Sunday, November 24, 2019

#31: Old News

In the aftermath of the battle, there’s a mixture of elation over having survived, and desperation over the losses and what the immediate future looks like for Dagger’s Deep and its grieving residents.  One of the first major appointments is a new militia captain, a warrior named Kallevir.

In examining the Stormlord’s maul, I am unable to discern any of its magical properties beyond that fact that it radiates an aura of evocation magic, destructive arcane forces.  I have Zargon examine the weapon to try and determine its provenance as well, but the bard knows as little as I.  I take up the maul as my own as well as the Stormlord’s talisman, an iron-forged disc with engraved lightning bolts, the symbol of Talos.  I add this token to my string of fetishes.  Zargon and Audric divide the other spoils, tucking away a pouch of small gemstones and distributing what remains to the town.

Audric and I take up station at the shrine over the course of the next few days, triaging Dagger’s Deep’s most wounded and treating those wounds to the extent we are able with the powers bestowed upon us by our respective gods.  Our efforts are appreciated by the settlement, and by the end of second day, the burials commence.  The folk of Dagger’s Deep have been working tirelessly to craft wooden coffins and dig the long trenches that will house the fallen.  Everyone is present for the ceremonies, including Odesia, who seems nearly catatonic, unable to cope with the loss of her unborn child’s father.

Zargon spends several days in recovery and training, honing his abilities and refining his arcane knowledge, spending much time mumbling to himself in languages none of us understand.  Selben, as well, spends time cloistered away in his tent, poring over Ethelenda’s spellbook as well as his own.

The following morning, Daegahr approaches and informs us flatly that he intends to return to Mirabar immediately, having business to tend to and others to care for.  Though he bears us no ill will, he is not interested in prolonging his stay.  He has already spoken to Odesia, offering to return her to Mirabar, an offer that she declined.  We tell him that we’ll check in on him if we decide to make the trip ourselves, and he departs without further words.

That same day, a small fishing boat comes upriver, and a haphazard party is gathered to greet the craft.  The men are fishers from Mirabar, heading to waters where bountiful fishing abounds.  We share a warning regarding the river creatures we encountered, and the men thank us for the knowledge.  The traffic gives hope that Perhegan may one day turn a profit from his venture.

Perhegan’s daughter Edine looks over Odesia, but the keravela woman remains quiet and distant.  Edine has a brightness about her and is very pleasant to be around; there’s hope that her personality will help Odesia through her grief.

A few days after the burials, men begin filling the crater left by the lightning bolt that slew Pol Rallinoth; in the effort, they discover something and call us to investigate.  At the bottom, the earth struck by the lightning is found to be flat, crafted, rough-hewn stone.  I jump into the crater with the men and spend time trying to discern the size or scope of the discovery.  In every direction we attempt, as far as several paces, we find the same flat surface, indicating a rather large construction.

Zargon sequesters himself, attempting to expand his arcane repertoire, while Audric and I focus our efforts on the curious stone.  Renewal approaches, saying that he has something to show us, something found in the keep itself.  He leads us down into the waterlogged basement cellar, where women and children took shelter during the attack; we never thought much of it, being little more than an unusable storage chamber, and it smells dank and moldy.

Apropos...
Renwal conjures forth a magical light at an empty point in space near the far wall, displaying the smudged outline of a circle carved amid the stonework.  It is situated in the general direction of the structure outside, potentially indicating a tunnel opening.

Examining the cellar, it’s close to river level, perhaps slightly below it.  Given the direction of the tunnel, however, pointing away from the river, it’s unlikely to be flooded with river water beyond.  Audric examines the curious circle, attempting to divine whether it has arcane properties, and shrugs before finally heaving into the stone with a shoulder, budging it an inch.  Before I can complain to him about calling me rash, he heaves again, and the stone slab pushes forth as if a door on a hinge, opening into a three-foot diameter tunnel of carved stone.

Audric sends his familiar Lume into the tunnel, and before long the cat disappears into the darkness.  She returns safely a few moments later, and Audric says that he’s going to attempt to crawl through the tunnel.  Before doing so, I layer a few abjurations upon the warrior, not feeling completely comfortable about the confined space, but feeling better knowing I departed what protections I could.

Headfirst, he crawls into the tunnel, wriggling through the sludge.  After a few minutes of worming his way through muck, he reaches what appears to be a wooden door.  We discuss the risks involved, ultimately deciding to attempt entry after arguing with Zargon about the right to whatever glory waits beyond.

