D&D General Replacing 1d20 with 3d6 is nearly pointless

[DND_Reborn]

Just to throw this out there, my favorite method (but I know will never catch on) is 4d6-4 for a range of 0-20 and avg. 10.

 

[JiffyPopTart]

I'm partial to an Xd2 binary system (0 or 1 on the die face). I really like it requiring the 1000 dice needed to roll an at-bat in Dynasty League Baseball.

J/K but I don't have much to add because I'm missing the point on why a bell curve isn't more predictable.

 

[DND_Reborn]

I don't have much to add because I'm missing the point on why a bell curve isn't more predictable.

I must have missed if anyone said 3d6 isn't more predictable...

 

[NotAYakk]

Which the Bell Curve has... That is the point.

The distribution of 3d6 is shaped a bit like a Bell Curve.

The fact it is shaped somewhat like a Bell Curve is irrelevant to the use people are putting it to. Almost all of the impact is from the variance, not the fact it is Bell Curve shaped.

The Bell Curve -- the normal distribution -- has whatever variance you feel like. 3d6 is shaped more like the normal distribution -- like a Bell Curve -- but that fact is not relevant to the actual impact on the actual game resolution.

Now, you could use a d20, and have all the big numbers you're talking about, and have approximately the same probabilities, but that seems like a lot more work IMO than just using the 3d6 and adding them up (a simple enough task for most gamers anyway... I do know a few who struggle. ).

Adding up multiple numbers every roll is harder than doubling stuff once. It slows the game down.

But I'm not stopping anyone from doing it.

...uh... huh.

So... is your gripe that people like rolling 3d6+Mods rather than 1d10+Mods+5 -5DC/AC/Otherfunctionstoshoehorninthisalternatemethod?

I'm not griping?

I'm pointing out that people seem to attribute properties to the "curvyness" of the 3d6 distribution.

Like it's fairly obvious you could jump through a series of hoops to create a 1d10+5 system if you REALLY WANTED TO. But the only reason I see to do it is that you just -really hate- rolling 3 dice instead of 1 dice. Is that really all there is, here?

There isn't many hoops? Just lower DCs (including AC) by 5, and replace d20 with d10. You are now done.

You are rolling 1d10 instead of 3d6. If you really want to, you can tweak the nat 1/nat 10 rules however you want.

From what I can tell, people who use 3d6 make some "auto success/crit/fail" system and attach it as well.

Use whatever such system you want. But, again, when I see people talking about using 3d6, they don't wax poetic about the crit fail/success system they have attached to it. They talk about the "Bell Curve".

The Bell Curve is a nice easy to communicate concept that makes 3d6 work better to show off character skill investment over randomization. That's it. That's all. There's no need to go into even more complicated systems to try and get the same result.

Again, the fact the distribution is curved has nothing to do with the game properties that come out of it.

Possibly people are using it as a lie to convince people to use it; a sales pitch. Or maybe they don't understand how it works. I'm explaining how it works, and why the curvyness has basically nothing to do with the in-play outcome you get at the table.

I'm very confused, right now.

Maybe you are ascribing to me an agenda I don't have?

This is basically it:

People talking about "The Bell Curve" making the game act like X or Y is like someone waxing about why the red paint on their Porsche makes their car go faster.

I point out that the red paint has nothing to do with the Porsches speed.

Then people object and say the red Porsche is very fast.

And I say that this has nothing to do with the red paint on the Porsche.

And what I hear back is... but the red Porsche goes fast, and people like fast cars, that is why the red paint makes the Porsche fast.

I have zero objection to the fact this red Porsche is fast. I'm just saying it has nothing to do with the red paint on it, and you can get a car that isn't a red Porsche and go just as fast. It could be blue. Or even not a Porsche at all.

 

[DND_Reborn]

The distribution of 3d6 is shaped a bit like a Bell Curve.

The fact it is shaped somewhat like a Bell Curve is irrelevant to the use people are putting it to. Almost all of the impact is from the variance, not the fact it is Bell Curve shaped.

While the normal distribution is A bell curve, it is not THE bell curve. There are other distributions which are also bell curves. But is a common mistake--thinking THE bell curve is the normal distribution. The normal distribution is a bell curve, of course...

So, 3d6 is not "shaped a bit like a bell curve" (no caps, ok? Again, there is not a singular "Bell Curve"), it IS a bell curve.

The Bell Curve -- the normal distribution -- has whatever variance you feel like. 3d6 is shaped more like the normal distribution -- like a Bell Curve -- but that fact is not relevant to the actual impact on the actual game resolution.

It is very relevant when compared to the d20, as my two examples show. So, yet again (since you don't seem to want to comment on them):

For example, suppose you need a 7 or better to succeed (attack, ability check, or save). With a d20, you have 70% of 7 or better, with 3d6 you have over 90% chance to succeed.

Flipping the script, if you need a 15, your chances are 30% (d20) and just 9.26% (3d6).

