Skewed Dice & Nested Tables

11 May, 2025

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

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

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

1	2	3	4	5	6	7	8	9
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

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

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

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

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

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
	▦	▦	▦

↓

FORCE A \ FORCE B	Attack	Defend	Withdraw
Attack	▦	▦	▦
Defend	▦	▦	▦
Withdraw	▦	▦	▦

↓

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.

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.↩