Routes and Routs

Skewed Dice & Nested Tables

Skewed Dice & Nested Tables Skew can be achieved by rolling multiple dice and choosing the highest or the lowest. What if we could get skew with a single roll? Interpret these tables either as lookup tables to be used to transform a conventional d24 to a result from 1-10, or as the number of time a number from 1-10 is repeated on the faces of a custom d24.

Everyone knows what a rainbow looks like, many have heard ROYGBIV. We will use this as a mnemonic device building off 'Red Right Skew'. This would make identifying and grabbing the correct die trivial.

Right Skew, High Kurtosis, Red

rsDie_H 1 2 3 4 5 6 7 8 9 10
1 5 10 15 18 20 21 22 23 24
2 6 11 16 19
3 7 12 17
4 8 13
9 14


Right Skew, Moderate Kurtosis, Orange

rsDie_M 1 2 3 4 5 6 7 8 9 10
1 4 8 12 16 19 21 22 23 24
2 5 9 13 17 20
3 6 10 14 18
7 11 15


Symmetrical, High Kurtosis, Yellow

symDie_H 1 2 3 4 5 6 7 8 9 10
1 2 3 5 8 13 18 21 23
4 6 9 14 19 22
7 10 15 20
11 16
12 17


Symmetrical, Moderate Kurtosis, Green

symDie_M 1 2 3 4 5 6 7 8 9 10
1 2 4 6 9 13 17 20 22 24
3 5 7 10 14 18 21 23
8 11 15 19
12 16


Bimodal Symmetrical Die, Cyan

biDie 1 2 3 4 5 6 7 8 9 10
1 4 7 10 12 13 14 16 19 22
2 5 8 11 15 17 20 23
3 6 9 18 21 24


U-Shaped, Blue

uDie 1 2 3 4 5 6 7 8 9 10
1 6 9 11 12 13 14 15 17 20
2 7 10 16 18 21
3 8 19 22
4 23
5 24


Left Skew, Moderate Kurtosis, Indigo

lsDie_M 1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 7 10 14 18 22
6 8 11 15 19 23
9 12 16 20 24
13 17 21


Left Skew, High Kurtosis, Violet

lsDie_H 1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 8 11 16 21
7 9 12 17 22
10 13 18 23
14 19 24
15 20


Rationale: It is simpler to roll one die and read the result than it is to roll multiple dice and apply a procedure, however simple. This matters if you're doing it frequently. Using tables/custom dice allows tailored distributions and U-shaped distributions, which are hard to achieve with ordinary dice1.

The intended application would be a system for mass combat, where different match-ups between units under different conditions would be given as a matrix and each match-up assigned one of the above dice. You could nest a matrix within the cell of another according to various schemes: Imagine with me a table annexing half your dinner table, where you in a swift motion look up terrain, action, and unit type to know which rainbow-coloured die to grab and roll. Speed! Decision!

TERRAIN Broken Rough Stable
â–¦ â–¦ â–¦


↓


FORCE A \ FORCE B Attack Defend Withdraw
Attack â–¦ â–¦ â–¦
Defend â–¦ â–¦ â–¦
Withdraw â–¦ â–¦ â–¦


↓


ATTACKER \ ATTACKER Peltasts Infantry Cavalry Elephants
Peltasts biDie lsDie_M lsDie_H lsDie_M
Infantry rsDie_M symDie_H lsDie_M lsDie_H
Cavalry rsDie_H rsDie_M uDie symDie_M
Elephants lsDie_M rsDie_H symDie_M biDie


↓


COMBAT RESULT Infantry v Infantry
1 A -3 Rout / B Advance
2 A -3 Recoil / A -1 Advance
3 A -2 Stand Check / A -1 Advance?
4 A -2 Stand / B -1 Stand
5 A -1 Stand / B -1 Stand
6 B -1 Stand / A -1 Stand
7 B -2 Stand / A -1 Stand
8 B -2 Stand Check / A -1 Advance?
9 B -3 Recoil / A -1 Advances
10 B -3 Rout / A Advance


Such dice could be useful for other applications, perhaps rolling for injury with different skews according to different armour types, weather, or random encounter generation.

  1. For a range 1-10 you could, I suppose, roll 2d10 and take the values farthest from 5 or 6, but this reeks of thinking, which should be offloaded maximally to processes.↩