Though confined by the tunnel, Audric lays a shoulder into the heavy door, pushing it free from its position as it crashes forward, revealing a large chamber of perhaps 30 by 50 feet.  The ceiling is higher, allowing Audric to stand more comfortably, and surprisingly the stone is dry, though the air is still musty.

Very little in the chamber is intact.  There are broken pieces of wood that are remnants of barrels, crystals of salt littering the ground such as those used to store dry goods and meats, and the fragmented bones of a human skeleton that had been resting against the door before Audric heaved it inward.  Large boulders block an opening across the chamber, surrounded by scorch marks and smelling faintly of ash and cinders. Audric relays all of this back through the tunnel.

In the waning moments of his arcane divination, Audric discovers a cloth garment from which radiates a dim magical aura.  Picking it up, he realizes that it’s a cloak that had blended in nearly perfectly with the surroundings; from within its folds he withdraws a bloodstone, a smooth stone with black and red ripples the size of a small egg.  Carved into the bloodstone is a small circle, perhaps the size of a ring.

Also within the cloak is an old, folded piece of parchment, which Audric brings back to the crowded cellar.  Unfolding the document, a cryptic set of writings is revealed, several partial sentences or perhaps all nonsense, numbers that may be dates; we’re not able to make sense of it all without further research.  The handwriting looks to be of the same hand, though the script different sizes, as if written at different times and with different levels of urgency.

Using bits of rope to map out the distance from the blocked portal to the entryway and laying out a similar length of rope above ground, it appears that the stone surface discovered in the pit of the lightning strike corresponds with the chamber discovered beneath.  The scorch marks and scent are old in comparison to the lightning, likely not connected in any way.

The only words from the parchment that anyone in Dagger’s Deep recognizes is Fort Kaeylnor, a small fort situated near a village north in the Khedrun Valley.  “Is that Oldkeep?” Audric asks, recalling our encounter with the troll there.  As for Audric, he recognizes one of the names—Mystryl—and explains that she predated Mystra as the goddess of magic.


“Close the conduit” especially seems to cause Audric considerable consternation, harkening back to the runes discovered in Oldkeep and Moonglow Cave, as well as the magics unleashed by Malchor Harpell—or perhaps by the ring—that led to our temporal displacement.

“Is there a library in Mirabar?” I ask.  The consensus is that there are likely libraries in Mirabar, but none of any particular note.  If more information is to be found, we must travel to the fortress and seek it there.  The initial excitement at finding the document eventually leads, for me at least, to a feeling of dread, of being trapped by powers or circumstances outside our control.

Convening to discuss the matter, we decide that a visit to Mirabar is indeed in order—if nothing else to resupply, and perhaps bolster the defenses of Dagger’s Deep by hiring a few men—and we begin to lay out the details of our potential trip.

Friday, November 22, 2019

Statistical differences between rolling methods

Sean and I have been discussing rolling methods for ability scores, particularly in the context of PCs vs. henchmen. Consider the two following methods for generating a set of abilities (sourced from the 2e PH, p. 13):
  • Method II. Roll 3d6 twice and take the higher of the two values.
  • Method V. Roll 4d6, discard the lowest roll, and add up the other three.
For player characters, I've long employed Method V (4d6 drop lowest) with a caveat that the player can roll up to three sets; if the player discards one set to roll another, the discarded set cannot be used. This gives the player the ability to discard an underwhelming set or swing for the fences to try to attain a great set, but also adds an element of risk, especially if the third and final set (which must be accepted) turns out to be poor.

For most NPCs and hirelings, I employ Method II, which tends to generate more averages sets. I don't use any re-roll caveat for NPCs. They get what they get.

Because, in our campaign, henchmen have the ability to replace fallen PCs over the long-term, we want to make sure we're in agreement on the rolling method to use. Most AD&D players intuitively know that Method V is more likely to generate high scores (15+) than Method II, but what if we evaluate the methods more deeply? Let's say, for example, that we're looking to create a ranger, which requires two scores of 14 or higher and two additional scores of 13 or higher.

