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Oraeth sets to work trying to map out where the Endless Threnody might have gotten to, but eventually taps the comms. "No dice. I can't come up with anything that makes much sense. Having a hard time working out what the dead might want to do in this kind of situation. Technically they could have set a course for home without the drift drive. I mean, they'll get there eventually even if it takes 350 years."
Computers to find Endless Threnody: 1d20 + 7 + 2 ⇒ (1) + 7 + 2 = 10
Well I guess this adventure is over :P
Rik, you want to give that a go?
EDIT: I forgot to add the ship's +2 at first. Maybe hitting DC10 makes a difference.

GM Garrett |

Endless Threnody Sensors: 1d20 + 7 ⇒ (7) + 7 = 14
Distance: 3d6 + 5 ⇒ (2, 6, 5) + 5 = 18
So, after fiddling around with the sensors for a while you're unable to find any trace of your quarry. Then, just as you're considering opening up the sensor array and doing some antagonistic calibration yourself you hear a ping from behind you. As you turn to look at the screen you see it, 18 hexes away and pointing right into your rear arc.
The Eoxian freighter is a massive vessel made of bone and steel. The front of the ship is a single enormous red lens, appearing as a sullen, bloody eye. The ship bristles with bone protrusions, as though it were some horned, skeletal beast. Some of the bones are charred and broken, indicating past battle damage. Laser cannons protrude from the front and sides of the freighter; but its rear weapon mounts are a twisted wreck. Gaps between the bones show the ship’s interior, but this is not from battle damage—this ship was never intended to accommodate living creatures.
Here's the space map. You're the blue arrow and the Threnody is the red one.
Here's your ship stats:
LORESEEKER TIER 2
Starfinder Society Pegasus (Starfinder Society Roleplaying Guild Guide)
Medium explorer
Speed 10; Maneuverability good (turn 1); Drift 1
AC 13; TL 13
HP 55; DT —; CT 11
Shields Basic 40; forward 10, port 10, starboard 10, aft 10
Attack (Forward) light laser cannon (2d4)
Attack (Port) light laser cannon (2d4)
Attack (Starboard) light laser cannon (2d4)
Attack (Turret) coilgun (4d4)
Power Core Pulse Green (150 PCU); Drift Engine Signal Basic; Systems basic medium-range sensors, crew quarters (good), mk 1 duonode computer, mk 2 armor, mk 2 defenses; Expansion Bays cargo hold, escape pods, science lab, tech workshop
Modifiers +2 Computers, +1 Piloting; Complement 4–7
Interesting things to note include the bonuses to Computers and Piloting checks, you'll want to remember those. Also, note that you'll add your pilot's ranks in Piloting to your AC and TL, so it's a bit better than what you see there in the stat block.
This puts us into the Engineering and Helm phases. For engineering the engineer can give a system a boost (since there's no damage). Once we're past that the pilot will have to give me an initiative check to see who has to move first. The Science Officer will also get a chance to take an action during the Helm phase.
In my limited experience with SFS PBPs I find space combat drags a little bit. The important thing for keeping it moving appears to be getting the initiative and the actual movement to happen, most things that happen before that and after that can be resolved largely out of order, it's just the actual movement that requires multiple people to interact synchronously. If you think you're likely to be out of contact when your turn actually comes up, feel free to put in your move early and we'll work it in when it comes up, you can always change it if something super unexpected happens.

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Mobius' adrenaline pumps into high gear upon seeing the Eoxian starship. "Alright crew, let's get this dead thing even deader. Get it M.I.C.H.? Because they're dead and -- oh never mind! You never really liked my jokes. Just give me the uploaded data when I read Starships 101. I need to remember anything to keep this baby flying in top shape." Activating Memory Module He cracks his knuckles and turns to I'm assuming the captain is Kadlos. "Awaiting your orders captain."

