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Sunday, June 28, 2020

Bending the Curve - Adding a Long Tail to Your Random Rolls


   The classic 2d6 and 3d6 die roll conventions provide a normal or Gaussian distribution, commonly referred to as a Bell Curve.  This is great when we are looking to simulate an evenly distributed range of scores, such as the classic six characteristics, but what about when we would like to randomly determine an NPC level?  That presents a use where the the bulk of the results should be towards the lower bound, while the upper bound is potentially indeterminate, in other words an asymmetrical curve.

     One of the classic asymmetrical curves is the Pareto Curve, which has been popularized as the 80-20 rule, where in management 80% of your problems are caused by 20% of your people; or 20% of your people do 80% of the work.  Helpdesk ticket closure times are another good example, where the bulk of the them are closed in a fairly short range of time, but others, especially those requiring equipment replacement, extend the overall time range far to the right.  Back when I was at GE Fleet Services, I would check the 3rd quantile, or the mark at which the technician had closed 75% of their tickets, rather than their average time to close.



     Looking at a 2d6 distribution we find, 97.22% probability that you roll less than a 12; 91.66% less than an 11;  83.53% less than a 10 and 72.42% less than a 9.  We can create a reasonable long tail distribution very simply.   Whenever an 11 or 12 is rolled, roll another d6 and add it to 10, producing a 2-16 distribution.



 

     3d6 distributions give me the opportunity to illustrate that you don't need to stay with the same size die when creating a long tail.   You have a 83.8% chance of rolling less than a 14 on 3d6.   So to create the long tail, I would roll another die whenever the 3d6 is 15 or more and add it to 14.   If I use a d6, it only gives a 3-20 distribution, not much of an increase over 3-18.  By using a d10 instead, I create a 3-24 distribution range, producing a significant tail at the high end.


     I used anydice to look at the probabilities.  Their calculator will allow you to see the percentages for any combination of dice.  

     I haven't come up with as simple a way to do a long left hand tail, but I don't have a use case either.  If I get one I'll probably just flip the scale at the bottom and read from right to left.

     As I said, the use case I identified is random NPC levels, I'd be interested in hearing of any other use cases you might come up with.



Saturday, June 27, 2020

CSIO - Random Encounters Sailing the Roglaroon



Image of Maelstrom from Modron 2nd Ed
    Adding to the area specific Random Encounter tables I developed last year, I've updated by Cross System Source Table to read.

d20 Game System d20 Other System
01-10 AD&D 01-10 Empire of the Petal Throne
11-15 ACKS 11-12 Call of Cthulhu
16 Gamma World 13-14 Dreamlands
17 Metamorphosis Alpha 15 Space 1889
18 (1-3) Runequest
(4-6) Warhammer FRP
16 (1-3) Barsoom
(4-6) Dark Eye
19-20 Other 17 Traveller
18 Carcosa
19-20 Infernum

    This time I'm going to use the technique from ACKS by dividing the encounters up types, in this case movement type.  Swimmers, any creature that can survive an indefinite period in the water; Flyers and Vessels, any object propelled across or under the surface of the water - these range from orcs using a log to swim across the river, to sailing ships to the Apparatus of Kwalish.  Swimmers will be 40% of the encounters, Flyers 10% and Vessels 50%.  (OK, I started here, but ended up adjusting it to take into account ocean creatures swimming further up the estuary, and the Death Tree, which tosses exploding cherries at you, couldn't resist invoking the Rule of Cool.) Any Swimmer that can dive under the water has the choice to avoid the encounter completely, so while 90% of the creatures in the estuary are Swimmers, many of them won't be seen.

  There are three encounter areas on the Roglaroon.
    Mermist Tail (Hexes 2623, 2624,2625, 2726)  From the City State to bend west of Caravan Crossing, this area dominated by the inflow of the Conqueror River and the waters leaching out of the Mermist Swamp.  The estuary changes width rapidly along this stretch. Saltwater species are rarely encountered in this area.

