The "I Didn't Comment in Another Thread" Thread

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I could swear someone put up the numbers within the past year and 3d6 + x worked surprisingly similar to d20 + 2x. (Assuming my memory isn't messing with me).

I roll to disbelieve. Among other things the upper and lower reaches of 3D6 are actually smaller than a D20 can produce (i.e. they're less than 5%).
 

It does. There's some discussion of it on stack exchange. So if you switch to a 3d6 system, the bonuses matter a lot more, which can mess up the assumptions about DCs.

Shifting an extent game to a different die system almost always breaks something. That's why you design your game with the die system in mind in the first place.
 


I've done horror in 5e without doing either of those things.
I've successfully (if my players' responses are any indication) run horror D&D games numerous times. Uncertainty and creepiness are what I've used, rather than any mechanics. (That said, no one was running high level characters, which make all sorts of adventure modes more challenging to pull off.)
 

I've successfully (if my players' responses are any indication) run horror D&D games numerous times. Uncertainty and creepiness are what I've used, rather than any mechanics. (That said, no one was running high level characters, which make all sorts of adventure modes more challenging to pull off.
These were ongoing, relatively long-term campaigns that took turns. Some of those turns were in Tier 3, if not Tier 4 (I'd have to look at session notes).
 

I roll to disbelieve. Among other things the upper and lower reaches of 3D6 are actually smaller than a D20 can produce (i.e. they're less than 5%).

I think I have the math right here to show that a d20 can be made to work pretty close to a 3d6 for attacks and skill checks. Consider these two set-ups:

A: 3d6 + attacker bonus vs. 10 + defense bonus
B: d20 + 2*attacker bonus vs. 9 + 2*defense bonus

and ignore an auto-hit on 20 or auto-miss on a 1 when using the d20.

Allow the attack bonus to go from 0 to 5 (so corresponding to up to a +10 bonus in 5e with a d20) and the defense bonus to go from 1 to 11 (so a DC of of 11 to 31 in 5e with the d20). In that case the biggest difference is approximately 4.63% (less than a +1 bonus/penalty on a d20) and approximately 36.3% of the differences are less than 1% (which I would argue would be really hard to notice in practice). The 4.63% holds if you expand the ranges it's examined over, and the percent of differences less than 1% grows as the grid fills up with 0%'s and 100%'s.

The 3d6 does certainly changes things a bit near the edges; you get chances of about 4.6%, 1.9%, and 0.5% for the next three spots where the d20 would have a 0% in the hard difficulties, and then some chances to miss on the other side for the easy difficulties where the d20 would 100% hit. (See the tables in the second spoiler below).


x<-3:18
nx<-c(1,3,6,10,15,21,25,27,27,25,21,15,10,6,3,1)
xx<-rep(x,nx)
prob3d6<-matrix(0,nrow=11,ncol=6)
for (defbonus in 1:11){
for (attbonus in 0:5){
prob3d6[defbonus,attbonus+1]<-sum((xx+attbonus)>=(10+defbonus))/216}}
y<-1:20
probd20<-matrix(0,nrow=11,ncol=6)
for (defbonus in 1:11){
for (attbonus in 0:5){
probd20[defbonus,attbonus+1]<-sum((y+2*attbonus)>=(9+2*defbonus))/20}}

colnames(prob3d6)<-0:5
rownames(prob3d6)<-10+1:11
colnames(probd20)<-2*(0:5)
rownames(probd20)<-9+2*(1:11)

round(prob3d6,3)
probd20
summary(c(prob3d6-probd20))
sum(abs(c(prob3d6-probd20))<0.01)/length(c(prob3d6-probd20))

For 3d6 (rounded to three decimal places)
-----0------1-----2-----3------4-----5--
11 0.500 0.625 0.741 0.838 0.907 0.954
12 0.375 0.500 0.625 0.741 0.838 0.907
13 0.259 0.375 0.500 0.625 0.741 0.838
14 0.162 0.259 0.375 0.500 0.625 0.741
15 0.093 0.162 0.259 0.375 0.500 0.625
16 0.046 0.093 0.162 0.259 0.375 0.500
17 0.019 0.046 0.093 0.162 0.259 0.375
18 0.005 0.019 0.046 0.093 0.162 0.259
19 0.000 0.005 0.019 0.046 0.093 0.162
20 0.000 0.000 0.005 0.019 0.046 0.093
21 0.000 0.000 0.000 0.005 0.019 0.046

For d20: Columns are Attack Bonus, Rows are DC
----0---2---4--6---8--10
11 0.5 0.6 0.7 0.8 0.9 1.0
13 0.4 0.5 0.6 0.7 0.8 0.9
15 0.3 0.4 0.5 0.6 0.7 0.8
17 0.2 0.3 0.4 0.5 0.6 0.7
19 0.1 0.2 0.3 0.4 0.5 0.6
21 0.0 0.1 0.2 0.3 0.4 0.5
23 0.0 0.0 0.1 0.2 0.3 0.4
25 0.0 0.0 0.0 0.1 0.2 0.3
27 0.0 0.0 0.0 0.0 0.1 0.2
29 0.0 0.0 0.0 0.0 0.0 0.1
31 0.0 0.0 0.0 0.0 0.0 0.0

Summary of Differences
---Min------1st Qu----Median---3rd Qu.----Max.
-0.046296 -0.025000 0.000000 0.025000 0.046296

Percent of Differences Less than 1%
0.3636364
 
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