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GM: On another table, I saw that there's some Errata for our ship's stats - click here to see Thurston Hillman's post about it, if you like. It's pretty minor: AC and TL are both 12 instead of 13, and the ship's duonode computer grants two floating +1 bonuses each round that any two crew members can claim on their turn.
Kadlos punches comms to call back to the engineering bay, "Engineer, get us more power to the engines - we've got to get closer for our turret to have maximum effectiveness, and we're a long way off right now." (Recommending the Divert (Engines) action if you feel comfortable attempting it.)
He turns to Mobius at the helm and says, "Pilot, we're about to be under fire. Fly as fancy as you can to make us less of a target, then get us into their rear arc as quickly as you can - let's take advantage of their damaged cannons." (Recommending the Evade stunt if you feel comfortable attempting it.)
Turning to Oraeth, he says, "Science Officer, I need to know exactly what we're dealing with here. Get me as much intel on them as you can, and get ready to rebalance the shields if they get a good hit on one of our arcs." (Recommending the Scan action if you feel comfortable attempting it.)
Calling over to the gunnery station, Kadlos tries to help inspire Tamerriv's confidence in his firing ability. "Gunner, our turret has excellent range for firing on our enemy, and I'm sure you can hit them! You're cleared to as soon as Mobius gets you into position!" Encourage (Gunnery) vs. DC 17: 1d20 + 10 ⇒ (12) + 10 = 22 = Tamerriv gets a +2 bonus on his Gunnery check! With the +2 from computers should make you a +6 to hit, though we have a 10 hex range increment on that turret. Don't worry about firing multiple cannons for now, since it'd give you a -4 to each hit - unless you're feeling really lucky!

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Rik is in the engineering bay, waiting. Nothing seems to happen, so he starts peeling and eating some seeds. "I guess that's my job, sitting here bored with no one to talk and..."
Suddenly, a call from the bridge makes him stumble.
"Engineer, get us more power to the engines - we've got to get closer for our turret to have maximum effectiveness, and we're a long way off right now."
"Damn, that took me by surprise, lol."
He gets to the panels and quickly tries to redirect the flux of power from one zone to another.
"Sure, Cap'n, I'm on it!"
Divert (Engines) DC 10 + TIERx2 (12) 1d20 + 9 ⇒ (15) + 9 = 24
"It is done!"

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"Alright captain. Let's see what their pilot can do." He tries to size up the Eoxian starship as he navigates the Loreseeker to a favorable position.
Piloting Initiative: 1d20 + 10 + 1 ⇒ (9) + 10 + 1 = 20

GM Garrett |

Ok, you bring the sensors to bear and are able to determine the following bits of information: the Endless Thenody is a Large freighter with no life signs at all, speed of 6 and average maneuverability (turn 2). It also has an AC and TL of 11, 100 hull points remaining and no shields at all.
The Threnody gets a Initiative Check: 1d20 + 8 ⇒ (11) + 8 = 19
That means they have to move first, and I've already moved them forward 6 hexes.
You can now finish the Helm phase and once we know where your ship ends up we can take care of the Gunnery phase (since all Gunnery actions happen simultaneously the gunners can act whenever they like).
Don't forget to apply those floating +1 bonuses to something!

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Tamerriv straps into the turret and familiarizes herself with the controls.
Her spirits are buoyed by the Captain's words as she takes aim and fires.
Coilguns have a range of 20 hexes, so I believe no penalty applies.
Not sure if both duonode bonuses have been used yet. Using one if it's available. Can people please make it clear when you're claiming one?
Coilgun, Targeting Computer, Encouraged, duonode bonus: 1d20 + 2 + 2 + 2 + 1 ⇒ (3) + 2 + 2 + 2 + 1 = 10 Damage: 4d4 ⇒ (2, 1, 4, 1) = 8
I don't like the look of those guns. If you can get behind it we'll be much safer.

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Looks like Tammirev's the only one that's taken one so far - we have one remaining that Mobius could use on his piloting check to evade enemy fire.
"Pilot, pull in some extra computing power to keep us clear of their fire - let's press our advantage!"

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"You got it captain. Hey Rik! Good job on diverting power to our engines. Now let's try to get behind that ship."
Stunt, Evade: 1d20 + 11 + 1 ⇒ (6) + 11 + 1 = 18 AC and TL +2
He tries his best to maneuver the Loreseeker and give the enemies a hard time hitting them.
Also using our floating +1

GM Garrett |

"You got it captain. Hey Rik! Good job on diverting power to our engines. Now let's try to get behind that ship."
FYI, I think you need to make some more turns to do that, but you can get approximately there. Note that each turn can only be one facing, it looks like you did two facings at the second turn there... I'll take care of their return fire and the results of your attack later tonight.