  Dearthwood Reach (Hexes 2825, 2925, 3024, 3124, 3223, 3323, 3422,3522)  The long straight stretch between the bend and the River Hagrost.  The water becomes increasingly saline towards the Hagrost end.  Saltwater species frequently are encountered in this area.

  Roglaroon Proper, aka The Gullet (Hexes 3522, 3521, 3520, 3519, 3518, 3517, 3516, 3615, 3614, 3613, 3713, 3712)  From the River Hagrost to the Mouth, the estuary is a body of salt water inhabited by ocean creatures.

Aquatic Creatures mentioned in The Guide to the City State of the Invincible Overlord, Booklet I, Installment J and Modron.
   Gods:
     Ran the Cruel, Goddess of Death CSIO p55
     Sea Goddess (Unnamed, so I assume Modron), CSIO p14
     Manannan - CSIO p33
     Modron, Goddess of Rivers, Modron p5

Monsters:
    Maelstrom, Giant Sea Snake works for the City State, Modron p 6
    Giant Octopus, CSIO p33
    Giant Leech, CSIO p28
    Giant Shark, Modron p26

Sophonts
    Kopoacinths, CSIO p 10
    Aquatic Elves, CSIO p17
    Mermen, CSIO p28, p36, p38
    Tritons, CSIO p28
    Sea Hag, CSIO  p38, Modron p5
    Sahuagin,  Modron p26


d20  Mermist Tail Dearthwood Reach Roglaroon Proper
01 AD&D Shedu AD&D KopoacinthACKS Sahuagin
02 AD&D
Man, Merchant
ACKS NPC PartyAD&D Whale, Small
03 AD&D
Man, Merchant
AD&D Man, MerchantAD&D Man, Merchant
04 AD&D
Man, Merchant
Gamma World KeeshinAD&D Elasmosaurus
05 AD&D Gar, Giant Runequest FishermenAD&D Man, Merchant
06 AD&D Sea Hag AD&D Man, Merchant AD&D Man, Pirate
 (Orcs in small craft)
07 Warhammer Amoeba Roglaroon ProperAD&D Man, Merchant
08 AD&D Owl, Giant Roglaroon ProperGamma World Menarl
09 AD&D Beaver, Giant AD&D Man, PirateAD&D Triton
10 AD&D
Man, Buccaneer
AD&D Otter, GiantACKS Pegasus
11 AD&D Nixie AD&D Man, WarshipDark Eye Krakenewt
12 AD&D
Man, Buccaneer
ACKS Lizard ManAD&D Octopus, Giant
13 ACKS Thief ACKS Roc, SmallAD&D Man, Merchant
14 Warhammer
Chameoleech*
AD&D HippopotomusAD&D Man, Buccaneer
15 Roglaroon Proper Roglaroon ProperCall of Cthulhu Shantak
16 AD&D Kaolinth AD&D Man, MerchantAD&D Shark, Giant
17 AD&D
Man, Warship
Roglaroon ProperAD&D Crocodile, Giant
18 AD&D Gar, Giant Call of Cthulhu
 Nightguants
AD&D Elf, Aquatic
19 Empire of the
Petal Throne  Qu'uni
Metamorphosis Alpha
Death Tree
ACKS Sea Dragon ("Maelstrom")
20 Infernum Malcubi AD&D MermanAD&D Man, Warship
Flyers are italicized
Roglaroon Proper - re-roll on that column for the encounter
* The Chameoleech is best described as a cross between a Giant Leech and a Mimic.

Mostly this is as I rolled it using the appropriate random tables.  Had to make some adjustments to bring the flyers in at the right numbers on the Mermist Tail, added in the Aquatic Elves, Sahuagin and Sea Hag from the canon, and I took the AD&D entry "Man, Pirate (Tribesmen with small craft)" and decided that that would represent Orcs of the Purple Claw.

Tuesday, June 23, 2020

CSIO - Troubles with the Roglaroon

Estuary of Roglaroon
     I have issues with the Estuary of Roglaroon, geologic and economic issues with it.

