Monthly Archives: February 2021

Monopoly Hex Flower Game Engine

A little thought experiment … can you Hex Flower up the game Monopoly?

Roughed this out – and I’m not sure about the split hexes yet (and the train stations need work). I would fancy this whole thing up, but there is something else I should be doing … better get back to that then! 

Alternative Monopoly game board:  

Monopoly Hex Flower Game Engine Concept

Colours came out a bit funny so here’s a key:
Left column: Yellow; Free Parking; Orange
Second column: C.Chest; Visiting Jail; Chance; Taxes
Middle column: Pink; Brown; Go; Light Blue; Dark Blue
Third column: Utilities; C.Chest; Train Stations; Chance;
Right column: Green; Go to Jail; Red 

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InHotS the cover imageMe on DriveThru; at the moment I’m mainly pimping my procedural:
:: High Seas ‘Hex Crawl’ – In the Heart of the Sea,
:: Wilderness Hex Crawl – In the Heart of the Unknown,
:: Dungeon/network generator – In the Heart of the Delve & Dangerous

Large D6 dice pools | adding more swing with ‘harmonic’ equivalents

A while ago I posted this: Non-Homogenous Random Table and this on ‘split-dice‘ and even more here. The below builds on some of these ideas.

Content warning
If you are a mathematician the words I use below are bound to be formally inaccurate, sorry!  If you are sane, the below content is more than likely to be extraordinarily unnecessary, and probably useless, except perhaps in the most specific kinds of circumstances, sorry!

Thank you for making this lunacy possible (<– please consider donating to this great resource).

I did this thinking, and I decided to post it here in case anyone ever wonders about the same, at some point, and finds this post, however unlikely that might be …

Never to be deterred by a hopeless cause, I began to wonder about D6 bell curves using lots of D6s.

I think this began because I supposed that dice pool games using large dice pools sum all of these D6s, but upon reflection, I suspect that is not the case.

Anyway … I began to think that the result of summing lots of D6s would be boring because it’s bound to return mostly the same number, i.e. the peak area of the curve. So, how to add more ‘swing’ to the curve, but to retain the same overall range?

To cut a long story short, there are sort of “harmonics”, where you can (i) roll the same number of dice and (ii) the overall result range is the same, but (iii) where different groups of dice are rolled … these different sets give different probability profiles.

For example:

(i) Homogeneous D6 dice set (ii) ‘Harmonic’ equivalent  set Result range:
2D6 D8+D4 both give 2-12 and use 2 dice
3D6 D10+2D4 both give 3-18 and use 3 dice
4D6 D12+3D4 both give 4-24 and use 4 dice
8D6 D20+7D4 both give 8-48 and use 8 dice

The rub here is that using split dice (i.e. “harmonic” dice sets) give bell curves with more swing than a regular homogenous dice sets. The bigger the gap between the dice sizes in the non-homogeneous dice, the more swing there is. Below compares (i) D6 sets and (ii) their ‘harmonic’ dice set equivalents and (iii) overlapping the ends of (i) and (ii) for ease of comparison:


(i) Anydice: output 2d6 output 3d6 output 4d6 output 8d6


(ii) Anydice: output d8+d4 output d10+2d4 output d12+3d4  output d20+7d4


(iii) Anydice: output 2d6 output 8d6 output d8+d4 output d20+7d4

So, if you want to flatten a D6 bell curve, simply replace the number of dice with one of the non‑homogenous equivalents above.  I won’t bore you with more graphs (at least for now), but take my word for it, the biggest D-number you can introduce in the ‘harmonic dice set’,  the bigger the flattening effect. So, if you want to replace 8d6 with a ‘harmonic set’ equivalent you are better off using D20+7D4 rather than two sets of D12+3D4 (see table above for these ‘harmonic’ equivalents).

So, we have 2D6, 3D6, 4D6 and 8D6 covered (i.e. the rolls where there are ‘harmonic’ equivalents) – but what to do with 7D6? Good question. You could use D12+3D4 plus 3D6 (i.e. replacing the biggest harmonic set). You could even go on to replace the 3D6 part of D12+3D4 plus 3D6 with the harmonic set D10+2D4 (but this extra tweak adds little benefit).

But, there is an even stronger way to flatten the curve: use D20+7D4 and subtract D6. What we are doing here is going to the next largest ‘harmonic’ (equivalent to 8D6) – but to bring the dice range back into alignment with 7D6, we are subtracting a D6. Below shows this:  the top line is 7D6, the middle line is D12+3D4+3D6 (and D12+3D4+D10+2D4) and the bottom line is using this subtraction method:


Anydice: output 7d6 output d12+3d4+3d6 output d12+3d4+d10+2d4  output d20+7d4-d6.