I would say 70 vs 90% and 30 vs 9.26% are relevant and impactful. YMMV, of course.

Now, like you posted above, a d10+5 would give you the same (roughly) probabilities for rolling 7+ and 15+ (90% and 10%) as 3d6, but it would only be viable in the range from 6-15, so not quite as robust as 3-18 (which admittedly is not as robust as d20...), which is excluding about 10% of the possible results (the 3, 4, 5, 16, 17,and 18...)

Adding up multiple numbers every roll is harder than doubling stuff once. It slows the game down.

But I'm not stopping anyone from doing it.

But you are adjusting pretty much every random aspect related to d20 rolls--which in 5E is A LOT.

Rolling 3d6 doesn't slow down the game, really... (I've actually conducted experiments on this with my players--granted a very small sample size LOL, but that's what I have to work with, so take it as anecdotal).

 

[Steampunkette]

I'm not griping?

I'm pointing out that people seem to attribute properties to the "curvyness" of the 3d6 distribution.

There isn't many hoops? Just lower DCs (including AC) by 5, and replace d20 with d10. You are now done.

You are rolling 1d10 instead of 3d6. If you really want to, you can tweak the nat 1/nat 10 rules however you want.\

1d20 system: 5% chance of any value coming out.
1d10 system: 10% chance of any value coming out.
3d6 system: Heavily weighted toward the values closer to the middle coming out, significantly lower chance of extremes.

If you want values near the middle to come out, use the 3d6 system. The Bell Curve is a real mathematical thing and creates an intentionally weighted center.

The Red Porsche doesn't go faster. But you roll 10 more often in a 3d6 system than a 1d20 system. AND THAT IS THE POINT. (12.5% is bigger than 5%, obviously)

The 1d10+5 system is nifty? But you still wind up with an absolutely even distribution of possible rolled values between 6 and 15, so it doesn't ACTUALLY help with the core design goal of the 3d6 system making things weight to 10 rather than a perfectly even distribution.

Even if it has an "80% chance of rolling between 7 and 14" it doesn't actually -mean- the same thing as 7-14 in a 3d6 system.

 

[Cadence]

That isn't the Bell Curve that does it.

It is just the lower variance.

1d10 has a variance of 99/12. So replace 1d20 with (1d10+5) and you get basically the same game as 3d6.

Or, lower all DCs by 5. Unarmored is 5 AC, spell saves DCs are 3+blah, etc.

And roll 1d10 instead of 1d20 for your checks.

No curve in 1d10. Almost the same probabilities as rolling 3d6 vs default DCs.

Between 7 and 14? Subtract 5! Between 2 and 9. Guess what the chance of a d10 between 2 and 9 is? 80%.

Guess what the chance of 3d6 between 7 and 14? About 80%.

Not a coincidence.

But people build systems using 3d6 and not for 5+1d10 and talk about the bell curve, I suppose because they think it matters.

For 1d10, you'd probably want a crit failure system for 1s and 10s that isn't auto-success/failure. Almost anything would do, up to and including "flip a coin; heads, you auto-succeed on 10 or auto-fail on 1".

Assuming the code in spoilers at the bottom is correct. Please let me know if it looks off and I'll fix it.

I feel silly that it surprised me, but one of the biggest differences for the d20 using doubled attack and defense modifiers vs. the 3d6, is that the former has a 55% chance of succeeding on a need-a-ten roll and the later has a 62.5% chance.

After lining them up by making the base target 11, I was surprised the difference in kurtosis wasn't more noticeable. That was a nice catch you had noticing that just doubling the modifiers made them line-up so well.

The big difference now is at +/- 5, 6, and 7 where the d20 with doubled mods has no chance of success and the 3d6 has around a 4.6%, 1.9%, and 0.4% chance of failure/success respectively. So, it really comes down to whether one cares wants the chances of success out there, or not.

As a side note, I wasn't expecting the d10+5 vs. 11 to be exactly the d20-doublemod-vs. 11, so that would be even easier if you don't mind missing those tails. They don't match with the base target of 10.

For completeness, since it is probably the usual motivating thought to go down this rabbit hole, here is the d10 vs. 3d6 both targeting 10. Notice the advantage the 3d6 gets when targeting 10.

Spoiler: R Code

od20.prob<-rep(0.05,20)
td6.prob<-c(0,0,1,3,6,10,15,21,25,27,27,25,21,15,10,6,3,1,0,0)/216
od10p5.prob<-c(0,0,0,0,0,rep(.1,10),0,0,0,0,0)

outmat<-matrix(0,nrow=19,ncol=7)
attmdef<-(-9:9)
colnames(outmat)<-c("d20","d20dbl","d20dv11","td6","td6v11","d10p5","d10p5v11")
rownames(outmat)<-attmdef



