d20, 2d10, or 3d6 vs level-appropriate ACs

Homebrew

I worked this up today after seeing a discussion on G+ about the merits/flaws of rolling 1d20, 2d10 or 3d6 as a mechanic for D20 systems. The sheets compare attack success probabilities against level appropriate ACs among the three mechanics.

Some definitions:
Fighter BAB - straight BAB
Cleric BAB - straight BAB
Wizard BAB - straight BAB
High Attack - "High" monster attack bonus from the Pathfinder PRD
Low Attack - "Low" monster attack bonus from the Pathfinder PRD
Target AC - Level-appropriate monster AC by CR from the Pathfinder PRD﻿

Attack Probabilities

BTW, I am not a statistician, so take it easy on me if I made any mistakes.

2d10 and 3d6 do the same thing. They produce a bell curve. So the question is how much of a bell curve do you want if at all? The benefits of a bell curve are that actions tend to pool in the middle the great the curve. So static bonuses matter more because you are more likely to perform at your average level.

The benefits of a d20 are that probabilities are easier to figure out. Everything is linear and that's very easy to translate.

On a d20 +7 equates to +35% chance to succeed. On 3d6 the same bonus would be +3. The advantage on the d20 is that you have more granularity. The advantage on 3d6 is that the outcome is going to be less "swingy" so +3 is going to simply adjust the average up by 3 points and you are going to hit that pocket more than not.

The question of using one over the other really only matters after you have asked yourself what sort of success to failure ratios you want you players to have in your game.

As for 3d6 in D&D...the SRD has alternate rules for this. They...aren't so good.

WPharolin wrote:

The question of using one over the other really only matters after you have asked yourself what sort of success to failure ratios you want you players to have in your game.

When you plot those probabilities against comparable attack bonuses and ACs, you see they do some weird stuff. If you have a relatively "high" attack bonus, you do best with 2d10 until you hit level 2, then 3d6 gives you better results all the way until level/CR 20

If you have a "low" attack bonus, 2d10 gives you better odds all the way through level 12, then 1d20 and 2d10 net you the same success rates. When you hit level 20, using a straight d20 gets you the best success chance.

I prefer a system based on curved rather than flat probablility, and rhere are some really outstanding game systems with 3d6 or other "curved" die rolls at their heart. GURPS in particular makes excellent use.

D&D/PF has long been built on a d20, however, and for good reasons. As complicated as we here on the forums like to make it, Pathfinder is a beginner game system.

Funnily enough, I had a thread about this right here. It included some statistical data and some issues you'd run into. One of the biggest issues is changing the way Improved Critical works.

Odraude wrote:
Funnily enough, I had a thread about this right here. It included some statistical data and some issues you'd run into. One of the biggest issues is changing the way Improved Critical works.

I didn't see that thread, thanks for bringing it to my attention. Ultimately, I don't think a D20 game can be ported to a multiple dice mechanic without reworking a lot of factors (threat ranges, ACs, etc.) Once you start getting outside of your normal target number range, the probability of success drops off pretty dramatically.

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Nebelwerfer41 wrote:
Odraude wrote:
Funnily enough, I had a thread about this right here. It included some statistical data and some issues you'd run into. One of the biggest issues is changing the way Improved Critical works.
I didn't see that thread, thanks for bringing it to my attention. Ultimately, I don't think a D20 game can be ported to a multiple dice mechanic without reworking a lot of factors (threat ranges, ACs, etc.) Once you start getting outside of your normal target number range, the probability of success drops off pretty dramatically.

Threat ranges become a huge part of how this gets hosed up. The chance of rolling a 20 on a d20 is 5%. The chance of rolling a 20 on 2d10 is 1%. The chances of rolling an 18 on 3d6 is < .5%. Similarly for the low ends of the scales for rolling 1, 1, and 3. So critical failures are hosed up.