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@GM your numbering scheme makes me think you have the wrong target for Smiley. He attacked the one immediately adjacent (West) of him. When I specified "to his right" I was thinking of him having entered the room and facing South. Apologies for any confusion.

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Nali speeds into the room next to Jacques in a panic. She skids to a halt, and slips her hand into his quiver to grab on of his adamantine arrows, before turning to fire at the winch across the room, in hopes to damage that corner of the trap.
If you'll allow me to take a shot on this round, then...
Attack(PBS): 1d20 + 8 + 1 ⇒ (4) + 8 + 1 = 13for(PBS): 1d8 + 1 + 1 ⇒ (8) + 1 + 1 = 10

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"Crap...", Malik mumbles under his breath as he observes the scene with the chains, and throws himself against the pillar to touch whichever unconscious prisoner he can reach.
Kinetic Healer, accepting a point fo burn in the process: 2d6 + 8 ⇒ (2, 4) + 8 = 14
If I can't reach anyone, use that roll as damage for an attack instead, with a +1 from BPS.

Shifty |

I have added numbers etc to the map for ease of reference
Kolris spots the spot he needs to work on and disables the mechanism for the chains next to him. He is confident that between the disabling, and the jammed statue from an earlier error, this sector is now safe.
Nali grabs an arrow, but it doesn't hit the target.
Malik runs in and heals one of the wounded who was merrily slipping to Pharasmas embrace. He spots Zeffiro attached to the column and positively identifies him (on map)
Zhatara stays outside and the doors snap shut with force, she can now only hear the horrors in the prison.
The chains thrash around again!
1d4 ⇒ 3
But only attack two of the sectors.
Attacks Smiley
Attack 1d20 + 9 ⇒ (1) + 9 = 10 <--Miss
Prisoner 3
Damage 2d4 + 5 ⇒ (2, 1) + 5 = 8
Prisoner 4(Zefiro)
Damage 2d4 + 5 ⇒ (1, 2) + 5 = 8
R2
Jacques
Kolris
Malik
Nali
Smiley
Zhatara
CHAINS
Prisoners
1
2
3 19 [dying]1d20 ⇒ 7
4 20
Chains
1
2 -1
3 Disabled
4 Destroyed
5 Destroyed
6
7
8

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"I will be able to keep a few more from dying, but you guys better hurry with those chains!", the half-orc shouts, attempting to touch another unconscious prisoner and fix his chakras. He gets more pale with every prisoner he touches.
Kinetic Healer: 2d6 + 8 ⇒ (1, 3) + 8 = 12
Preferably the bleeding/dying fellow.

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Jacques shifts position and takes aim at 1 and 7.
Bow,Rapid,PBS: 1d20 + 8 - 2 + 1 ⇒ (20) + 8 - 2 + 1 = 27
Damage?,Adamantine,PBS: 1d8 + 2 + 1 ⇒ (7) + 2 + 1 = 10
Bow(7),Rapid: 1d20 + 8 - 2 ⇒ (16) + 8 - 2 = 22
Damage?,Adamantine: 1d8 + 2 ⇒ (3) + 2 = 5
I think objects are immune to crits. Shouldn't matter anyways

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Would acid or fire damage harm the statues?
Knowledge, engineering: 1d20 + 6 ⇒ (15) + 6 = 21

Shifty |

Being chains and metal parts, Kolris thinks Acid would be appropriate
Jacques brings down another, but only damages a pulley with his second arrow.
R2
Jacques - attacked
Kolris
Malik - healed
Nali
Smiley
Zhatara
CHAINS
Prisoners
1
2
3 7
4 20
Chains
1 Destroyed
2 -1
3 Disabled
4 Destroyed
5 Destroyed
6
7 -5
8

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Smiley tries again to smash the one near him (#2).
Battleaxe, Power Attack: 1d20 + 6 ⇒ (11) + 6 = 17 Damage, Power Attack, Two Handed: 1d8 + 6 ⇒ (2) + 6 = 8