I wrote a quick app to generate random sets of ability scores using both methods. Scores within each set are arranged from highest to lowest, with sets that qualify for the ranger class marked with a letter r. Here are results for ten sets of scores for each method:
Method II results (3d6 twice, take higher):
  16  14  13  13  11  11  (r)
  16  13  12  12  10   8
  15  14  13  11   9   8
  16  15  14  12  11  11
  14  14  13  13  12  11  (r)
  13  11  11  11   9   5
  15  15  15  13  12   8  (r)
  15  14  14  12  12   8
  13  12  12  11  10   8
  16  14  14  13  12  11  (r)

Method V results (4d6 drop lowest):
  15  13  13  12  12  12
  14  14  12  10  10   8
  16  13  12  12   9   4
  17  15  13  11  11   7
  14  14  12   9   9   8
  14  14  12  11   8   7
  17  14  13  12  11   7
  15  12  11  10   9   8
  16  14  13  13  10  10  (r)
  15  15  14  13  10   8  (r)

Four rangers for Method II, only two for Method V. This are very small samples sizes, so let's run them again to observe the variance:
Method II results (3d6 twice, take higher):
  13  12  11  11  11   6
  14  13  13  12  12  12
  14  13  13  12  12  11
  17  16  12  11  10   9
  13  13  13  12  11  10
  15  15  12  10   9   8
  17  16  12  11   9   8
  15  14  14  10   9   9
  16  16  15  15  14   9  (r)
  17  13  13  13  12  12

Method V results (4d6 drop lowest):
  15  12  11  11  10   9
  15  14  13  12  12   7
  15  13  11  11  11   9
  16  14  12  11  10   8
  14  14  13  13  12  12  (r)
  15  15  14  13  11  10  (r)
  17  14  14  14  13  11  (r)
  16  16  15  12  10   8
  15  15  14  13  12   5  (r)
  18  14  13  12   9   9

This time, one ranger for Method II, four rangers for Method V (an opposite result). Obviously, we need more data. I'll have the application roll 100 sets for each method and take the averages (rounded down to whole numbers):
Method II averages:
  15  13  12  11  10   9

Method V averages:
  15  14  12  11  10   8

These are actually really close; in fact, the total number of ability points is the same with both methods. Through another few runs, I was able to verify that these exact averages still hold even with a very high (10,000) number of sets.

But the averages don't tell the full story. Again, we know from intuition that there's going to be tangible variance between the methods. If it's not in the total number of points, then where?

For starters, we know that, in order to get stuck with a score of 3 using Method II, we need to roll six 1s in a row. That means 6^6, or one in 46,656 scores. To get equally unlucky with Method V, you only need to roll four straight 1s, or 6^4, which is one in 1,296 scores.

That's a major difference: you're almost 40 times more likely to end up with a score of 3 using Method V (the 4d6 method) compared with Method II (the 3d6-twice method).

Let's see what the distribution of scores is over ten sets of scores using each rolling method:
Method II totals:
   3s:  0
   4s:  0
   5s:  0
   6s:  0
   7s:  0
   8s:  2
   9s:  6
  10s:  4
  11s:  5
  12s:  12
  13s:  7
  14s:  12
  15s:  6
  16s:  6
  17s:  0
  18s:  0

Method V totals:
   3s:  0
   4s:  0
   5s:  0
   6s:  2
   7s:  2
   8s:  2
   9s:  6
  10s:  3
  11s:  3
  12s:  12
  13s:  9
  14s:  5
  15s:  10
  16s:  3
  17s:  3
  18s:  0

That looks reasonable: fewer high but also fewer low scores when using Method II. How about for 1,000 sets?
Method II totals:
   3s:  0
   4s:  2
   5s:  11
   6s:  36
   7s:  101
   8s:  257
   9s:  424
  10s:  629
  11s:  839
  12s:  979
  13s:  926
  14s:  727
  15s:  513
  16s:  313
  17s:  184
  18s:  59

Method V totals:
   3s:  3
   4s:  25
   5s:  51
   6s:  99
   7s:  194
   8s:  269
   9s:  451
  10s:  585
  11s:  697
  12s:  794
  13s:  740
  14s:  737
  15s:  586
  16s:  430
  17s:  240
  18s:  99

Now we're starting to see the numbers at work. A thousand sets contain 6,000 individual scores; we have three scores of 3 using Method V, and none using Method II. Given that we were expecting only one in 46,656 scores with Method II but about one in 1,296 scores with Method V to result in a lowly 3, these results look pretty solid, though our sample sizes are still small enough that we're hitting a fair degree of variance.

