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<blockquote data-quote="Cadence" data-source="post: 8791431" data-attributes="member: 6701124">Assuming the code in spoilers at the bottom is correct.&nbsp; 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.[ATTACH=full]263232[/ATTACH]After lining them up by making the base target 11,&nbsp; I was surprised the difference in kurtosis wasn't more noticeable.&nbsp; That was a nice catch you had noticing that just doubling the modifiers made them line-up so well.[ATTACH=full]263233[/ATTACH]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&nbsp; 4.6%, 1.9%, and 0.4% chance of failure/success respectively.&nbsp; 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.&nbsp;&nbsp; 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.&nbsp; Notice the advantage the 3d6 gets when targeting 10.[ATTACH=full]263238[/ATTACH][SPOILER=&quot;R Code&quot;]od20.prob&lt;-rep(0.05,20)td6.prob&lt;-c(0,0,1,3,6,10,15,21,25,27,27,25,21,15,10,6,3,1,0,0)/216od10p5.prob&lt;-c(0,0,0,0,0,rep(.1,10),0,0,0,0,0)outmat&lt;-matrix(0,nrow=19,ncol=7)attmdef&lt;-(-9:9)colnames(outmat)&lt;-c(&quot;d20&quot;,&quot;d20dbl&quot;,&quot;d20dv11&quot;,&quot;td6&quot;,&quot;td6v11&quot;,&quot;d10p5&quot;,&quot;d10p5v11&quot;)rownames(outmat)&lt;-attmdeffor (i in attmdef){&nbsp; &nbsp; outmat[i+10,1]&lt;-sum(od20.prob[(((1:20)+i)&gt;=10)])&nbsp; &nbsp; #d20+mod vs. 10&nbsp; &nbsp; outmat[i+10,2]&lt;-sum(od20.prob[(((1:20)+2*i)&gt;=10)])&nbsp; #d20+2*mod vs. 10&nbsp; &nbsp; outmat[i+10,3]&lt;-sum(od20.prob[(((1:20)+2*i)&gt;=11)])&nbsp; #d20+2*mod vs. 11&nbsp; &nbsp; outmat[i+10,4]&lt;-sum(td6.prob[(((1:20)+i)&gt;=10)])&nbsp; &nbsp;&nbsp; #3d6+mod vs. 10&nbsp; &nbsp; outmat[i+10,5]&lt;-sum(td6.prob[(((1:20)+i)&gt;=11)])&nbsp; &nbsp;&nbsp; #3d6+mod vs. 11&nbsp; &nbsp; outmat[i+10,6]&lt;-sum(od10p5.prob[(((1:20)+i)&gt;=10)])&nbsp; #d10+5+mod vs. 10&nbsp; &nbsp; outmat[i+10,7]&lt;-sum(od10p5.prob[(((1:20)+i)&gt;=11)])&nbsp; #d10+5+mod vs. 11}round(outmat,3)plot(-9:9,outmat[,2],xlab=&quot;Att minus Def&quot;,ylab=&quot;Pct Success&quot;,col=&quot;red&quot;,pch=20,&nbsp;&nbsp; main=&quot;Red = d20 Modx2 and&nbsp; Blue = 3d6; Base target=10&quot;)par(new=T)plot(-9:9,outmat[,4],xlab=&quot;Att minus Def&quot;,ylab=&quot;Pct Success&quot;,col=&quot;blue&quot;,pch=20)lines(-9:9,outmat[,2],col=&quot;red&quot;)lines(-9:9,outmat[,4],col=&quot;blue&quot;)plot(-9:9,outmat[,3],xlab=&quot;Att minus Def&quot;,ylab=&quot;Pct Success&quot;,col=&quot;red&quot;,pch=20,&nbsp;&nbsp; main=&quot;Red = d20 Modx2 and&nbsp; Blue = 3d6; Base target=11&quot;)par(new=T)plot(-9:9,outmat[,5],xlab=&quot;Att minus Def&quot;,ylab=&quot;Pct Success&quot;,col=&quot;blue&quot;,pch=20)lines(-9:9,outmat[,3],col=&quot;red&quot;)lines(-9:9,outmat[,5],col=&quot;blue&quot;)plot(-9:9,outmat[,1],xlab=&quot;Att minus Def&quot;,ylab=&quot;Pct Success&quot;,col=&quot;red&quot;,pch=20,&nbsp;&nbsp; main=&quot;Red = d20 and&nbsp; Blue = 3d6; Base target=10&quot;,ylim=c(0,1))par(new=T)plot(-9:9,outmat[,4],xlab=&quot;Att minus Def&quot;,ylab=&quot;Pct Success&quot;,col=&quot;blue&quot;,pch=20)lines(-9:9,outmat[,1],col=&quot;red&quot;)lines(-9:9,outmat[,4],col=&quot;blue&quot;)[/SPOILER]</blockquote>

[QUOTE="Cadence, post: 8791431, member: 6701124"] [B][I]Assuming the code in spoilers at the bottom is correct. Please let me know if it looks off and I'll fix it.[/I][/B] 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. [ATTACH type="full" alt="1664937473607.png"]263232[/ATTACH] 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. [ATTACH type="full" alt="1664937616550.png"]263233[/ATTACH] 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. [ATTACH type="full" alt="1664938863552.png"]263238[/ATTACH] [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")[/SPOILER] [/QUOTE]

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