for (i in attmdef){
outmat[i+10,1]<-sum(od20.prob[(((1:20)+i)>=10)]) #d20+mod vs. 10
outmat[i+10,2]<-sum(od20.prob[(((1:20)+2*i)>=10)]) #d20+2*mod vs. 10
outmat[i+10,3]<-sum(od20.prob[(((1:20)+2*i)>=11)]) #d20+2*mod vs. 11
outmat[i+10,4]<-sum(td6.prob[(((1:20)+i)>=10)]) #3d6+mod vs. 10
outmat[i+10,5]<-sum(td6.prob[(((1:20)+i)>=11)]) #3d6+mod vs. 11
outmat[i+10,6]<-sum(od10p5.prob[(((1:20)+i)>=10)]) #d10+5+mod vs. 10
outmat[i+10,7]<-sum(od10p5.prob[(((1:20)+i)>=11)]) #d10+5+mod vs. 11
}

round(outmat,3)


plot(-9:9,outmat[,2],xlab="Att minus Def",ylab="Pct Success",col="red",pch=20,
main="Red = d20 Modx2 and Blue = 3d6; Base target=10")
par(new=T)
plot(-9:9,outmat[,4],xlab="Att minus Def",ylab="Pct Success",col="blue",pch=20)
lines(-9:9,outmat[,2],col="red")
lines(-9:9,outmat[,4],col="blue")

plot(-9:9,outmat[,3],xlab="Att minus Def",ylab="Pct Success",col="red",pch=20,
main="Red = d20 Modx2 and Blue = 3d6; Base target=11")
par(new=T)
plot(-9:9,outmat[,5],xlab="Att minus Def",ylab="Pct Success",col="blue",pch=20)
lines(-9:9,outmat[,3],col="red")
lines(-9:9,outmat[,5],col="blue")


plot(-9:9,outmat[,1],xlab="Att minus Def",ylab="Pct Success",col="red",pch=20,
main="Red = d20 and Blue = 3d6; Base target=10",ylim=c(0,1))
par(new=T)
plot(-9:9,outmat[,4],xlab="Att minus Def",ylab="Pct Success",col="blue",pch=20)
lines(-9:9,outmat[,1],col="red")
lines(-9:9,outmat[,4],col="blue")

 

[Argyle King]

You realize that you are now arguing with a point made over two years ago?

If it were made, questions about the meaning wouldn't persist after two years.

 

[NotAYakk]

1d20 system: 5% chance of any value coming out.
1d10 system: 10% chance of any value coming out.
3d6 system: Heavily weighted toward the values closer to the middle coming out, significantly lower chance of extremes.

Again, many posts about the effect of takng the CDF and dividing by the variance.

Examples where I did it.

Explanations why the curve part doesn't matter.

And... people still think the curve is somehow the important part.

If you want values near the middle to come out, use the 3d6 system. The Bell Curve is a real mathematical thing and creates an intentionally weighted center.

Yes, I know the shape.

And it does not matter, because the integral of the shape, subtracring the average, and horizintally scaling by the SD makes the curvyness effect small enough it would take a huge sample to detect it.

And roll over games efdectively integrate the curve, which smooths it enough.

The Red Porsche doesn't go faster. But you roll 10 more often in a 3d6 system than a 1d20 system. AND THAT IS THE POINT. (12.5% is bigger than 5%, obviously)

That is the red paint.

Play d10+5 vs DC.
Play 3d6 vs DC.
Play d20 vs (DC-10)*2+10.5

The difference is red paint.

The fat part of the 3d6 doesn't matter enough.

The 1d10+5 system is nifty? But you still wind up with an absolutely even distribution of possible rolled values between 6 and 15, so it doesn't ACTUALLY help with the core design goal of the 3d6 system making things weight to 10 rather than a perfectly even distribution.

except it plays the same.

Really.

That is what I am saying. The gap between 1d10 flat curve roll-over and 3d6 roll over is surprisingly small.

Go to anydice and graph it. I have above in previous posts.

Even if it has an "80% chance of rolling between 7 and 14" it doesn't actually -mean- the same thing as 7-14 in a 3d6 system.

... yes it does?

You dice roll says pass or fail.

If the pass/fail rate is almost identical in two systems, then the difference is cosmetic - red paint.

My entire point is that the impact of the bell curve of 3d6 is red paint. If you graph P(3d6>=K) (probability you get a K or higher in 3d6) 90%+ of the graph is only slightly off a stait line. In the range K from 6 to 15, P(3d6>=K) is within a few percent of (K-5)*10%.

I didn't know it was as close as it is until I tried it. And it really is close.

 

[Cadence]

My entire point is that the impact of the bell curve of 3d6 is red paint. If you graph P(3d6>=K) (probability you get a K or higher in 3d6) 90%+ of the graph is only slightly off a stait line. In the range K from 6 to 15, P(3d6>=K) is within a few percent of (K-5)*10%.

I didn't know it was as close as it is until I tried it. And it really is close.

The tails (or lack there of) still feel like a thing (4% or 1% vs impossible is a huge difference in lots of cases, right?).

Is a big point simply that most people haven't been focusing on that part of the curve in trying to explain why they like one method vs. the other?