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Kolris decides that they need to focus on Zefiro. If they couldn't save him, the mission... and all of its complications... would be for naught. He rushes towards that quadrant, retrieving a vial of acid from his pouch. He quickly pulls up next to Zefiro and throws it, hoping to burn away the chains from whatever mechanism inside the statue controls them.
"Hang in there, Zefiro, we're trying to get you out of here!"
Move: 30', drawing flask
Standard: attack statue 7
Ranged touch, acid flask, 2 range increments, inspiration: 1d20 + 4 - 4 + 1d6 ⇒ (8) + 4 - 4 + (5) = 13
Damage, acid: 1d6 ⇒ 4

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Nali snags another arrow from Jacques, grumbling, "Need these myself," Before firing again at the one that Smiley's slowly denting.
Attack(PBS): 1d20 + 8 + 1 ⇒ (10) + 8 + 1 = 19 For(PBS): 1d8 + 1 + 1 ⇒ (8) + 1 + 1 = 10

Shifty |

Smiley unloads into the mechanism again, forming another dent - but the metal is very hard and difficult to bend. Nali puts an adamantine arrow through it though, ending the problem.
Kolris lobs acid on another set of pulleys to great effect, they foul and snap almost immediately.
1d4 ⇒ 1
The chains lash again!
Attacking Kolris
Attack 1d20 + 9 ⇒ (11) + 9 = 20
Damage 2d4 + 5 ⇒ (2, 1) + 5 = 8
Lashing prisoner 3
Damage 2d4 + 5 ⇒ (1, 4) + 5 = 10
Lashing prisoner 4(Zefiro)
Damage 2d4 + 5 ⇒ (4, 1) + 5 = 10
The lashed prisoner and Zefiro lose consciousness and begin bleeding out...
Prisoners
1
2
3 -17
4 -30
Chains
1 Destroyed
2 Destroyed
3 Disabled
4 Destroyed
5 Destroyed
6
7 Destroyed
8
R3
Jacques
Kolris
Malik
Nali
Smiley
Zhatara
CHAINS

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"Nali, I don't have an angle on the pulley on your left. Grab an arrow and go for that one. I'll take the one on the right."
Jacques waits for Nali to gtab the arrow, then moves closer to the last pulley on his right (#8)
Bow, PBS: 1d20 + 8 + 1 ⇒ (17) + 8 + 1 = 26
Damage,Adamantine: 1d8 + 2 + 1 ⇒ (5) + 2 + 1 = 8

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Kolris retrieves his wand of cure light wounds from his belt, and frantically starts trying his best to activate it to help Zefiro.
Use Magic Device DC 20: 1d20 + 3 ⇒ (3) + 3 = 6
Unable to get it to work, Kolris yells to the others. "Somebody help me heal Zefiro!" He holds the wand out, ready for someone with proficiency to grab it.
Kolris moves a bit closer while he retrieves another flask of acid, throwing it when he's just close enough to target accurately.
Move: 10' west, drawing flask
Standard: attack statue #8
Ranged touch, acid flask: 1d20 + 4 ⇒ (18) + 4 = 22
Damage, acid: 1d6 ⇒ 6

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Just remembered that Kolris has a potion from the guards. In option 1 above, he will use the potion on Zefiro instead of the wand.

Shifty |

@Malik - As far as the prisoners go, they are both in a roughly equal state - one more hit and they'd certainly be dead
Jacques does a great job of destroying another pulley.
Kolris doesn't manage to trigger his wand...
R3
Jacques - attacked
Kolris - UMD attempt
Malik
Nali
Smiley
Zhatara
CHAINS
Chains
1 Destroyed
2 Destroyed
3 Disabled
4 Destroyed
5 Destroyed
6
7 Destroyed
8 Destroyed

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Fair enough. Hold my beer!
Malik touches the nearest unconscious prisoner to fix them up, and then runs to the other to protect them from the chains with his own body.
Kinetic Healer: 2d6 + 8 ⇒ (6, 3) + 8 = 17

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Smiley moves closer in and readies a potion for whoever needs it.

