Is a D20 ability/skill test system better than a 3D6 test system?
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The full article on this (with numbers) can be found here:
& magazine #14 – Animal Companions;
please see pages 29 to 35
TLDR summary
1) For a ‘mundane tasks’ (where even competent (or good) characters could pass or fail) use roll-under using D20
2) For ‘genius task’ (needing genuine skill or ability) use roll-under using 3D6, or if especially especially difficult 4D6.
Below is a snippet for the core idea and some examples:
Basis: Comparing the two graphs (linear vs not):
Examples of possible applications:
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At the moment I’m mainly pimping my procedural adventure ‘Carapace‘ about a giant ant colony
and my ‘1998 Dungeon‘.
Goblin's Henchman 
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Also see http://blessingsofthedicegods.blogspot.com/2018/07/flexible-reaction-rolls.html for how you can use a similar idea to vary the reaction roll used by a variety of games. Rather than a modifier, positive or negative added to a 2d6 roll: vary the dice – see the post for a better discussion.
I also like using d4+d6+d8, because I like the method zzarchov came up with for a d8 table which had results broken down by a further d6 and d4 table, plus special results if you got doubles (1,1 or 2,2, or… up to 6,6) , triples(1,1,1 or 2,2,2 etc – up to 4,4,4), or a run (1,2,3 or 2,3,4 etc up to 4,5,6).
If I added a d10 into the mix, I could get so many combinations off the one throw. Aside from the d4+d6+d8 already mentioned, I’d have d10, d20, d30, d40, d60, and d80 results easily possible.
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