I'm working with my friend on a new (we think) dice system for a homebrew RPG (soon to hit the TTRPG world by storm, no doubt). A design goal is that players' statistical success rate at common-but-difficult tasks, appropriate to their experience/level, is about 75%*. I'm wondering if there is a way, given the Difficulty of a roll, to determine which pool(s) of dice would be suitable to succeed at it more often than not.
Alright so, obviously, you need to know what our plan is. Any likeness to other dice systems (I've noticed some corollaries to Genesys myself) is completely coincidental. This is still very much in production, but the general rules/expectations are:
- creatures form a pool of dice from various aspects such as ability score, weapon/tool quality, and skill(s)
- die pools range from 2 dice minimum to probably around 7
- pools are comprised of d4-d12, increasing as a character invests in that aspect
- the pool is rolled and a tally is made, counting numbers of successes against the roll's Difficulty
- a 4-7 is 1 Success
- an 8-11 is 2 Successes
- a 12 is 3 Successes
- difficulties are expected to range from 1-8 or so given the typical output of the above standards
For example, a heroic army commander making an attack might roll 1d10 for their strength, 1d8 for being in melee combat, 1d8 for their spear quality, 1d12 for their legendary prowess with spears, and 1d6 for their knowledge of human anatomy. They end up with a pool of 1d12+1d10+2d8+1d6. Rolling for multiples of 4, they have a good chance (~86%) to roll at least 3 Successes and a decent chance (~67%) for 4+. They could even get exceptionally lucky and roll in the ballpark of 8-10 with exceptionally low (less than 3%) odds.
I made an anydice program to check the expected output of various pools using the system. I like a lot of aspects about it, but I'm finding that I'm not sure how to reverse-engineer it. I could keep making various pools until I find that 75-ish percent that I'm looking for, for various Difficulties, but I'm interested if there is a faster way.
*This is an attempt to overcome observation bias as much as it is to ensure parties are successful in their quests and such.