Shifty |

An alchemist can utilize spell-trigger items if the spell appears on his formulae list, but not spell-completion items (unless he uses Use Magic Device to do so) - as you have Cure Light Wounds, you can use the wand without CMD etc
Kolris's wand DOES go off...
Malik moves toward the last at-risk prisoner and heals the fellow!
1
2
3
4 -24
R3
Jacques - attacked
Kolris - UMD attempt
Malik - heal
Nali
Smiley - ready
Zhatara
CHAINS
Chains
1 Destroyed
2 Destroyed
3 Disabled
4 Destroyed
5 Destroyed
6
7 Destroyed
8 Destroyed

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Nali nods to Jacques, grabs one last arrow from his quiver, then skitters forward to fire at the last of the working winches.
Attack(PBS): 1d20 + 8 + 1 ⇒ (13) + 8 + 1 = 22For(PBS): 1d8 + 1 + 1 ⇒ (8) + 1 + 1 = 10

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Unfortunately, Kolris is an Investigator, not an Alchemist, and that is a crucial difference here.
Investigators and Spell Trigger: Investigators’ alchemy class feature is missing a sentence that appears in the alchemist allowing him to use spell trigger items. Does that mean the investigator can’t use spell trigger items?
Investigators cannot use spell trigger items. The omitted sentence was intentional.

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Nali gets her wand out and starts to heal Zefiro as the others work on freeing the 4 captives from their bonds.
CLW1: 1d8 + 1 ⇒ (6) + 1 = 7
CLW2: 1d8 + 1 ⇒ (6) + 1 = 7
CLW3: 1d8 + 1 ⇒ (8) + 1 = 9
CLW4: 1d8 + 1 ⇒ (2) + 1 = 3
"We have goal now. Time to run?" She asks as she returns the wand to her wrist sheath.

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"Bon soir, mes amies" Jacques says to the newly rescued prisoners.
"There is likely to be some attention given to us on the way out. We would be advised to think up some diversion or another way out.
Pechance, has any of you heard something from the guards that would aid us in escaping without further struggle?"

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"There was a plan. Unfortunately, there have been some complications."
Turning to the other team members.
"What of it then? Should we continue the guise as guards escaping the struggle? Simply bolt out the door and attempt to lose ourselves in the crowd?
We should at least find guard uniforms for these Bellflowers. It might be useful if we used some blood splattered uniforms. We could pretend that we were escorting them to get healing."

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Kolris considers their situation. "What if we disquise Zefiro and the Bellflowers as injured guards, using the bloody uniforms." He takes an extract from his pouch. "With this extract, I can make myself appear as one of the known guards... probably Galvar."
"We can use the injuries as a reason for needing to move quickly. As we leave, we can direct any incoming guards back into the prison to assist in capturing the troublemakers."

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"Maybe we could climb through the pipes in the toilet? I mean it has to lead to a sewer, right?", Malik joins in, apparently more pale than usual.

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"When you get down there is a bad time to kearn it is just a pit. Sewers are also notoriously hard to navigate. Without prior planning, I'd not like to try that route.
I think bluffing our way out the front door with Kolris' potion sounds ideal."

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Nali looks over at Malik. "Are you okay?" she asks as she gestures to the wand that she just returned to the sheath that she keeps it in.
"It is also a festival out there. Maybe lose trackers in crowd?" she adds to the escape plot as she leads their quarry toward the door.
Are any of the NPC's still wounded?

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"I've been exerting myself more than usual. Nothing a good sleep can't handle. But...", he pulls out his own wand - "... I still have a wound from the fight earlier. Would you mind?", he hands over the wand to Nali, indicating a smaller wound on his arm.
Feel free to use some of it on Zefiro and the Bellflowers if needed.

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Throwing on some uniforms and going out the front door?
That sounds like the plan. Kolris is going to make himself look like Galvar, we are going to dress the prisoners up like wounded soldiers, and we go out the front door.

