. Badger's current AC, would 22 hit?
Goblin (red) Damage vs Mr. Badger (including 3d6 sneak damage): 1d4 + 3d6 ⇒ (3) + (6, 2, 6) = 17
ROUND 3:
Goblin (yellow) -17
Arxoias
Goblin (orange) -17 (grappled?, evil eye (skills, 7 rnds))
Goblin (red) -8
Rani -24
Orenjii -13
Renart -26 (grappled?)
(Bold may act)

MVulpius |

Renart's CMD is 25 (27 vs grapple) right now (though he has agile maneuvers so it is due to adding dex from rage not str).
Mr. Badger's AC is only 17 so that will hit, though the goblin would not be flanking since you don't threaten while in a grapple unless you are a 9th level strangler brawler or some other exception to the rule.

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Renart will maintain the grapple and strangle the life out of the grappled goblin.
"Why you little..."
Grapple: 1d20 + 14 + 5 ⇒ (11) + 14 + 5 = 30
Strangle: 1d6 + 2 + 2d6 ⇒ (5) + 2 + (2, 1) = 10
Mr. Badger will continue savaging the orange goblin, switching to red if they drop.
bite: 1d20 + 9 ⇒ (11) + 9 = 201d6 + 5 ⇒ (2) + 5 = 7
claw: 1d20 + 9 ⇒ (4) + 9 = 131d6 + 5 ⇒ (5) + 5 = 10
claw: 1d20 + 9 ⇒ (6) + 9 = 151d6 + 5 ⇒ (3) + 5 = 8

GM Mike...R |

Rani's thrust against the grappled goblin finds its mark, yielding a plaintive yelp from the embattled creature. His circumstances are worsened further as Renart begins to strangle him and them Mr. Badger finally renders him unconscious with a vicious bite.
Regarding flanking while grappled, my understanding is that you lose the ability to take attacks of opportunity while grappled, but still threaten for other purposes, as you can still make attacks while grappled. Having done a bit of a search, just to double check my understanding, that does look to be the common view (e.g. see the discussion in this thread).
ROUND 3:
Goblin (yellow) -17
Arxoias
Goblin (orange) -40 (unconscious, dying, grappled, evil eye (skills, 7 rnds))
Goblin (red) -8
Rani -24
Orenjii -13
Renart -26 (grappled)
Mr. Badger -17
(Bold may act)

MVulpius |

That would be weird since my archetype implies that you need an exception from that to threaten an area while grappled.
Practiced Strangler (Ex): At 2nd level, when a strangler has the grappled condition, she does not take a –4 penalty to Dexterity and does not lose her Dexterity bonus to AC. At 9th level, a grappling or grappled strangler still threatens an area and is still able to make attacks of opportunity while grappling or grappled; when pinned, she is not denied her Dexterity bonus and does not take a –4 penalty to Armor Class. This ability replaces AC bonus.
If this were true there would be no point in adding that. But then again inconsistent rules are a hallmark of PF1e.
Anyways, if we are ruling it that way, Mr. Badgers last attacks would be 2 higher from flanking.

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Just throwing my 2 cents, the only exception I know about threaten without the ability of making AoO is Total Defense, as specified in Melee Tactics Toolbox p.8 Discussion Link. And as always, specific trump general.

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Orenjii glares at the red goblin, making it harder for it to hit the Pathfinders.
evil eye: -2 to attack rolls for 7 rounds, reduced to 1 round on a DC 16 Will save.

GM Mike...R |

Anyways, if we are ruling it that way, Mr. Badgers last attacks would be 2 higher from flanking.
With the extra bonus from flank the second claw from Mr. Badger almost hit, but still wasn't quite enough (and I guess would have been against red anyway with orange having gone down).
Goblin (red) will save vs Evil Eye: 1d20 + 1 ⇒ (20) + 1 = 21
Orenjii assails the mind of the cornered goblin with her evil eye, however it would seem this goblin is made of sterner stuff that his fallen colleague and manages to fend of the worst of the hex's power.
The goblin being chased by Arxoias runs into the western cave to assist her remaining ally, drawing her dogslicer and attempting to stab Rani...
Goblin (yellow) attack vs Rani: 1d20 + 10 ⇒ (5) + 10 = 15
...but misses.
ROUND 3:
Goblin (yellow) -17
Arxoias
Goblin (orange) -40 (unconscious, dying, grappled, evil eye (skills, 7 rnds))
Goblin (red) -8 (evil eye (attacks 1 rnd))
Rani -24
Orenjii -13
Renart -26 (grappled)
Mr. Badger -17
(Bold may act)