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it looks like you did two facings at the second turn there
Oops..you're right. Must have slipped my mind while drawing the arrows and adjusting the token. LOL. I did the adjustments already. Thanks for noticing that GM.

GM Garrett |

Sadly, Tamerriv misses her shot with your turret. Fortunately, the Endless Threnody lines up it's main gun...
Main Gun vs AC 15: 1d20 + 8 ⇒ (5) + 8 = 13
And it misses.
Next we're back to the Engineering and Helm phases. Feel free to submit actions out of order (up to the initiative at the beginning of the Helm phase anyway) as needed and I'll resolve them all together once they're in.

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Gone through half of his seeds, Rik awaits patiently, energy diverted to the engines, until he receives order of changing it to a different system.

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Kadlos keys the comms again, "Engineering, divert power to the weapons - if we can get a lock on them, it'll help us take them down that much faster." (Divert: Weapons)
"Science Officer, that's good information to know about them. Help our weapons target their gunnery system - let's see if we can keep them from being as much of a threat to us." (Target System: Gunnery)
"Good maneuvering, Pilot. Bring us alongside or behind them, continuing with evasive maneuvers if you can - and keep us out of the arc of that forward cannon! I'm going to assist with the light lasers." (Stunt: Evade)
"Gunnery, stay focused on attacking with that turret. When Mobius brings us alongside the enemy, I'll attack with one of our light lasers. We'll both pull in the duonode to help our attacks!"
When the time is right, Kadlos pulls up the gunnery interface on his display, attempts to target the enemy, and fires one of the Loreseeker's light laser cannons.
(Kadlos fires as long as they don't end up behind us - if they do, he'll attempt to encourage Gunnery again.)
Light Laser Cannon ATK vs. Endless Threnody: 1d20 + 3 + 1 ⇒ (12) + 3 + 1 = 16
Light Laser Cannon DAM vs. Endless Threnody: 2d4 ⇒ (4, 2) = 6

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Roger, Cap'n. Copy that.
Tamerriv lines up her sights and fires. Using one duonode bonus.
Coilgun, Targeting Computer, duonode bonus: 1d20 + 2 + 2 + 1 ⇒ (15) + 2 + 2 + 1 = 20 Damage: 4d4 ⇒ (1, 1, 1, 1) = 4
That's more like it, but that damage roll? Come on, dicebot!

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Umm, you have to redo the check each round, the diverting power action only lasts until the next round.
Ah, uh, sorry lol
"Damn! Weapons, that's it! On my wayyy!"
Rik drops most of the seeds left while trying to do as told, cursing and sweating frenetically.
Divert (Weapons) DC 10 + TIERx2 (12) 1d20 + 9 ⇒ (20) + 9 = 29
Edit: Can this crit be used for something extra? Idk, extra power to weapons, or diverting to an extra device? Just asking.

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Oraeth steadily works to focus the targeting system on the weapons array of the other ship, but the steady growl of cursing in languages from across the Pact worlds makes it pretty clear that he hasn't had much luck with that so far.
Computers: 1d20 + 7 + 2 ⇒ (3) + 7 + 2 = 12

GM Garrett |

Ok, so the Endless Threnody's pilot makes her initiative check:
Initiative from the Bad Guys: 1d20 + 8 ⇒ (16) + 8 = 24
And beats you, so Mobius will have to move first. Once he does that I'll handle the Threnody's movement and resolve all the shooting at stuff.

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Mobius brings the Loreseeker near the rear arc of the Eoxian ship."Ok. I was able to bring us close to their rear arc but be wary. Looks like they're up to something. This is too easy, we can't be too complacent." He gives instruction to his exocortex. "M.I.C.H., download evasive flight plan now! I really have a bad feeling about this."
Stunt, Evade: 1d20 + 11 + 1 ⇒ (13) + 11 + 1 = 25
Also using the +1 bonus. And Rik, sadly there are no special bonuses from nat 20s on engineering actions.

GM Garrett |

The Endless Threnody manages to make some lumbering turns, getting out of your front arc but remaining accessible from one side. It then unloads on you with a light laser canon: Light Laser Canon: 1d20 + 7 ⇒ (2) + 7 = 9 which goes wide. Your shots both hit, dealing a total of 14 points of damage due to the power diverted to the weapons.
Ok, back to the Engineering and Helm phases!

