Skip to content

LordFckHelmchen/WrathAndGloryXPOptimizer

BranchesTags

Repository files navigation

Wrath & Glory XP Optimizer

Evert wondered if it is better to choose Agility over separate points into Ballistic Skill & Stealth? Ever thought that your current character has only Intellect but no points left for anything else?

This repo contains a Mixed-Integer Non-Linear Programming (MI-NLP) optimization solution to spending the optimal amount of XP on selected attributes, skills & traits in the role-playing game Wrath & Glory by Cubicle 7.

For simple character management, I recommend using the Character Forge @ Doctors of Doom. The XP optimizer can then be used on a created character to minimized the spent XP. Just pass in your desired target values (e.g. total value for Cunning, Tech & Deception and your desired Strength) and the optimizer will figure out the best distribution to use with minimal XP.

If you encounter any errors/wrong numbers please post your input & the expected values so I can debug them. If you have any recommendations, feel free to leave some comments.

The optimizer is written for the core ruleset v2.1. It does not take into account any species/archetype based bonuses/prerequisites - but these should be fine given that they use the same XP cost tables.

Installation

  • Install Python (3.8 or better) if not already done.

  • Switch to folder of this project, open terminal & install requirements

    pip install -r requirements.txt

  • Try, if it works (shows help content)

    python xpOptimizer.py -h

Usage

NOTE: You always have to specify the tier of your character!

The optimizer takes the tree-of-learning rule into account, but assigns the skill ratings randomly (within the min-xp constraint). Simply move the 1s around to your liking - the xp cost stay the same.

Purely via command-line arguments

For few target properties it is best to use the command-line arguments, e.g. if you want to optimize your tier 1 character with Strength 3 and Max Wounds 5, type:

python xpOptimizer.py --Tier 1 --Strength 3 --MaxWounds 5

which will output the following markdown table:

## Tier
1

## Attributes
Name       | Total  | Target | Missed
---------- | ------ | ------ | ------
Agility    | 1      | -      | -     
Fellowship | 1      | -      | -     
Initiative | 1      | -      | -     
Intellect  | 1      | -      | -     
Strength   | 3      | 3      | NO    
Toughness  | 3      | -      | -     
Willpower  | 1      | -      | -     

## Skills
Name           | Rating | Total  | Target | Missed
-------------- | ------ | ------ | ------ | ------
Athletics      | 0      | 3      | -      | -     
Awareness      | 0      | 1      | -      | -     
BallisticSkill | 0      | 1      | -      | -     
Cunning        | 0      | 1      | -      | -     
Deception      | 0      | 1      | -      | -     
Insight        | 0      | 1      | -      | -     
Intimidation   | 0      | 1      | -      | -     
Investigation  | 0      | 1      | -      | -     
Leadership     | 0      | 1      | -      | -     
Medicae        | 0      | 1      | -      | -     
Persuasion     | 0      | 1      | -      | -     
Pilot          | 0      | 1      | -      | -     
PsychicMastery | 0      | 1      | -      | -     
Scholar        | 0      | 1      | -      | -     
Stealth        | 0      | 1      | -      | -     
Survival       | 0      | 1      | -      | -     
Tech           | 0      | 1      | -      | -     
WeaponSkill    | 0      | 1      | -      | -     

## Traits
Name          | Total  | Target | Missed
------------- | ------ | ------ | ------
Conviction    | 1      | -      | -     
Defence       | 0      | -      | -     
Determination | 3      | -      | -     
Influence     | 0      | -      | -     
MaxShock      | 2      | -      | -     
MaxWounds     | 5      | 5      | NO    
Resilience    | 4      | -      | -     
Resolve       | 0      | -      | -     

## XPCost
Name       | Cost
---------- | ----
Attributes | 20  
Skills     | 0   
Total      | 20

If you prefer json instead of markdown, use the --return_json flag:

python xpOptimizer.py --Tier 1 --Strength 3 --MaxWounds 5 --return_json

which will create:

{
  "Tier": 1,
  "Attributes": {
    "Total": {
      "Agility": 1,
      "Fellowship": 1,
      "Initiative": 1,
      "Intellect": 1,
      "Strength": 3,
      "Toughness": 3,
      "Willpower": 1
    },
    "Target": {
      "Strength": 3
    },
    "Missed": []
  },
  "Skills": {
    "Rating": {
      "Athletics": 0,
      "Awareness": 0,
      "BallisticSkill": 0,
      "Cunning": 0,
      "Deception": 0,
      "Insight": 0,
      "Intimidation": 0,
      "Investigation": 0,
      "Leadership": 0,
      "Medicae": 0,
      "Persuasion": 0,
      "Pilot": 0,
      "PsychicMastery": 0,
      "Scholar": 0,
      "Stealth": 0,
      "Survival": 0,
      "Tech": 0,
      "WeaponSkill": 0
    },
    "Total": {
      "Athletics": 3,
      "Awareness": 1,
      "BallisticSkill": 1,
      "Cunning": 1,
      "Deception": 1,
      "Insight": 1,
      "Intimidation": 1,
      "Investigation": 1,
      "Leadership": 1,
      "Medicae": 1,
      "Persuasion": 1,
      "Pilot": 1,
      "PsychicMastery": 1,
      "Scholar": 1,
      "Stealth": 1,
      "Survival": 1,
      "Tech": 1,
      "WeaponSkill": 1
    },
    "Target": {},
    "Missed": []
  },
  "Traits": {
    "Total": {
      "Conviction": 1,
      "Defence": 0,
      "Determination": 3,
      "Influence": 0,
      "MaxShock": 2,
      "MaxWounds": 5,
      "Resilience": 4,
      "Resolve": 0
    },
    "Target": {
      "MaxWounds": 5
    },
    "Missed": []
  },
  "XPCost": {
    "Attributes": 20,
    "Skills": 0,
    "Total": 20
  }
}

File-based input via command-line

If you have several properties you want to set, or simple want to keep single file for your character, use the json-file with the --file command-line argument. The json file is a simple flat json with at least the tier field. For example if you want to optimize your tier 3 character with

  • Agility 5
  • BallisticSkill 11
  • Cunning 7
  • Deception 8
  • Stealth 12
  • Defence 6 (note the British spelling!)
  • Max Wounds 10

then create a file (e.g. TestChar.json) with the following content:

{
  "Tier": 3,
  "Agility": 5,
  "BallisticSkill": 11,
  "Cunning": 7,
  "Deception": 8,
  "Stealth": 12,
  "Defence": 6,
  "MaxWounds": 10
}

then call (assuming the file is in the same folder as the optimizer script):

python xpOptimizer.py --file TestChar.json

Derivation of the optimization formulas

NOTE: The following section is best view in a latex-capable markdown viewer, otherwise the formulas will not be rendered and be readable only to the Tex-fetishist

Definitions

Name Abbreviation Related Attribute #Affected Skills/Attributes
Tier Tier - 3
Attributes
Agility Agi - 3
Fellowship Fel - 3
Initiative Ini - 3
Intellect Int - 3
Strength Str - 3
Toughness Tou - 3
Willpower Wil - 3
Skills
Athletics Athl Str -
Awareness Awar Int 1
Ballistic Skill BaSk Agi -
Cunning Cunn Fel -
Deception Dece Fel -
Insight Insi Fel -
Intimidation Inti Wil -
Investigation Inve Int -
Leadership Lead Wil -
Medicae Medi Int -
Persuasion Pers Fel -
Pilot Pilo Agi -
Psychic Mastery PsMa Wil -
Scholar Scho Int -
Stealth Stea Agi -
Survival Surv Wil -
Tech Tech Int -
Weapon Skill WeSk Ini -
Traits
Conviction Conv Wil -
Defence Defe Ini - 1 -
Determination Dete Tou -
Influence Infl Fel - 1 -
Max Shock MaSh Wil + Tier -
Max Wounds MaWo Tou + 2 * Tier -
Passive Awareness PaAw Awareness / 2 -
Resilience Resi Tou + 1 -
Resolve Reso Wil - 1 -
Wealth Weal Tier -
Name Symbol
Attribute
Names $A = \left{Agi, Fel, Ini, Int, Str, Tou, Wil\right}, |A|=7$
Rating $r_a \in \left{r \in \mathbb{N}: 1 \leq r \leq 12\right}, a \in A$
Ratings (Set) $R_A = \left{r_a : \forall a \in A\right}$
Ratings (Vector) $\vec{r}A = \left(r{Agi}, r_{Fel}, r_{Ini}, r_{Int}, r_{Str}, r_{Tou}, r_{Wil}\right)^T$
Skill
Names $S = {Athl, Awar, BaSk, Cunn, Dece, Insi, Inti, Inve, Lead, Medi, Pers, Pilo, PsMa, Scho, Stea, Surv, Tech, WeSk}, |S|=18$
Rating $r_s \in \left{r \in \mathbb{N}: 0 \leq r \leq 8\right}, s \in S$
Ratings (Set) $R_S = \left{r_s : \forall s \in S\right}$
Ratings (Vector) $\vec{r}S = \left(r{Athl}, r_{Awar}, r_{BaSk}, r_{Cunn}, r_{Dece}, r_{Insi}, r_{Inti}, r_{Inve}, r_{Lead}, r_{Medi}, r_{Pers}, r_{Pilo}, r_{PsMa}, r_{Scho}, r_{Stea}, r_{Surv}, r_{Tech}, r_{WeSk}\right)^T$
Overall
Target values $\vec{b}, b_i \in \mathbb{N}_0, |\vec{b}|_0 \geq 0$, can be defined for skill & property values (except Wealth since Tier is fixed & passive awareness since it is derived from awareness)