     Geographically, the estuary describes a shallow U, short on the left side where it bends through the edge of Dearthwood  past the Mermist Swamp, longer and more angled on the right from River Hagrost to the mouth.  In between, despite some jagged edges, it's an almost straight line, no bends or meanders for some forty miles at the original 5 mile hex scale, 120 miles at the 15 mile hex scale I have seen some substitute.  And it's incredibly uniform in width during that stretch, maybe 2 miles across at the start and three miles at the very end.
     What could cut such a uniform channel?  Normal stream erosion wanders as the water flows through soil and rock of varying hardness, producing a typically serpentine shape of a river.  The landscape also produces significant changes in the river's width, passing through softer, more erosion prone soils to produce riverine lakes, like Lake Pepin on the Mississippi.   Glaciers cut narrow channels when they encounter hard rock, producing fjords, but the banks of the Roglaroon aren't mountainous.  I'm left with considering a glacial outburst flood as the agent to carve the channel.  If we examine the area bounded by Ered Losthian, the Cloudwall Mountains, Quean's Waste and Ered Cantreff in the south and the Howling Hills and the hills of Dearthwood in the north; we can posit a small glacial lake of over 7,000 square miles in extent, with a moraine dam stretching between the hills just east of Caravan Crossing.  Canonically, Wilderlands is a post-Ice Age world, this gives a plausible reasoning for the strange geography of the estuary.
     Related, how far up stream does the saline effect the water?  I would argue that based on the geography, the waters of the Roglaroon are basically salt water all the way up to the Hagrost, with water of diminishing brackishness from there to the City State.  Fortunately for the City State, it gets it's drinking water from an aqueduct out of Oracle Lake, which Groaning Falls protects from contamination by storm surge.

          Moving to economics, I've been having trouble imagining how ships get 140 miles up the estuary  to the City State, it appears so narrow in scale that I didn't think sailing ships would have room to tack across the channel.  However, digging into the detailed information in the Chivalry and Sorcery supplement Bireme and Galley,* yes, caravels at least are nimble enough to tack back and forth across the current and are approximately the size of the ships shown on the reprints of the City State maps.
     This of course led me to crunch numbers to determine how long it would take a ship to sail from the City State to Modron.   There's a lot of factors involved, more with sailing ships than I had worry about driving steam ships.  Sometimes the current fights you, sometimes it accelerates you and of course a tidal current is never constant.   Sometimes the flood is so strong that you have to anchor for a few hours or be carried backwards.  In general, your velocity made good on course (VMC), and hence distance traveled, is the cosine of the angle between the course you are steering and the tack you are on, times your true speed over ground.   Because I need to take the relationships between tide, wind and heading into account, I can run it in a spreadsheet (or write code functions if I feel like it), but haven't been able to reduce it to a simple formula yet.
  So, assuming the maximum tidal current in the Roglaroon is 5 knots; the ship departs the City State at the last of the flood tide; and the ship's true speed over ground equals nominal speed from Bireme and Galley based on the wind strength.
  The fastest time is a mere 9 hours in a Strong Northwest Wind.
  The slowest time is 60.5 hours in a Light Northeast Breeze.

Breakdown:
   Five knot tidal current.  The Thames in London runs 4-6 knots.
   Departing on the last of the flood tide, just before slack water means the ship will ride it's anchor cable to face downstream, reducing any maneuvering to leave port.
   Nominal speeds based on wind strength from Bireme & Galley for a Caravel
            Light - 3.5 knots
            Strong Wind - 9.5 knots

 Bireme and Galley doesn't list actual wind speeds, so my estimation of their definition are based on the Beaufort scale.

Light Breeze    Beaufort Scale 2-3      4-10 knots
Good Breeze    Beaufort Scale 4         11-16 knots
Good Wind       Beaufort Scale 5         17-21 knots
Strong Wind     Beaufort Scale 6         22-27 knots

Average Voyage - Overall 27.1 hours
Average Voyage - Light Breeze   38.8 hours
Average Voyage - Strong Wind   15.3 hours
Predicted Voyage - Light Breeze at true speed over ground  28.5 hours 
Predicted Voyage - Strong Wind at true speed over ground  10.5 hours

* Looks like the pictrues have disappeared from the Bireme and Galley post

Tuesday, June 9, 2020

Meet the Party - C&S in CSIO

Werebear illustration from AD&D
Monster Manual. 