In fact, this ‘subtraction’ method can be used even a few steps further backwards,  before it starts to give ‘wayward’ results. Here’s (i) homogeneous D6’s (ii) non-homogenous dice to replace the largest D6 set (iii) the D20+7D4 plus/minus D6s to give/restore the appropriate dice number:


(i) Anydice: output 2d6 output 3d6 output 4d6 output 5d6 output 6d6 output 7d6 output 8d6 output 9d6 output 10d6


(ii) Anydice: output d8+d4  output d10+2d4 output d12+3d4 output d12+3d4+d6 output d12+3d4+2d6 output d12+3d4+3d6 output 1d20+7d4 output 1d20+7d4+d6 output 1d20+7d4+2d6


(iii) Anydice: output d20+7d4-6d6 output d20+7d4-5d6 output d20+7d4-4d6 output d20+7d4-3d6 output d20+7d4-2d6 output d20+7d4-d6  output 1d20+7d4 output 1d20+7d4+d6  output 1d20+7d4+2d6

Basically, the D20+7D4 plus/minus D6s is the strongest way to flatten the curve, but (obviously) is quite complex, and after subtracting more than 2 or 3 D6s starts to give results that extend beyond the normal range and/or can give a negative number, i.e.:

d20+7d4 plus/minus D6s method In place of: % Exceeds end ranges
(doubled to cover both ends)
% which is Zero or less  
output d20+7d4-6d6

output d20+7d4-5d6

output d20+7d4-4d6

output d20+7d4-3d6

output d20+7d4-2d6

output d20+7d4-d6

output 1d20+7d4

output 1d20+7d4+d6

output 1d20+7d4+2d6










25.16    (50.32)

15.46    (30.92)

7.84      (15.68)

2.89      (5.78)

0.6        (1.2)

0.04      (0.08)






So you can subtract about 3D6s before the subtraction method gives an appreciable chance that a result will extend beyond the normal range, or give a number zero or less

The big picture is you can start from a bigger ‘harmonic’ set and subtract one or more D6s, as opposed to starting from a smaller harmonic and adding one or more D6s … if you can tolerate all the mathematical jiggery-pokery that is!  Phew.

A final piece of craziness, sort of building on this idea – if you’ve ever wanted a D100 bell curve, well you could try 5D20-20D10+108!


Anydice: output (5d20-20d10)+108

This curve is centred between 50 and 51 and the chance of exceeding 100 or being below 0 is 0.25% each way.

Did you really read all that? Well take a Chuffty Badge you lunatic!

One day, this might be of interest to someone!

– – –

InHotS the cover imageMe on DriveThru; at the moment I’m mainly pimping my procedural:
:: High Seas ‘Hex Crawl’ – In the Heart of the Sea,
:: Wilderness Hex Crawl – In the Heart of the Unknown,
:: Dungeon/network generator – In the Heart of the Delve & Dangerous

Random Social Interaction Hex Flower Generator

Download a (readable)  image_preview .pdf version

I’ve been interested in making a random social interaction generator for a little while, perhaps part of a random mystery generator. Lot’s of ideas but nothing concrete. So, recently, I saw a few things that made me think of this … it might need some work, but I figured I’d put it out there and get some feedback.

The main idea is to use a Hex Flower (HF) as a frame to hold NPCs in place and then use rules to link them. So, in this case the HF is doing something a little different to my ‘normal’ HFs.

I had a go at typing this idea up in WordPress’s ‘WYSIWYG’ editor, but life is too short for that. So, here is an example of a social Interaction HF generated using this method, taken from the pdf document:

Random Social Interaction Hex Flower dt

Of course, people are free to create social interaction types that fit their game.

So, could this be done just using normal random tables – sure. But, I quite like that the information is presented visually as a sort of flow/information diagram.

If you want to see how this is done here’s a screen clip of the template, but a more readable and fuller  image_preview .pdf version is PWYW on DriveThruRPG.

Random Social Interaction Hex Flower Generator Cover page

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What’s a Hex Flower Game Engines anyway ?

I’ve had quite a few new visitors to my blog recently (probably related to the Planar Compass: Issue 2 Kickstarter for Zine Quest 3), looking at my Hex Flower Game Engines (HFGE).

Hex Flower Game Engines are like a random table but with a ‘memory’ (well sort of). You can see some HFGE examples here and here.

TL:DR = Basically, in a HFGE the next random event is guided by the last event (AKA this is the ‘memory’). This can lead to continuity in the random events (think transitioning weather). Navigation rules can also be used to skew the events in a preferred direction (e.g. towards mild weather) but still allowing for some chaos in the system (e.g. a sudden thunderstorm).

I decided to bring together a lot of what I’ve learnt about Hex Flower Game Engines and their design in one place, in a downloadable .pdf document.

This ‘pay what you want’ metal best seller can be downloaded from here: image_preview  Link

This document is not intended to be prescriptive, but it might be a good jumping off point if you are interested in the topic and/or want to make your own Hex Flowers.

Screen clipping:
Here’s an outline image of the document:

Overview image.png

I have also prepared a 12 part YouTube ‘talk through‘ video, where I talk through the PDF document page-by-page.

Cover image:

Hex Flower Game Engines Cover

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Me on DriveThruDriveThru; at the moment I’m mainly pimping, well this ^

What floats your Astral boat ? | Planar Compass 2

This is now Live on Kickstarter

I’m excited to let people know that I’m collaborating on Issue 2 of Planar Compass for Zine Quest 3, which is written for OSE.

PC I2 ZQ3e

I’m working on some Hex Flower goodness to navigate/traverse the astral sea and on a living dungeon.



See Issue 1 (where it all began with Zine Quest 2)

PC issue 1

For a video review of Issue 1, please see Questing Beast
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