Monday, April 27, 2020

3d6 vs. AC Hit Rolls

TL; DR: Table of % chances to Hit using various permutations of 3d6 vs. ascending AC 9 to 18, instead of d20.


Av.
Ex Rng
to Hit AC 9
10
11
12
13
14
15
16
17
18
3d6
10.5
8-14
74%
63%
50%
38%
26%
16%
9%
5%
2%
*%
3d6 -1
9.5
7-13
63%
50%
38%
26%
16%
9%
5%
2%
*%
-
3d6 -2
8.5
6-12
50%
38%
26%
16%
9%
5%
2%
*%
-
-
3d6 -3
7.5
5-11
38%
26%
16%
9%
5%
2%
*%
-
-
-
3d6 +1
11.5
9-15
84%
74%
63%
50%
38%
26%
16%
9%
5%
2%
3d6 +2
12.5
10-16
91%
84%
74%
63%
50%
38%
26%
16%
9%
5%
3d6 +3
13.5
11-17
95%
91%
84%
74%
63%
50%
38%
26%
16%
9%
4d6 DL
12.2
9-15
90%
82%
73%
62%
49%
35%
23%
13%
6%
2%
4d6 DH
8.8
6-12
51%
38%
27%
18%
10%
6%
3%
1%
*%
*%
3d6 adv
12
10-14
93%
86%
75%
61%
45%
30%
18%
9%
4%
1%
3d6 dis
9
7-11
55%
39%
25%
14%
7%
3%
1%
*%
*%
*%
4d6
14
11-17
95%
90%
84%
76%
66%
56%
44%
34%
24%
16%


  • DL drop the lowest.
  • DH drop the highest.
  • adv/dis advantage/disadvantage (reroll for a higher/lower result).
  • Av. average roll, rounded to one decimal place.
  • Ex Rng expected range of most rolls, based on rounded averages and standard deviation.
  • ascending AC.
  • *% rounds to lower than 1%.
  • - cannot be achieved on an adjusted roll.
  • all percentages are rounded up or down to nearest whole number (for spacing reasons).
I used a combination of AnyDice and Rumkin Die Roll Stats to compile this; any mistakes are mine, from input or interpretation.

For the homebrew D&D-adjacent system I've used and continue to tinker with, there's a 3d6 Hit Roll (4d6, drop lowest, for Fighters and monsters), vs. base AC 9 and the leather/chain/plate scale from BECMI etc. No bonuses to Hit or to AC from Ability Scores. Base damage is the margin-of-success; crits on triples (less than 3% chance). There are Parry and Dodge options. 

I currently use AC 15 (plate/Heavy) as the hard cap for the system, and there are (good?) mechanical as well as narrative reasons for adventurers to favour lighter protection. 

I've extended the AC line to cover the base ACs of most retro clones (10), plus Basic Fantasy RPG (11) and Lamentations of the Flame Princess (12), up to the maximum unadjusted roll of 18.

While primarily interested in the 3d6 and the 4d6DL rolls, I've included adjustments -3 to +3, 4d6DH, advantage/disadvantage, and straight 4d6 (but ignoring rolls above 18) for comparison.

Addendum (28/04/2020).

Link to the d20 SRD entry for Bell Curve Rolls (3d6, but also 2d10), for reference.

You could use the Dragonwarriors Armour Factor progression instead of D&D adjacent, which would bring the numbers down a bit if you don't like how strong Heavy/Plate gets: padded leather +1, hardened leather +2, ring mail +3, chain +4, plate +5.

For the tinker homebrew, shields do not contribute to AC, but there's no reason not to use them RAW for your preferred system if you're using this.

Also for the homebrew, monster ACs tend to be the same as Unarmoured, but a tough hide (Elephant) might be +2 (leather); a scaly hide (Crocodile) might be +3 (BECMI scale mail); a shell/carapace (Giant Beetle) +5 (BECMI banded), and a Living Stone Statue equal to Heavy/Plate at +6 (though could also be AC 9, but only ever takes one point of damage per hit and you risk breaking your weapon).











6 comments:

  1. I've been toying around with another dice permutation: 4d6, but count any 6s rolled as zeroes. If you use the standard D&D target numbers (or use the Target 20 formula and add Descending AC + Level or HD to the roll, with a result of 20+ meaning success,) then the chance to hit AC 9 is almost the same as for the 1d20-based tables in OD&D, but tougher armor types become harder to hit. Here are the details converted to your format for comparison:

    4d6 Drop 6: Avg 10 Range 7-13 To Hit AAC 9 56% AAC 10 44% AAC 11 34% AAC 12 24% AAC 13 16% AAC 14 10% AAC 15 6% AAC 16 3% AAC 17 1% AAC 18 *%

    ReplyDelete
    Replies
    1. One of the reasons I'm interested in that system is that, if I make each armor tier +1 to defense instead of +2 as in D&D, the chances to hit become practically identical to the standard D&D chances. It's the closest I can get to the official results while only using d6s.

      Another reason is that those dropped 6s can be used for other things, like a side effect for every 6 rolled.

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    2. Interesting; using the dropped sixes feels very Tunnels & Trolls.

      I like the way you've created a virtual almost-d20 (4-20) - I was proper adult years old before I got interested enough in the maths to learn you couldn't just substitute 2d10 or 3d6 because they were near enough, but I would have jumped on this (it also brings a little bit of GURPS to rolls vs. Ability Scores, with its 3/4 17/18 workaround).



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    3. It's actually a closer almost-d20 than it appears: 4d6 is 4-24 range, but 4d6 drop 6 is 0-20. Of course, the probabilities are still bell curve rather than linear, like a true d20. But the more I've thought about it over the years, the more this seems like it might be what I want, or at least something I can live with.

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    4. Absolutely right, of course: numbers was never my strong point, and I wish I'd cared/concentrated more during my formative years - I feel the lack now.

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    5. Oh! A #d6-drop-6s might work for Ability Score checks/saves, with escalating numbers of dice for difficulty but always a chance of success.

      Again, that feels like an alternative timeline Tunnels & Trolls mechanic.

      Delete