     I want to use some of the background posts I've been doing in the Wilderlands to run some soloplay Chivalry & Sorcery.  I've already detailed creating the Power Word Magician Mordacris in C&S.  Here's the rest of the party, I generated them using my C&S 1e character generator spreadsheet - which did identify an issue in how it handles Bastardy.

   





Ysolt



Human Female
Age 20


Level 1

XP
0
5’ 5”
110 Dr







Characteristics

DEX
13
ST
20(2)
CON
19
PA
15
BV
17
IQ
16
WIS
19
CHA
21
ALGN
5



Combat

Body
21
Fatigue
9
Carry Cap
638Dr
Military Ability
10.9
Command Level
6.45
PCF
14.33

Blows
Damage
%HIt
%Parry

Light Weapons
2
3*WDF
+20%
-20%

Heavy Weapons
1
4*WDF
+18%
-12%

% Shield Parry
+18%
Dodge
-22%



Social
     Daughter of Simon, a Freehold Farmer of Tharbian background owing fealty to Baron Jaquob. She is his fifth child and is considered "Good Child". Her Superhuman strength makes her a formidable fighter.  Her dexterity, appearance, bardic voice, intelligence and wisdom - combined with her impressive strength give her a truly commanding presence. She has black hair, bronzed skin and light blue eyes.
She is a Neutrally aspected Leo and gets no bonus to experience.
Her father is a regular supplier of herbs and other spell components to Mordacris' master Athelbur. She has been hired to escort Mordacris to collect some rare spell components on the far side of Dearthwood.

Social Status
8
Basic Influence Factor
18.5

Languages: Common, Tharbian

Useful Skills:

Local Knowledge - identification of crops and livestock common in the area, as well as their state of health. Similarly, she is aware of types of major predators and they're preferred prey. She knows of the major locations around the City State, but has never visited most of them.

_________________________________________________________________________________


Wulfgar



Human Male
Age 22


Level 1

XP
0
5’ 7”
130 Dr







Characteristics

DEX
7
ST
14
CON
12
PA
11
BV
15
IQ
17
WIS
9
CHA
12
ALGN
20



Combat

Body
10
Fatigue
6
Carry Cap
221Dr
Military Ability
3.9
Command Level
1.95
PCF
5.66

Blows
Damage
%HIt
%Parry

Light Weapons
-
3*WDF
+5%
-5%

Heavy Weapons
_
3*WDF
-
-

% Shield Parry
-3%
Dodge
-5%



Social
Son of Arthur, a peddlar in the City State, he is the 6th child and is considered a "Credit to the Family".  He is an apprentice Assassin in the Thieves Guild, providing muscle and look out services for their heists. He is a poorly aspected Aquarius and suffers a -5% experience penalty. As an Assassin, he only gets 1/2 experience from using his thief skills, but full experience for fighting. He has black hair, olive skin and green-brown eyes. He is a childhood friend of Mordacris and is looking for some time out of town until the Watch forgets his face.


Social Status
2
Basic Influence Factor
8
  
Languages: Common

Useful Skills:
Thief Skills
Detect Trap +35%
Disarm Trap +5%Pick Pocket +5%
Chance of Discovery 45%/10% (at Night)



Local Knowledge - intimately familiar with the streets of the City State, it's markets, shops and temples. He has a 40% chance of finding his way across roof tops to any destination in the city and a 15% of finding his way through the catacombs underneath. He knows a number thieves in the Guild, but does NOT know of the ancient Master Thieves in the catacombs underneath the guildhouse. He can dispose of stolen goods and any items found on adventure through the Thieves Guild.