Cost functions

XP Cost Symbol Formula Range Note
Attribute (cumulative) $c_A\left(r_a\right)$ $(k - 1) \cdot (k + 2) + 2.5 \cdot (r_a - k) \cdot \left(r_a + k - 3 \right),~~k = \min(r_a, 3)$ $\left[0,280\right]$ See below
Skill (cumulative) $c_S\left(r_s\right)$ $\sum^{r_s}_{i = 1} 2i \Leftrightarrow r_s^2 + r_s$ $\left[0, 72\right]$ Rule of Triangular Numbers

XP cost for attributes

The attribute cost is originally given as table:

$r_a$ $c_A(r_a)$ $\Delta c_A(r_a)$ $\Delta^2 c_A(r_a)$
1 0 0 0
2 4 4 4
3 10 6 2
4 20 10 4
5 35 15 5
6 55 20 5
7 80 25 5
8 110 30 5
9 145 35 5
10 185 40 5
11 230 45 5
12 280 50 5

The incremental attribute cost in tabular form can be rewritten as: $$ \Delta c_A\left(r_a\right) = \begin{cases} 0 & \text{if } r_a = 1 \ 2r_a & \text{if } r_a \in {2, 3} \ 5 \cdot (r_a - 2) & \text{if } r_a \geq 4 \ \end{cases} $$

In the following, we will use the rule for Triangular Numbers, which is given for the range $\left[1, b\right], b \in \mathbb{N}1$ by: $$ \sum^{b}{i = 1} i = \frac{b \cdot (b + 1)}{2} $$

and can be extended to arbitrary ranges $\left[a + 1, m = a + b\right], a \in \mathbb{N}0$ by: $$ \begin{aligned} \sum^{m}{i = a + 1} i &= \sum^{m}{i = 1} i &- &\sum^{a}{i = 1} i \ &= \frac{m \cdot (m + 1)}{2} &- &\frac{a \cdot (a + 1)}{2} \ \end{aligned} $$

which, when resolving $m = a + b$, is equal to: $$ \sum^{a + b}_{i = a + 1} i = \frac{b \cdot (b + 2a + 1)}{2} $$

The switch criterion between the cases of the incremental attribute cost can be defined as: $$ k = \min({r_a, 3}) $$

The cumulative attribute cost is given by: $$ c_A\left(r_a\right) = \sum^{r_a}_{i = 1} \Delta c_A\left(r_a\right)\ $$

which, using the switch criterion and the rule for Triangular Numbers, can be rewritten asy: $$ \begin{aligned} c_A\left(r_a\right) &= 0 + \sum^{k}{i = 2} 2i &+ &\sum^{r_a}{i = k + 1} 5 \cdot (r_a - 2) \ &= 0 + 2\sum^{1 + (k - 1)}{i = 1 + 1} i &+ &5 \cdot \left(\sum^{k + (r_a - k)}{i = k + 1} r_a - \sum^{r_a}_{i = k + 1} 2 \right) \ &= 2 \cdot \frac{(k - 1) \cdot ((k - 1) + 2 + 1)}{2} &+ &5 \cdot \left(\frac{(r_a - k) \cdot ((r_a - k) + 2k + 1)}{2} - 2 \cdot (r_a - k) \right) \ &= (k - 1) \cdot (k + 2) &+ &2.5 \cdot (r_a - k) \cdot \left(r_a + k - 3 \right) \end{aligned} $$

which, when resolving the switch criterion, results in the alternate form: $$ c_A\left(r_a\right) = \begin{cases} (r_a - 1) \cdot (r_a + 2) & \text{if } r_a \leq 2 \Rightarrow k = r_a \ 2.5 \cdot \left( r_a \cdot (r_a - 3) + 4 \right) & \text{if } r_a \geq 3 \Rightarrow k = 3 \ \end{cases} $$

