Rubik’s Cube | revisted

I made a blog post about using a Rubik’s cube to generate charater stat’s here. I think it’s a neat method. A free .pdf is on DriveThruRPG.

BUT, ever tumble down a rabbit hole?

I got thinking more about the Rubik’s cube and realised that there are 54 squares on the cube (i.e. 6 x 9), and that this is a quarter of 216; 216 of course being the number of possible results of rolling 3D6 (i.e. 6 x 6 x 6). So, if you drew an X through each square you could populate a cube with 216 options.

Since I could not think of an elegant way of exploiting this perfect coincidence, I started to think of a way to make use of the near symmetry of these numbers and came up with this idea:

1. Rubik’s cube is a 3D6

• You mark up the cube in the below fashion
• Note, two of the central squares have modifiers (i.e. -1 and +1)
• You thoroughly jumble the cube, and whatever number is in the top left-hand corner (as you hold it) is the ‘roll’
• Apply the modifier in the central square (if there is one).
• Do this 6 times, one for each stat.

 

I’ve grouped these numbers in sets to make marking up the cube easier.

Probability analysis:

	% Likelihood
Result	3D6 method	Rubik’s Cube method
3	0.5 (1 of 216)	0.3  (1/6 of 48)
4	1.4	1.7  (5/6 of 48)
5	2.8	2.1  (1 of 48)
6	4.6	4.2 (2 of 48)
7	6.9	6.3  (3 of 48)
8	9.7	10.4  (5 of 48)
9	11.6	12.5  (6 of 48)
10	12.5	12.5  (6 of 48)
11	12.5	12.5  (6 of 48)
12	11.6	12.5  (6 of 48)
13	9.7	10.4  (5 of 48)
14	6.9	6.3  (3 of 48)
15	4.6	4.2  (2 of 48)
16	2.8	2.1  (1 of 48)
17	1.4	1.7  (5/6 of 48)
18	0.5	0.3  (1/6 of 48)

If we plot the probability of the results using the 3D6 method (orange spots) vs the Rubik’s cube method (blue diamonds) above we get this:

So, this Rubik’s cube method matches the probability curve of the 3D6 method fairly closely.

Why would you even consider ‘rolling’ a character this way  … well, that’s your problem.

I suppose it could used as part of an interesting 3D6 saving throw mechanic. To add a bit of (alternative) drama.

2. Rubik’s cube is a 4D6 (drop the lowest)

• You mark up the cube in the below fashion
• Note, four of the central squares have modifiers (i.e. -1, -2, +1 and +2)
• You thoroughly jumble the cube, and whatever number is in the top left-hand corner (as you hold it) is the ‘roll’
• Apply the modifier in the central square (if there is one).
• There’s a tiny/one chance of getting a 19 … keep it, or knock it back to an 18
• Do this 6 times, one for each stat.

If we plot the probability of the results using the 4D6 (drop the lowest) method (green line) vs the Rubik’s cube II method (purple line) above we get this:

For comparison, 3D6 vs 4D6 (drop the lowest) methods:

Again, this Rubik’s cube method matches the probability curve of the 4D6 (drop the lowest) method fairly closely. Again, I’m not going to tell you how to roll your characters.

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More of my stuff on DriveThruRPG: https://www.drivethrurpg.com/browse/pub/9524/Goblin039s-Henchman