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"You got until the end of your life to run away from me and my bullet." Arxoias moves up and shoots at yellow.
PBS vs touch: 1d20 + 9 + 1 ⇒ (5) + 9 + 1 = 15 Deadly Aim: 1d12 + 10 + 1 ⇒ (12) + 10 + 1 = 23

GM Mike...R |

The goblin manages to duck out of the way of Arxoias' shot. Meanwhile her companion stabs twice at Mr. Badger...
Goblin (red) attack vs Mr. Badger (inc Evil Eye): 1d20 + 8 - 2 ⇒ (11) + 8 - 2 = 17
Goblin (red) attack vs Mr. Badger (inc Evil Eye): 1d20 + 8 - 2 ⇒ (17) + 8 - 2 = 23
Goblin (red) Damage vs Mr. Badger: 1d4 ⇒ 3
Goblin (red) Damage vs Mr. Badger: 1d4 ⇒ 1
...landing both strikes and then stepping forward out of the corner.
ROUND 4:
Goblin (yellow) -17
Arxoias
Goblin (red) -8 (evil eye (attacks 1 rnd))
Rani -24
Orenjii -13
Renart -26
Mr. Badger -21
(Bold may act)

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Orenjii's action depends on whether Rani's crit completely murders Yellow.
+1 Returning Harrow Card: 1d20 + 7 ⇒ (18) + 7 = 25 +1 within 30 ft.
Piercing Damage: 1d4 + 2 ⇒ (1) + 2 = 3 +1 within 30 ft.
Card Drawn: 1d3 + 1d3 + 1d6 ⇒ (1) + (3) + (2) = 6
{LAW/NEU/CHA},{GOOD/NEU/EVIL},{STR/DEX/CON/INT/WIS/CHA}
"The Avalanche. We shall roll over you and your companions with the full force of the Pathfinder Society."
evil eye: -2 to attack rolls for 7 rounds, reduced to 1 round on a DC 16 Will save.

GM Mike...R |

Rani crit damage: 1d4 + 5 ⇒ (3) + 5 = 8
Goblin (yellow) will save vs Evil Eye: 1d20 + 1 ⇒ (18) + 1 = 19
Rani's well placed strike hits the goblin especially hard, however she still has enough wits about her to shake off the worst effects of Orenjii's evil eye.
ROUND 4:
Goblin (yellow) -31 (evil eye (attacks 1 rnd))
Arxoias
Goblin (red) -8
Rani -24
Orenjii -13
Renart -26 (grappled)
Mr. Badger -21
(Bold may act)

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Mr. Badger will drop out of rage and step into flank with Rani, attacking the red goblin.
bite: 1d20 + 6 + 2 ⇒ (8) + 6 + 2 = 161d6 + 2 ⇒ (2) + 2 = 4
claw: 1d20 + 6 + 2 ⇒ (12) + 6 + 2 = 201d6 + 2 ⇒ (5) + 2 = 7
claw: 1d20 + 6 + 2 ⇒ (1) + 6 + 2 = 91d6 + 2 ⇒ (3) + 2 = 5
Renart will drop the limp goblin, draw a hurlbat, throw it at the yellow goblin before stepping towards it.
Hurlbat: 1d20 + 12 ⇒ (3) + 12 = 151d6 + 2 ⇒ (3) + 2 = 5

GM Mike...R |

Mr. Badger manages to strike the goblin with his claw, however the hurlbat thrown at the other goblin goes wide.
The goblin which had just arrived from the eastern cave (yellow) clearly decides she has had enough and withdraws from the fight, back the way she came.
ROUND 5:
Goblin (yellow) -31 (evil eye (attacks 1 rnd))
Arxoias
Goblin (red) -15
Rani -24
Orenjii -13
Renart -26
Mr. Badger -21
(Bold may act)

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The gunslinger which had previously arrived at the eastern cave clearly decides she has had enough and shoots at yellow goblin twice.
Musket vs Touch, PBS: 1d20 + 7 + 1 ⇒ (18) + 7 + 1 = 26 Deadly Aim: 1d12 + 10 + 1 ⇒ (1) + 10 + 1 = 12
Rapid Shot vs Touch, PBS: 1d20 + 7 + 1 ⇒ (15) + 7 + 1 = 23 Deadly Aim: 1d12 + 10 + 1 ⇒ (7) + 10 + 1 = 18
"There is no outrunning my bullets, goblin scum."