________________________________________________________________________________


Adenin



Werebear Male
Age 17


Level 1

XP
0
6’ 0”
180 Dr


MKL 1




Characteristics (Human)

DEX
1
ST
8
CON
10
PA
20
BV
17
IQ
17
WIS
20
CHA
20/22/14
ALGN
7



Combat

Body
11
Fatigue
3
Carry Cap
144Dr
Military Ability
8.8
Command Level
5.4
PCF
6.54

Blows
Damage
%HIt
%Parry

Light Weapons
-
3*WDF
+8%
-8%

Heavy Weapons
-
3*WDF
+5%
-

% Shield Parry
-
Dodge
-8%



Social
     Baron Jaquob was an avid hunter in his youth. Once while out hunting, he spent an afternoon of dalliance with the daughter of a woodcutter. The following summer, he slew a sow bear and captured it's single cub. Upon death, the bear transformed back into the form of the woodcutter's daughter.  When the moon waned, the cub changed into a beautiful baby boy.
     The baron has never acknowledged the boy's paternity, but has raised him as his ward in his household. Adenin's clumsiness and middling strength, combined with his stellar intellect has caused his protector to obtain a place for him as a Priest of Uller. He has been sent to the Temple of Odin in the City State for training. His god-like appearance gives him a 22 Charisma with members of the opposite sex, 20 Charisma with members of the same sex and a 14 Charisma when dealing with members of either sex who are Ugly. (Those unfortunates with a Personal Appearance of less than 8.) He is a poorly aspected Aquarius. He receives +5% experience as a Cleric, -5% experience as a Fighter and a Magic User.
     As part of his training, he has been assigned to spend three weeks in an isolated cell in the eastern fringes of the Dearthwood. He will travel there with Ysolt and Mordacris. He has auburn hair, gray eyes and his complexion is a light yellow (Hex #FAFAD2 if you're having trouble visualizing it.)


Note: The spreadsheet didn't show him as an unacknowledged Bastard, and didn't calculate the Social Status correctly.  But the error gave me the idea of having him be the ward of his biological father.  And the rest is backstory.

Social Status
10
Basic Influence Factor
21
  Magick
Clerical Miracles Number/day: 1
Miracles Known
Cure Minor Wounds (6-10 point restored to Body and Fatigue. May be received 1/day by any character)
Note: He had a 60% chance of also having Purify Food & Water, but rolled too high. He can try again when he achieves 2nd level.


Miraculous Magical Effects
     All Clerics have a 60% - 5% per Alignment over 1 to be able to cast spells as a Primitive Talent Magic User, again he rolled too high. Clerics with Intelligence, Wisdom and Charisma of 15+, have the same percentage chance cast spells as a Shaman. He rolled a 28, the three weeks in the cell is when he will encounter his Totem Spirit (predetermined to be a bear). Until then he cannot cast spells.

Concentration Level
3.9
Personal Magick Factor
9.8

Magick Level
1
Spell Level
1

Direct
Injurious
Effect
Volume
Multiplier
(Missiles)
Volume
Multiplier
(Material)
Time
Factor
Spell
Range
2*EDF
2*
5*
4*MKL
10’ *MKL

Languages: Common, Tharbian

Spells:

Useful Skills:
Multiclass - Raised as a noble, he can fight as a Knight. He can earn experience as a fighter, cleric or magic user. Any experience will be based on the most favorable way of calculating it.

Local Knowledge - identification of crops and livestock common in the area. Similarly, he is aware of types of hunting prey and they're preferred habitats. He knows of the major locations around the City State, but has never visited most of them. He knows of major nobility in the City State and can correctly identify their heraldry and major manor locations 90% of the time. He is not personally acquainted with them.


Characteristics (Bear)

Body 70 Weight 900Dr Move 60/180

Armor 5 Hit +35% Dodge -25%

4*WDF MLC 6 Claws - 3 attacks, 14 points of damage each. H Weapon Bash
2*WDF MLB 3 Fangs - 2 attacks, 8 points damage each. L* Weapon Bash.
Hug - costs one blow. 3-18 damage (AC less than 6) 2-12 damage= AC greater than 5). May toss for 5-30 feet with a 25% chance of the victim being Stunned.