Shifty |

The NPC's are healed
Everyone is dressed as a guard
Kolris looks like Galvar
Donning the outfits the party leaves the prison with the four Bellflowers. Outside, the street is mysteriously quiet, as though the obvious fighting in the prison that was followed up by bloodied guards screaming out into the street was a bit of a downer on the whole 'street festival' vibe. There are a few people on the street though - a group of figures are striding up the street in a very determined and deliberate manner. They are rather serious looking men with stern faces and Chelish tabards - it is the interrogators - including the feared (and legendary) Interrogator Vasenti. Behind them, a your Halfling contact mouths the word RUN and 'accidentally' cuts the tie rope to a tent which crashes down, momentarily distracting the trio.
In the distance you can hear more guards rallying each other to this location
***
CHASE
*You are now in a chase to the docks.
*Rather than resolve it phase by phase, I will aim to do it in 'chunks' of two turns.
*You will get the action options for each turn, and every party member can have a crack.
*The aim is to get as many collective successes as possible, not just one check.
*You can aid another though.
*You could always dice down and try going toe to toe... #whatcouldgowrongamIrite?
R1 - Parade
Parade: The runaways cross the path of a Loyalty Day parade, complete with floats, banners, and dancers. You can bring the parade to a halt with ranged attacks against AC 15 that deal at least 6 points of damage to the various decorations (multiple attackers can contribute to
this total), a successful DC 16 Acrobatics check to barge through the marching lines, or by casting any conjuration spell of 1st-level or higher to create an impediment.
R2 - Supply Delivery
Supply Delivery: You come across a wagon loaded with supplies for the celebrations. They can stall oncoming guards with a successful DC 16 Handle Animal or wild empathy check to panic the draft animals, a successful DC 16 Disable Device check to unhinge the wagon and send it rolling down the street, or successful DC 13 Strength check to throw the supplies everywhere.

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As they run by, Jacques quickly draws an arrow in order to help creating an opening for the group to run through.
Bow: 1d20 + 8 ⇒ (12) + 8 = 20
Damage: 1d8 + 2 ⇒ (6) + 2 = 8
He also does his his best to guide the party through the remaining revelers. Do we get to move faster by attempting both checks, like a normal chase?
Acrobatics: 1d20 + 4 ⇒ (10) + 4 = 14 Within assist range for anyone that doesn't want to attempt a check of their own.

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After passing the revelers and knocking down one of their banners to create confusion, Jacques sets to work attempting to create more diversions by causing a cart to spill in the street.
Disable Device: 1d20 + 7 ⇒ (9) + 7 = 16

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When their contact mouths for them to flee, Kolris waits no longer than it takes to glance back and make sure that everyone else is following. No heroes needed to be made here today; they just needed to get out of town. He begins running.
Round 1
And they run right into the path of a parade float. Kolris quickly begins dodging through and around the float and its horses, picking a way through the crowded parade that the others can hopefully follow.
Acrobatics DC 16: 1d20 + 7 ⇒ (10) + 7 = 17
Round 2
He then joins Jacques in attempting to unhinge a supply wagon to send it rolling back down the street behind them, causing chaos to slow the pursuit.
Disable Device DC 16: 1d20 + 10 ⇒ (12) + 10 = 22

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Not looking to fight in his current state and location, Malik dashes across the obstacles in the parade, jumping over carts and boxes, doing his best to avoid the people.
Acrobatics: 1d20 + 11 ⇒ (12) + 11 = 23
Once he sees the Pathfinders mess with the cart, he attempts to help it move, even in his weakened state.
Strength: 1d20 + 0 ⇒ (7) + 0 = 7

Shifty |

Kolris and Jacques come rolling through the parade with the speed and grace of the finest street performers - sliding between revellers and overhead an arrow pierces a stuffed effigy, showering sweets into the crowd who begin dashing about to collect them!
Meanwhile, supply wagons shift into the MOST inconvenient places...
R1 & 2
Jacques - Pass/Pass
Kolris - Pass/Pass
Malik
Nali
Smiley
Zhatara

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Smiley remembers the time all seven brothers chased him through a crowded marketplace, trying to sell him into slavery (for a day -- they're not monsters), but he tried to escape by jumping and rolling through the various crates and displays.
Acrobatics DC16: 1d20 + 6 ⇒ (7) + 6 = 13
Much like that day, however, he is not as nimble as he had hoped. At least the previous time he got a lot of sips of beer (and a keg to take home) from the brewer he was "enslaved" to for a day. He's pretty sure this crowd won't be so kindly if they catch him.
Taking advantage of the out-of-control cart, Smiley tries to knock a table of apples over as he passes.
Strength DC13: 1d20 + 3 ⇒ (11) + 3 = 14
Lucky I passed by that cart of apples! Har!