GM Mike...R |

Goblin (red) attack vs Rani: 1d20 + 8 ⇒ (9) + 8 = 17
Goblin (red) attack vs Rani: 1d20 + 8 ⇒ (6) + 8 = 14
...missing both times, before backing towards the cave wall.
ROUND 5/6:
Arxoias
Goblin (red) -15
Rani -24
Orenjii -13
Renart -26
Mr. Badger -21
(Bold may act)

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Rani, looking a bit annoyed that there are no flanking opportunities, steps and stabs Red.
rapier: 1d20 + 10 ⇒ (20) + 10 = 30 piercing: 1d4 + 5 ⇒ (3) + 5 = 8
crit confirm: 1d20 + 10 ⇒ (14) + 10 = 24 piercing: 1d4 + 5 ⇒ (3) + 5 = 8
Maybe that'll make her feel better.

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This one does not seem susceptible to the android's hexes, so Orenjii tosses another card.
+1 Returning Harrow Card: 1d20 + 7 ⇒ (18) + 7 = 25 +1 within 30 ft.
Piercing Damage: 1d4 + 2 ⇒ (1) + 2 = 3 +1 within 30 ft.
Card Drawn: 1d3 + 1d3 + 1d6 ⇒ (1) + (3) + (2) = 6
{LAW/NEU/CHA},{GOOD/NEU/EVIL},{STR/DEX/CON/INT/WIS/CHA}
"The Avalanche. We shall roll over you and your companions with the full force of the Pathfinder Society."
That card really wanted to be drawn, as it was the same one for the conditional action I didn't use last turn.

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A tired Mr. Badger will try his best to finish off the last goblin so he can take a short nap.
bite: 1d20 + 6 ⇒ (16) + 6 = 221d6 + 2 ⇒ (2) + 2 = 4
claw: 1d20 + 6 ⇒ (5) + 6 = 111d6 + 2 ⇒ (1) + 2 = 3
claw: 1d20 + 6 ⇒ (15) + 6 = 211d6 + 2 ⇒ (6) + 2 = 8

GM Mike...R |

Mr. Badger finishes off the remaining goblin with a bite and then a claw.
Searching the bodies of the goblins the party find a number of useful looking items: 12 alchemist's fire, 6 smokesticks, 6 thunderstones, 3 masterwork studded leather armour (small), 6 masterwork dogslicers (small), 3 shortbows (small), 56 arrows (small), 8 tindertwigs, 192 gp,
A broader search of the area indicates that the goblins seem to have set up home in the group of caves on this side of the bridge. In addition to the cave with the dripping ceiling, the party find two additional caves. The first is the cave to the northeast, from where one of the goblins attacked Orenjii. This cave contains two clumps of crystals which light the room with inner radiance, flickering like greenish torches. The second is the cave to the southeast, dull brown mushrooms grow from the floor in many places throughout this cave, but they have completely covered the southern wall, obscuring the stone. Scattered remnants of tiny cages, complete with miniature iron bars now rusted and crumbling, are piled to the west.
The cave with the glowing crystals appears to have been the goblins main base of operations and contains a number of goblin sized sleeping areas, along with a small number of knick-knacks that the goblins had collected. Most of these items are worthless, but one set of goggles does detect as magic.
Examining the crystals more carefully the party also spot something rather unsettling, as both clumps seem to contain the skeletal remains of a goblin around which the crystals appear to have grown.
Looking into the cave with the mushrooms several members of the party spot that many of the mushrooms on the southern wall have stalks that look to have grown in the shape of tiny faces, mouths open in a scream of agony.

GM Mike...R |

The party have now explored the whole area beyond the bridge. As we are rapidly approaching the mid point of the timeslot for this game, I'll also reveal the area just to the west of the bridge to help keep things on track timewise.
Heading back across the bridge to the cave on the far side, the party enter remaining tunnel which they had not yet explored. It slopes downward towards a pond of luminescent liquid that fills the area below, fed by a stream to the northeast that slowly tumbles down a set of falls before emptying into the pool. Mucilaginous and thick, the substance roils about slowly, squelching as it moves.
Having explored all of the western caves, where do the party what to go next? There are currently two unexplored exits: The one accessed by heading east along the northern bank of the stream, and the other heading east from the first cave the party entered.
In terms of healing, feel free to take averages on rolls for healing outside of combat if you want to do that.

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Take 10 on Perception to tell that there're CMW potions and jump potions
Arxoias will reload her gun with another cold iron bullet. She will recommend the team to backtrack to the last place where a path is branched off (the northern path from west side of the bridge) and continue from there.