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Piloting Initiative: 1d20 + 11 ⇒ (14) + 11 = 25
"Nice shooting crew. So far, so good. I'll do my best to keep us out of that nasty looking cannon up front."
Mobius does his best as he tries to evade incoming fire from the Endless Threnody
Will roll for stunt now and resolve movement after the results of the initiative.
Stunt, Evade: 1d20 + 11 ⇒ (10) + 11 = 21

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Oraeth continues trying to lock on to the skeletal freighter. The frustration rolling off of him is palpable at this point.
Computers (Targeting Weapon Systems): 1d20 + 7 + 2 ⇒ (4) + 7 + 2 = 13
Damn paizo boards! Why you hate this character so much?

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Kadlos looks up from his display for a moment to nod at Mobius. "Good plan, Pilot. I don't want to get caught by that thing even once if we can help it."
He taps the comms down to the engineering bay. "Engineer, I want you to divert power to our weapons again. You made a solid difference in our last volley! Tap into the Duonode just in case."
Turning to Oraeth, he shakes his head, "Shake it off, Science Officer. They're a tricky ship to pin down. Keep trying - we'll get them!"
Tapping a link to call up to Tamerriv, he shouts, "Excellent shot, Gunner! Light them up with the turret again - I'll try to get a shot with a light laser, or see what I can do to help with your firing solution. Pull in the computer to assist!"
Light Laser ATK: 1d20 + 3 ⇒ (10) + 3 = 13
Light Laser DAM: 2d4 ⇒ (2, 1) = 3
Encourage Gunnery vs. DC 17: 1d20 + 10 ⇒ (15) + 10 = 25

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Buoyed by her captain's praise, Tamerriv fires off another shot.
Coilgun, Targeting Computer, duonode bonus: 1d20 + 2 + 2 + 1 ⇒ (6) + 2 + 2 + 1 = 11 Damage: 4d4 ⇒ (3, 1, 2, 1) = 7

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Rik is picking the seeds from the ground when he receives his next orders.
"Weapons! Yeah! Duo-whatever, of course! On my way!"
The seeds go back to the ground and Rik growls lightly.
Divert (Weapons) DC 10 + TIERx2 (12) 1d20 + 9 + 1 ⇒ (3) + 9 + 1 = 13
1 Flying Bonus used.

GM Garrett |

The Endless Threnody's initiative check is...
Endless Threnody Initiative: 1d20 + 8 ⇒ (17) + 8 = 25
And it's a tie, which means the pilot with fewer ranks in Piloting goes first. The Threnody's pilot has 2, so the PCs will have to move first.

GM Garrett |

The Endless Threnody cunningly anticipated your maneuver and rather than moving executed a Turn in Place so it would be able to bring it's main gun to bear.
Main Gun Attack: 1d20 + 7 ⇒ (14) + 7 = 21
Main Gun Damage: 4d8 ⇒ (5, 5, 6, 2) = 18
That burns right through your front shields, which are reduced to zero. The ship rocks as you take 8 points of Hull Damage, which fortunately isn't enough to cause a critical. You're getting close though, and with those shields down you're riding on the edge of disaster.
Simultaneously, both of your shots hit, doing a combined total of 10 damage to the Threnody's Hull, which sends shards of bone drifting away from the ship, although not as much as you'd like. This pushes it over a critical threshold...
Threnody Crit: 1d100 ⇒ 39
Which Weapon: 1d3 ⇒ 2
You appear to have damaged it's Port Light Laser Canon. It's still clearly in the fight though.
Endless Threnody: 24 Hull Damage, Damaged Port Light Laser Canon
The Good Guys: 0 shields in front, 8 Hull Damage
Ok, everyone take your engineering and helm actions. In case it allows Mobius to make his move sooner, the Threnody will get the following initiative roll:
Threnody Init: 1d20 + 8 ⇒ (7) + 8 = 15