Total XP cost

The total cost is given by: $$ \begin{aligned} C\left(\vec{r}A, \vec{r}S\right) &= \sum^{|A|}{a = 1} c_A\left(r_a\right) &+ &\sum^{|S|}{s = 1} c_S\left(r_s\right) \ &= \sum^{|A|}{a = 1} \left( (k - 1) \cdot (k + 2) + 2.5 \cdot (r_a - k) \cdot \left(r_a + k - 3 \right) \right) &+ &\sum^{|S|}{s = 1} r_s \cdot (r_s + 1)\ \end{aligned} $$

Problem statement

$$ \begin{aligned} \text{minimize } & C\left(\vec{r}_A, \vec{r}_S\right) \ \text{subject to } & M_A \cdot \vec{r}_A + M_S \cdot \vec{r}_S + \vec{c}=\vec{b} & &\text{target values} \ \text{and } & | \vec{r}_S |_0 \geq | \vec{r}S |\infty & &\text{"tree of learning"} \ \end{aligned} $$

with the maximal set of constraints for the target values given by: $$ \begin{matrix} Athl \ Awar \ BaSk \ Cunn \ Dece \ Insi \ Inti \ Inve \ Lead \ Medi \ Pers \ Pilo \ PsMa \ Scho \ Stea \ Surv \ Tech \ WeSk \ \ Conv \ Defe \ Dete \ Infl \ MaSh \ MaWo \ Resi \ Reso \ \end{matrix} \left( \begin{matrix} 0 & 0 & 0 & 0 & 1 & 0 & 0 \ 0 & 0 & 0 & 1 & 0 & 0 & 0 \ 1 & 0 & 0 & 0 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 & 0 & 0 & 1 \ 0 & 0 & 0 & 1 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 & 0 & 0 & 1 \ 0 & 0 & 0 & 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 & 0 & 0 & 0 \ 1 & 0 & 0 & 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 & 0 & 0 & 1 \ 0 & 0 & 0 & 1 & 0 & 0 & 0 \ 1 & 0 & 0 & 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 & 0 & 0 & 1 \ 0 & 0 & 0 & 1 & 0 & 0 & 0 \ 0 & 0 & 1 & 0 & 0 & 0 & 0 \ \ 0 & 0 & 0 & 0 & 0 & 0 & 1 \ 0 & 0 & 1 & 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 & 0 & 1 & 0 \ 0 & 1 & 0 & 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 & 0 & 0 & 1 \ 0 & 0 & 0 & 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 0 & 0 & 0 & 1 \ \end{matrix} \right) \cdot \vec{r}{A} + \left( \begin{matrix} \ \ \ \ \ \ \ \ \ \mathbf{I}{|S|}\ \ \ \ \ \ \ \ \ \ \ \ \ \mathbf{0}\ \ \ \ \ \end{matrix} \right) \cdot \vec{r}{S} + \left( \begin{matrix} \ \ \ \ \ \ \ \ \ \vec{0} \ \ \ \ \ \ \ \ \ \ 0 \ -1 \ 0 \ -1 \ Tier \ 2 \cdot Tier \ 1 \ -1 \ \end{matrix} \right) = \left( \begin{matrix} b{Athl} \ b_{Awar} \ b_{BaSk} \ b_{Cunn} \ b_{Dece} \ b_{Insi} \ b_{Inti} \ b_{Inve} \ b_{Lead} \ b_{Medi} \ b_{Pers} \ b_{Pilo} \ b_{PsMa} \ b_{Scho} \ b_{Stea} \ b_{Surv} \ b_{Tech} \ b_{WeSk} \ \ b_{Conv} \ b_{Defe} \ b_{Dete} \ b_{Infl} \ b_{MaSh} \ b_{MaWo} \ b_{Resi} \ b_{Reso} \ \end{matrix} \right) $$

About

No description or website provided.

Topics

optimization minlp rpg-tool gekko wrathandglory wrath-and-glory

Resources

Readme
Activity

Stars

2 stars

Watchers

2 watching

Forks

0 forks
Report repository

Releases 3

REST endpoint with logging Latest
Mar 8, 2021
+ 2 releases

Packages

No packages published

Languages