Background
:: 
pdf version of this method: Link
::Original post: Link (with Rule Sets)
:: Follow on post: Link (looking at lumpyness)
Video demo of Caterpillar Method for PC stat generation:
– – –
Me on DriveThru.
Mainly pimping my PWYW one-page procedural dungeon generator using Hex Flower Game Engines:
In the Heart of the Delve and Dangerous.
:: pdf version of this method: Link
I saw this post Dice are Statblocks on the Tarsos Theorem blog. I thought it was super neat and it made me wonder about other possible uses.
Basically – in this method you roll 3D6 and gather them up into a sort of dice caterpillar shape (see blue cubes above).
What is really neat here, is that more than just the top faces of the cubes are being used. The order of the cubes and the orientation of the cubes with respect to each other are also being used. Basically, there is a whole bunch of information being generated when the cubes are simply gathered into a ‘dice caterpillar’. Using all this extra information is a neat idea! Tarsos levels up.
Tarsos’ blog post prompted me to hastily dash this blog post off: Caterpillar Method’ for Character Stat Generation (i.e. a way to make the ‘standard’ 6 stats for a D&D type character with one roll of 3D6 arranged into the caterpillar shape).
That is, in my method you roll 3D6 once and use a ‘Rule Set’ to generate the 6 PC stats. Because, I wanted any PC generated by this method to be ‘reasonable’, I modelled the method against the ‘standard’ 6x3D6 method and got pretty good agreement, on average, over a big set (there is a graph in my post mentioned above).
But, this is a ‘Take 2’ blog post, as I think there is more to say. Specifically, Reddit had more to say (links to follow). I liked what Reddit had to say, so I dug deeper into the system. This system on average gives results that smooth-ish-ly modelled the standard 6x3D6 system … but on an individual basis, the results are lumpy.
But, lumpy in an interesting way. At least I think it is interesting.
Here is a breakdown of the probabilities of each stat, using ‘Rule Set 1’ (see my first post if you want to revisit the Rule Sets):
(dashed lines above are actually not possible, but included to help visulaize)
So, on balance, you should get a fairly playable if not somewhat ‘balanced’ PC, which always gets:
This idea of balanced stats has precedence in systems like Black Hack. In some ways it’s almost a hybrid between random and a ‘point buy’ system, because it has some self-balancing mechanisms baked in.
For example, below are (I believe) the best and worst PC stats you can get (weighted to give 18 or 3s respectively):
*** Reddit suggest that the above numbers shoud in fact be (I need to check my notes, but on the face of it, I think they are correct):
Just to spell it out, there is not even a theoretical way to get a character with 18, 18, 18, 18, 18, 18 (i.e. 3D6s do not have enough 6s on them).
In my original post, to get rolls closer to 6x4D6 drop the lowest, I baiscally had two ‘Heads’ instead of a ‘Head’ and a ‘Tail’. Another way to go would be to allow the player to decide which end is the Head and Tail after rolling.
Personally, I think this idea has ‘legs’ for all sorts of random/solo play RPGing. Time permitting, I’d like to make a random village by caterpillar-ing groups of 2 and/or 3 D6s. Or a random dungeon, rooms generated in the same way. So much information from one roll. The counter weighted faces are especially interesting as you may be able to link one random property to the other in an inverse relationship (or if you invert the table order, in a proportional relationship). And, with my system, I’m not even using all the information (e.g. the Face and Rump ends could be used together on a ‘D66’ table etc.).
– – –
Me on DriveThru.
Mainly pimping my PWYW one-page procedural dungeon generator using Hex Flower Game Engines:
In the Heart of the Delve and Dangerous.
:: 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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Me on DriveThru. At the moment I’m mainly pimping my procedural dungeon generator using Hex Flower game engines: In the Heart of the Delve & Dangerous. It’s PWYW and close to being ‘Silver Best Seller’ on DriveThru.
Goblin's Henchman 