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Kadlos reels from the impact of the ship. "Damage report, Engineering! Get me those shields back, whatever it takes!"
He points to Mobius, "Shake it off, Pilot, no way to get around that. Keep moving evasively - and see if we can keep them on our flank!"
The readout from Oraeth's attempts to balance the shields pops up on Kadlos' screen. "Keep trying, Science Officer. We can't leave our forward arc that exposed."
Tapping comms to Tamerriv, he says, "Excellent shot - hit them again! I'll fire the light laser once more - stay focused on that turret."
Gunnery Check ATK w/ Light Laser: 1d20 + 3 ⇒ (17) + 3 = 20
Gunnery Check DAM w/ Light Laser: 2d4 ⇒ (1, 2) = 3

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Piloting Initiative: 1d20 + 11 ⇒ (1) + 11 = 12 Ugh, seriously?! LOL
With alarms ringing throughout the ship, Mobius gives it all to maneuver the ship out of harms way.
Stunt, Evade: 1d20 + 11 + 1 ⇒ (6) + 11 + 1 = 18
Using the +1 from our duonode bonus

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Oraeth, you should take the other duonode bonus. We need those shields.
Just die already!
Coilgun, Targeting Computer: 1d20 + 2 + 2 ⇒ (6) + 2 + 2 = 10 Damage: 4d4 ⇒ (1, 3, 1, 2) = 7
Or stay dead, or...something.

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Remember that, with energy diverted to weapons, 1s are considered 2s when rolling damage.
A strong collision shakes the engineering bay, amking all of Rik's seeds scatter through the place. "Awww..."
He receives the orders, and acts consecuently. "Shields, of course! That makes sense, yeah! Make those twats pay for spilling my... er... Make them pay!"
Divert (Shields) DC 10 + TIERx2 (12) 1d20 + 9 + 4 ⇒ (16) + 9 + 4 = 29

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Ah, my bad, Oraeth. I missed that you already posted your action. Hopefully I didn't cause us to lose our second duonode bonus this turn.

GM Garrett |

The Threnody rotates in place again and takes a shot with it's main gun.
Main Gun Attack: 1d20 + 7 ⇒ (1) + 7 = 8
But thankfully it misses.
Meanwhile, you manage to tag it for 3 points with your light laser, but Temerriv misses with the turret. Rik did manage to get you 7 points of shield back on your front arc.
The Good Guys: 7 shields in front, 8 Hull Damage
On to the engineering and piloting phases again!
To keep things moving along, the Threnody's initiative is here:
Threnody Init: 1d20 + 8 ⇒ (8) + 8 = 16

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The console finally emits the soft chime of success and new shield parameters display on on the screen. Oraeth quickly shifts the levels to brings shields up in the front again.
Computers, Balance Shields (DC19): 1d20 + 7 + 2 ⇒ (10) + 7 + 2 = 19
Pilot's call on how to balance them. I'm posting in a hurry and have to run. No time to figure it out right now.

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Sorry, I have little idea on how Balance works. I'd say get one shield point from each arc and transfer them to the front. If that's not possible then I'll just let the captain decide.
Mobius lets out a sigh of relief and tries to remain focused in flying the Loreseeker to a strategic location.
Piloting Initiative: 1d20 + 11 ⇒ (17) + 11 = 28

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Out of 40 shield points max, we currently have 30. CRB 324 says we can redistribute those evenly, with any extra going to the front shields. So I think that's 7 port/aft/starboard and 9 fore, yes?

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Sounds good.
I guess the thing I wasn't sure about was how the 7 points provided by Rik's power diversion fit in. Spread out does that make it 9/9/9/10 for now? And if he fails the roll or moves power elsewhere, then 7/7/7/9 I think.

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As the shields boost back to greater power, Kadlos breaths a touch easier. "Well done, Engineering. Get some more energy to our weapons, so that we can be sure to do as much damage as possible."
Punching comms to Oraeth, he praises the Lashunta, "Excellent work, Science Officer, that will shore up our weak points. When you're set there, get me another scan of that ship! I want to know if there's anything we're missing about their capabilities."
Keying comms off, he calls over to Mobius at the helm: "Take us to the enemy's aft, Pilot. The less I see of that front cannon, the better!
Switching channels, Kadlos calls up to the turret, "Keep trying, Gunner! We'll chip away if we have to, but let's get a solid hit with that turret - I'll keep firing the light laser."
Light Laser ATK: 1d20 + 3 ⇒ (12) + 3 = 15
Light Laser DAM: 2d4 ⇒ (1, 1) = 2