d12 variant

Introduction

This is a variant of the standard d20 system put out by Wizards of the Coast. It came about while I was contemplating combat probabilities — more than that later. Anyways, the system involves rolling 2d12 for the base number rather than d20 — what that does is instead of giving a linear probability scale, a bell shaped distribution. What this does in effect is make easy things easier to do, and hard things harder to do (but not too much more as the max is 24 and getting a 20 is actually slightly easier). I’ll be posting up a table indicating the new probability scale. Now I’ve only run through a minimum of tests, so it’s not fully worked out, but I plan to continue to play with is as it seems to be working well so far.

Probability Tables

 

2D12
Target Number (TN)	%Odds of rolling TN	%Odds of rolling TN or higher
2	0.69444444	100.00000000
3	1.38888889	99.30555556
4	2.08333333	97.91666667
5	2.77777778	95.83333333
6	3.47222222	93.05555556
7	4.16666667	89.58333333
8	4.86111111	85.41666667
9	5.55555556	80.55555556
10	6.25000000	75.00000000
11	6.94444444	68.75000000
12	7.63888889	61.80555556
13	8.33333333	54.16666667
14	7.63888889	45.83333333
15	6.94444444	38.19444444
16	6.25000000	31.25000000
17	5.55555556	25.00000000
18	4.86111111	19.44444444
19	4.16666667	14.58333333
20	3.47222222	10.41666667
21	2.77777778	6.94444444
22	2.08333333	4.16666667
23	1.38888889	2.08333333
24	0.69444444	0.69444444

DC Changes

By using the d12 variant, not only does the proabability curve change from a linear curve to a bell curve, the average roll also increases from 10.5 to 13. This has the effect of making all low DC checks easier to accomplish, and conversely, high DC checks more difficult. Should one wish, the DC’s can be modified to accomodate the change. The following table shows the equivalent DC’s and their chances of success between d20 and the d12 variant.

For Armor Class, a base of 13 instead of 10 is used. Likewise for Spell save DC’s, and other similar mechanics that have a base of 10.