Here are the totals for 100,000 sets:
Method II totals:
   3s:  15
   4s:  184
   5s:  1056
   6s:  3819
   7s:  10642
   8s:  24747
   9s:  43524
  10s:  65439
  11s:  84711
  12s:  94523
  13s:  92145
  14s:  72943
  15s:  51490
  16s:  32525
  17s:  16626
  18s:  5611

Method V totals:
   3s:  473
   4s:  1917
   5s:  4722
   6s:  9581
   7s:  17370
   8s:  29011
   9s:  41925
  10s:  56347
  11s:  68252
  12s:  77520
  13s:  79661
  14s:  74389
  15s:  60690
  16s:  43464
  17s:  25012
  18s:  9666

For Method II, fifteen out of 600,000 scores ended up as 3, or one in 40,000, which is very close to the one in 46,656 ratio that we expect to normalize to over the long term. For Method V, we had 473 scores of 3, which is about one in 1,268... extremely close to the normalized ratio of one in 1,296.

If we add up all the scores of 7 or lower, Method II only generated 15,716 while Method V produced a whopping 34,063. If we add up all the scores of 15 or higher, Method II gave us 106,252 while Method V resulted in 138,832.

The takeaways are that you're more than twice as likely to get bad scores (7 or lower) with the 4d6 method, but only about 30% more likely to get high scores (15 and above). Method V, however, is almost twice as likely to generate very high scores (17 or 18), while Method II is far more likely to hit in the average range of 10 through 14.

Finally, here's a plot graph of the 100,000 set results, which makes everything nice and clear:

Click to enlarge

Though Sean and I still haven't decided exactly how to handle scores for a new henchmen, the above data definitely provides the right ammunition to help us make the best decision for our campaign. As an extra bonus, here are score distributions for two additional rolling methods described in the PH, along with an additional graph that charts all four methods.
  • Method I. Roll 3d6 for each score.
  • Method IV. Roll 3d6 twelve times, and take the six highest values.
Here are the side-by-side averages of all four methods:
Method II averages:
  15  13  12  11  10   9

Method V averages:
  15  14  12  11  10   8

Method I averages:
  14  12  11   9   8   6

Method IV averages:
  15  13  12  12  11  10

...along with the score distributions of the two new methods:
Method I totals:
   3s:  2817
   4s:  8353
   5s:  16620
   6s:  27915
   7s:  41657
   8s:  58653
   9s:  68882
  10s:  74966
  11s:  74945
  12s:  69277
  13s:  58329
  14s:  41804
  15s:  27916
  16s:  16701
  17s:  8340
  18s:  2825

Method IV totals:
   3s:  0
   4s:  0
   5s:  0
   6s:  1
   7s:  129
   8s:  2063
   9s:  14860
  10s:  50573
  11s:  98940
  12s:  123988
  13s:  114935
  14s:  83276
  15s:  55540
  16s:  33591
  17s:  16596
  18s:  5508

...and the final graph depicting all four methods:

Click to enlarge

(If you made it to the end of this post, congratulations!)

Monday, November 18, 2019

The parchment

Image of the worn sheet of parchment found folded within a cloak inside the hidden cellar below Dagger's Deep:


Wednesday, November 13, 2019

XP awards for sessions 29-30

The XP award for the past two sessions is wholly attributed to the party's contributions in the battle against the barbarian invaders; as such, Zargon receives a full share, even though Bill wasn't present for the return journey downriver.

The total award, less amounts reserved for Bonie and other NPCs, is 10,000, which divides to 2,500 XP per PC and 1,250 XP for Selben. Updated totals:

  • Audric - 12,903
  • Zeb - 3,000/35,448
  • Zargon - 10,003
  • Selben (h) - 8,101

Zargon has attained 5th level, and can advance upon completion of five dedicated days of training.

Recovered Items

Further, following are the noteworthy possessions recovered from the Stormlord, whose throat was torn out by Zeb. (It can be assumed that the other barbarians' and ogres' gear is mundane, and will be allocated to Dagger's Deep.)

  • Large, claw-ended maul (functions as a bastard sword, magical)
  • Chainmail, marked from use and mended in several places (non-magical)
  • Black-iron medallion, hung from an iron chain and bearing a depiction of lightning bolts (non-magical)
  • Leather pouch, carrying an assortment of small gemstones and a handful of nominal coins (non-magical)