d6+d3 - And Other Cursed Dice Curves

Nova over on Playful Void has a lovely little series called "Make Dice Work For You" - It's an excellent primer on dice, maths and using probability curves that I think every budding designer should read. As a bit of a probability sicko myself, I thought I'd share some of the more... Unconventional curves I'm using in my Sims-like skirmish game Project Tears. So without further ado, let's discuss the d6+d3 and other cursed dice curves...

Working in a d6-only system (as many skirmish games are) presents some unique challenges when writing random tables; Namely that you only meaningfully have access to a d6, d3 (d6, half, rounding up) and d2 (d6, divide by three, rounding up) - Meaning if you want to have a table with more than 6 results you need to get creative. You can simulate a d12 table by having d2d6 tables (as per equal opportunity dice - not to be confused with the weighted 11 result 2d6 table) and similarly you can get 36 results by doing d66 - Most of you have probably already encountered one such table before. But what if 6 results is too few and 11 or 12 results is too many? This is where the deeply cursed d6+d3 and its incredibly satisfying bell-curve comes in:

As we can see, a d6+d3 gives us 8 results, where the four most likely results are three times as likely to come up as the two least likely results, plus we have two more results that are a bit in between. This gives us a satisfying array of 4 common events, 2 semi-uncommon events and 2 rare events with those 2 rares being ever so slightly more common that the 20 or 1 on a d20 (5% chance). 

What does this look like in practice? Currently I'm using it for my "Strains" and "Scars" two "Bad Stuff Happens" tables for pilots whose M-ECs wreck or who suffer an emotional breakdown from losing all their Heart (HRT):

This allows me to have more unique and punishing results like a "Total Rewrite" or losing an eye feel legitimately rare in comparison to other more common strains and injuries. It also keeps the table small enough to fit on a half page spread, but big enough to feel varied (this is why I write in the layout ~~).

Its become a running gag with my friends that whenever I can't decide how big to make a roll table they remind me "why not d6+d3" and more often than not they're right! 6 results seems too few, and 12 too many, but 8? With a nice bit of weight on either end? That's just right ~ The main draw back of a d6+d3 table is there's no way in hell you're going to be able to sensibly add "advantage" and any +1/-1 modifiers really throw weight around pretty quickly. The d6+d3 is amazing, but must remain unmodified to be sensible. ***UNLESS [*1]

What about our big ol' d66 table? What if we want a whole bunch of results but 36 is too many? Enter the equally cursed and interesting "d66 read the highest first" table which offers up 21 unique results, 6 of which (the doubles) will be half as likely as the rest. This allowed me to have character "keys" (their personality + skills) that could be rarer and more powerful, while still having a fairly large roster of results - Here's that in practice:

This also was a space consideration to ensure all results + instructions could fit onto one readable spread! These are just a few of the stranger, yet satisfying, dice curves you can get in a d6-only system to add just the lightest touch of weight to your random tables ~

Are there any dice curves that live rent free in your brain?

[*1 : Bsky User Emmo Bee suggested and advantage/disadvantage where-in during advantage the lowest d6 is read as the d3 and during disadvantage the highest rolling d6 is read as the d3! Pretty neat! It needs sufficient explanation that I don't think I'd necessarily use it in a game unless d6+d3 was part of the primary resolution method, but I by and large dig it!]