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A Detailed Mathematical Model
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This model represents a mathematician's second attempt at making a mathematical model, and as such is very detailed, complex, and at times hard to keep track of. It is being kept on the web primarily as a courtesy to people who are already using it. If you are not a heavy gamer, and are not used to complex mathematical models, I strongly suggest that you use this simpler model. This document may still be useful, as a wealth of detail about mechanical devices and other creations, but newcomers are warned that using this as an actual model for game play may be difficult.
Section I: General model
Section I A: Getting Started
The parts of this document are as follows:
Another document, "From zero", introduces the concept of role play and deals with all of the non-numerical parts of getting started; this document tells how to deal with numbers and dice.
For basic introduction and getting the feel for the model:
Section I B attempts to explain some of the basic concepts. Section IV develops a sample character sheet, a sheet used to store basic information useful to play; it demonstrates what a player goes through in order to set things up. Section II F gives some numbers to use as reference points, for questions like "What should be the difficulty for thus-and-such?" Section III gives a quick key to abbreviations used throughout the work.
For developping a character sheet:
Section II A tells how to generate a character's attributes — numerical ratings that tell how talented a character is in various areas — and section II B tells how to adjust them for age, gender, and race. Section II D gives the basic list of skills and tells how they are to be adjusted by attributes. Section II H gives starting experience, and section II G tells how much experience it takes to raise a skill to a certain level.
For modelling play:
Section II I tells how, when a character attempts an action, to roll dice to decide whether the character, with skill A, succeeds at an action with difficulty B. Section II J deals with combat and damage. Section II K deals with random encounters of animals and people, and describes what animals are in the world. Section II L deals with equipment.
Optional rules and Other:
There are several optional rules which may be used to enhance play and give it more detail. Section I C is the first such section, dealing with skills ratings. Section II C gives miscellaneous numbers about the races. Section II E gives numbers referenced in II C. Section II M gives rules about the time taken for various actions, and performing actions simultaneously. Section V comments on the model.
Section I B: The Basic Idea
This is essentially a skill-based model, a modified version of another model to use dice. It requires the use of two six-sided dice of different colors — for the sake of simplicity, the two dice will be referrered to as r (red) and b (blue), and read as producing numbers ranging from 1 to 6. For example, 6*r+b would be read as ten times the number on the red die, plus the number on the blue die, which would in effect produce a random number from 7 to 42. It is, while not necessary, helpful in some cases to have two ten-sided dice.
In general for skills, attributes, ratings, etc., a 0 is average, and the number (positive or negative) tells how far above or below average that creature is. The scale is exponential; 10 points correspond to doubling/halving. So someone with a strength of 20 and a dexterity of -10 would have a strength of 2*2=4 times average, while someone with a dexterity of -10 would be half as dexterous as the average person. The game generally uses the attributes in the form given — essentially, how to adjust an average ability — and doesn't really deal with an absolute scale.
A character's skill will have an av (adjusted value), equal to the bs (base skill), minus the skill's dl (difficulty of learning), plus the character's al (ability to learn), plus the gaa (governing attributes addend). When the character attempts an action, the skill's difficulty will be subtracted from the av, and then dice will be rolled to see if the attempt was successful.
If an action is being taken against another character (for example, haggling), that person's av is the difficulty.
Section I C: Additional Rules
Some skills are related to each other by an ld (learning difference). If skill X and skill Y are related by an ld of 5, then a character's bs (exclusive of experience) in skill x is at least the number five less than his bs in skill Y. So a character who had a bs of 15 in skill X would have a minimum bs of 10 in skill Y. The ld's are additive (if X and Y have ld 5 and Y and Z have ld 10, X and Z have ld 15), but explicitly listed differences supercede the values that are calculated from additivity. If there are two or more ld's contributing point values to a specific skill, and/or a nonzero untrained base, the total is not the sum of the point values. It is the maximum.
Learning may take place under a tutor who has a skill of at least the skill level that the character is training to; in that case, the learning is at half price. The experience given starting characters takes this tutelage into account.
Section II: Charts
Section II A: Attributes
Several random numbers generated as r - b: the number on the red die, less the number on the blue die.
These values are numbered n1 through n36.
The attributes are read roughly as how far above or below the average they are: a +10 would be a fair amount above average (twice the average), while -10 would be moderately below average (half the average), with zero being average. The maximum possible is 25, and the minimum -25.
Here are the calculated attributes:
ag (Agility) n1+n2+n3+n4+n5 al (Ability to Learn) n1+n6+n7+n8+n9 ch (Charisma) n1+n6+n10+n11+n12 co (Constitution) n13+n14+n15+n16+n17 de (Dexterity) n1+n2+n3+n18+n19 in (Intelligence) n1+n6+n7+n20+n21 kn (Knowledge) n1+n6+n7+n22+n23 me (Memory) n1+n6+n7+n24+n25 pe (Perception) n1+n6+n26+n27+n28 sp (Speed) n1+n2+n29+n30+n31 st (Strength) n13+n14+n32+n33+n34 wi (Wisdom) n1+n6+n7+n35+n36
Section II B: Attribute Adjustments
All adjustments are addends: they are added to a character's base attribute. All adjustments are 0 unless otherwise specified.
Attribute: ag al ch co de in kn me pe sp st wiRace: Nor'krin 0 0 0 0 0 0 3 5 0 0 5 0 Tuz 0 0 0 5 0 0 0 0 0 0 10 0 Urvanovestilli 0 0 2 0 5 5 2 3 0 0 -10 0 Yedidia 0 0 5 0 0 3 0 0 10 0 0 0 Jec 0 0 0 0 0 0 0 0 0 0 0 0 Shal 0 0 0 0 0 2 0 0 0 -5 0 5 Janra 20 0 5 0 0 4 0 0 2 5 5 0
Gender: Male 0 0 0 0 0 0 0 0 0 0 5 0 Female 0 0 0 0 2 0 0 0 5 0 -5 0
Age: Child 5 10 2 10 0 -8 5 0 10 10 -4 -10 Young Adult 5 5 0 5 5 0 -4 0 5 5 5 0 Middle Aged 0 0 0 0 0 0 0 0 0 0 0 3 Old -4 -4 0 -4 -4 -3 5 -3 -4 -4 -4 5 Extremely Old -10 -10 0 -10 -10 -5 5 -8 -10 -10 -10 10
Section II C: Racial Non-Attribute Statistics.
A character's actual lifespan is calculated by multiplying the racial base by his constitution (constitution not adjusted for race, gender, or age), except for the border between child and young adult, which is not adjusted. For example, a Janra with a non-adjusted log of constitution of .8 would become a young adult at 16, middle aged at 41, old at 73, and extremely old at 89. A character will die of old age at an age of his maximum adjusted lifespan times the square root of x1, where x1 is uniformly distributed over [0,1].
Age: Child Young Adult Middle Aged Old Extremely Old Nor'krin 0-15 16-30 31-60 61-90 91-120 Tuz 0-15 16-25 26-40 41-50 51-60 Urvanovestilli 0-30 31-100 101-300 301-400 401-500 Yedidia 0-20 21-50 51-120 121-160 161-200 Jec 0-15 16-30 31-60 61-90 91-120 Shal 0-50 51-200 201-600 601-800 801-1000 Janra 0-15 16-50 51-90 91-110 111-120
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A Detailed Mathematical Model
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