‘Caterpillar Method’ for Character Stat Generation

:: pdf version of this method: Link

Follow up post: Here (lumpy in a good way)

Background
I saw this blog post (http://tarsostheorem.blogspot.com/2020/04/dice-are-statblocks.html) and liked it, and it made me think of the below … (for a brief moment it was as if G+ was alive again).

New method to generate standard D&D stats using one throw of the dice
Bored of the old ways? Got a sore wrist? Hate your DM … well we’ve got you covered!
Generate the standard six D&D stats using one throw of 3D6 (plus some rules).

Rule Set 1: Mimicking a traditional 6×3D6 method:
Roll 3D6, and quickly gather them into a ‘caterpillar’ shape:

TLDR: Add up the exposed faces; except the end cube where there is a subtraction.

Stat 1 = add up the front face (i.e. 1+6+4)=11
Stat 2 = add up the top face (i.e. 2+ 4+1)=7
Stat 3 = add up the rear face (i.e. 6+1+3)=10
Stat 4 = for the left-most cube (head of the caterpillar) add up all exposed faces; including the left-most face (i.e. 1+2+6+4)=13
Stat 5 = for the right-most cube (bottom of the caterpillar) as above, but this time subtract the right-most face (i.e. 4+1+3-2)=6
Stat 6 = for the central cube add up all exposed faces (i.e. 6+4+1)=11

PS – this is method is not suitable for 3D6 down the line, unless you randomise the order of ‘the line’ first.

The Stats
I did a ‘brute force’ Excel simulation, and I can’t be certain if the results are lumpy but the lumps are hiding in the averaged-out results, but anyway, this is what I got (for about 24,000 stats, about 4,000 PCs):

The green line is what you expect using a standard 6x3D6 system, and the blue line is my Excel simulation (fingers crossed I didn’t screw something up). So, the ‘3D6 caterpillar method’ using Rule Set 1 fits the standard 6×3D6 curve quite well. There are two weird artefacts at 7 and 14. I twiddled with the rules but this seems to be the best overall compromise for result vs rule simplicity. Also 7 and 14 in most games do not give a bonus or penalty.

But if you’re not a stickler for 3D6, then there is this for 4D6(drop the lowest):

Rule Set 2: Mimicking the traditional 6x4D6 and drop the lowest roll method:
Again, roll 3D6, quickly gather them into a ‘caterpillar’ shape:

TLDR: Add up the exposed faces; except the middle cube where it might be a 14

Stat 1 = add up the front face (i.e. as above) i.e. 11
Stat 2 = add up the top face (i.e. as above) i.e. 7
Stat 3 = add up the rear face (i.e. as above) i.e. 10
Stat 4 = for the left-most cube (caterpillar’s head) add all the exposed faces (i.e. as above) i.e. 13
Stat 5 = for the right-most cube (caterpillar’s bottom) add all the exposed faces (i.e. 4+1+3+2)=10
Stat 6 = for the centre cube add all the exposed faces (i.e. as above) – but if the front face is a 4, 5 or 6, add the bottom face (spoiler – this will always give a 14)

The Stats
Again, I did a ‘brute force’ Excel simulation, and this is what I got:

The red line is what you get with 6x4D6 (i.e. and with drop the lowest result) and the blue line is my Excel simulation (again fingers crossed I didn’t screw something up). The ‘3D6 caterpillar’ using the above rules follows this curve surprisingly well. There are not even substantial artefacts.

Rule Set 3: Simple method:
Roll 3D6, and quickly gather them into a ‘caterpillar’ shape:

TLDR: Add up the exposed faces; except the end cube where there is a subtraction.

Stat 1 = add up the front face (i.e. 1+6+4)=11
Stat 2 = add up the top face (i.e. 2+ 4+1)=7
Stat 3 = add up the rear face (i.e. 6+1+3)=10
Stat 4 = for the left-most cube (head of the caterpillar) add up all exposed faces; including the left-most face (i.e. 1+2+6+4)=13
Stat 5 = for the right-most cube (caterpillar’s bottom) add all the exposed faces (i.e. 4+1+3+2)=10
Stat 6 = for the central cube add up all exposed faces (i.e. 6+4+1)=11

The Stats
It would appear you’d get a PC with stats somewhat between 3D6 and 4D6 (drop the lowest).

How the 3 Rules sets stack up

Rule Set 1 – mimicking 3D6

Rule Set 3 – hydrid ‘simple’ method

Rule Set 2 – mimicking 4D6 (drop the lowest)

Green curve: 3D6, Red curve: 4D6 (drop the lowest); Blue curve: By Rule set

OK, well that’s it.
:O|

DISCLAIMER: If your character sucks, it’s your fault

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