Monthly Archives: February 2022

Thinking outside the Hex | ‘Hex Flower’ theory stuff

As many people following this blog will know, I’ve been making Hex Flowers with a navigation mechanic based on summing 2D6 (corresponding % probabilities shown on the right side) i.e.:


This ‘Navigation Hex’ being (part of) the rules for moving around a Hex Flower like this one:


I had a discussion with Jake Eldritch  (I will try and find the link) online about this idea, and concluded that 2D6 with a ‘disadvantage’ mechanic (i.e. roll 2 x D6 and take the lowest roll, e.g. a roll of 3 and 5 gives a 3 as the result) could give you this kind of ‘ Navigation Hex’ with fewer numbers around the edge:

22 b

Rather amazingly (to me anyway), it appears to have the same probability structure as above when I sum 2D6. You could argue that the ‘maths’ is simpler with the ‘disadvantage’ method, although not massively so. Here’s the ‘Anydice’ stats: 


But … recently it did make me wonder about other shapes, like an octagonal array with an octagonal ‘Navigation Oct’ or square array with a ‘Navigation Square?’ (or larger tiling shapes) – where the ‘disadvantage’ method might be simpler and more intuitive than summing two polygonal dice.

Here’s an example of an octagonal ‘flower’ with an octagonal “Navigation Hex”:


Summing 2D8 would give 16 at the top of the ‘Navigation Oct’,  then working clockwise around the ‘Navigation Oct’: 2-3, 4-5, 6-7, 8-9, 10-11, 12-13 and 14-15. That’s surely got to be harder than using the ‘disadvantage’ mechanic shown above. And, unless I’ve made an error gives the same probability structure.  

Just ‘noodling’ about the associated edge rules with the coloured arrows. Of course an ‘advantage’ mechanic could be used (instead of a disadvantage mechanic) to invert the probability structure.

For good form sake, here’s a 16 grid ‘flower’ using a 2D4 with a disadvantage mechanic (if you like a tip on your ‘flower’, perhaps use diamonds not squares):


… or even a square grid but with 8 possible directions of travel (including diagonals):


This post is more theoretical than anything, but does make using other shapes (other  than hexagons) to make flowers more accessible (I think). I have not worked out how strong the probability bias is (yet) for the octagonal and square “Navigation Hexes”, but intuition tells me, the more faces there are the less severe the probability bias.

Ok, that’s it.


To read up of Hex Flowers (there may be a pop quiz) please see my Hex Flower Cookbook where I discuss Hex Flower Game Engines and some background and possible uses 

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