d20 vs. 3d6 "dice heresy" by Chris Sims

[blargney the second]

It's a very flat bell. A gong, maybe?

 

[malraux]

One can map a bell curve onto a flat random number generator.

 

[TikkchikFenTikktikk]

(It's alive! It's moving! It's alive! The thread is alive!)

One aspect totally missing from this discussion is the whole "soft" side of the d20.

Rolling a d20 feels great. (Literally, I love the feel and sound of rolling a well-crafted d20. Rolling dice pools feels unwieldy and sounds worse.)

Rolling a d20 feels special, feels like D&D. It is only used heavily in D&D and in D&D-derived games.

The image of a twenty-sided die has almost become **the** symbol of D&D, along with the fire-breathing dragon ampersand.

The golden rule of D&D since v3, and especially, explicitly so in 4E is "When your character tries to do something that might fail, roll a d20." Rolling a d20 to hit goes back decades.

"Rolling 20s" is part of the gaming lexicon, and it's linked to D&D. To a lesser extent, so is rolling 1s. These happen often enough to be a communal experience and create a bond amongst D&Ders.

The d20 is part of D&D's brand equity.


Replacing the d20, or even just diminishing its role, with anything else could only be justified if the improvement to gameplay were **massive** or the replacement came with some ginormous amount of goodwill. I think six pages of debate have shown the improvement in gameplay by using 3d6 instead of d20 is arguable, not massive. And anything that makes D&D feel less special and more like Yahtzee or Farkle is a massive failure.

Replacing the d20 with a dice pool in D&D would be like the modern Christian church replacing the Father, Son, and Holy Ghost with just God.

 

[Cadfan]

The only thing I like about a bell curve distribution is that it makes each +1 to hit after the mid point less valuable than the one before, and each +1 to hit before the mid point more valuable than the one before. This gives players an incentive to go at least to the mid point, then a little beyond, but probably not to the top of the curve. By contrast in a flat distribution system each +1 to hit adds the same amount to expected damage up until you're only missing on a defined failure.

 

[Nifft]

The only thing I like about a bell curve distribution is that it makes each +1 to hit after the mid point less valuable than the one before, and each +1 to hit before the mid point more valuable than the one before. This gives players an incentive to go at least to the mid point, then a little beyond, but probably not to the top of the curve. By contrast in a flat distribution system each +1 to hit adds the same amount to expected damage up until you're only missing on a defined failure.

Right, and that's great if they're starting right in the middle, but IMHO it's generally bad for these reasons:

1/ Too much constraint placed on the DM (or module designer) to make sure everyone is always starting right in the middle.

2/ Too much pain if you're penalized to -1 or -2 below the middle.

3/ Too much reward for metagaming and in-fight math optimization. IMHO this is the true killer. I recall the bad old days of 3.0e Power Attack spreadsheets, and I don't want to put that much emphasis on "tactical engineering".

Cheers, -- N

 

[Votan]

2/ Too much pain if you're penalized to -1 or -2 below the middle.

In you are not careful, this can do the opposite of the stated intention of the use of 3d6 by making hitting functionally impossible. It's not that hard actually -- a few penalties applied to players and an enemy with a high AC can be only hit on a 16+ (annoying in d20, pretty much a game ender in 3d6).

I also noted that it really makes things like the psion's powers awful formidable (as a CHA penalty to hit can become devastating under this system).

 

[Argyle King]

hmm...


I'm not sure what to think yet. I'm still reading over the thread.


I have been experimenting with using 2d10 instead of a d20 for similar reasons.


While I'm familiar with 3d6 due to being familiar with GURPS, I had not considered trying to use 3d6 with D&D before.

 

[pawsplay]

How so?

, -- N

While each of the 20 rolls is a an even distribution, the actual die roll is not meaningful. There are actually only two results, hit or miss, and they are not the same probability in every scenario. The idea of normalizing attack bonuses and defenses in 4e is actually a way of creating a more bell-like distribution.

The bell curve was not invented to model 3d6 or a dice pool or whatever. It's what happens when you sample multiple times from a random distribution. Even though many things in nature, like the d20, begin as a completely random distribution, as the results are aggregated, the bell curve magically appears.

As I said before, the d20 and 3d6 are functionally identical in the amount of "randomness" they posses. Both are ultimately ways of deciding what fractional probability you will have to succeed. Using a 3d6 does not create a "bell curve." Rather, it just changes the graduations of probablity from bite-sized, 5% chunks of the entire distribution to chunks that vary in size. The result is not a change in the bell-curved of the distribution, but a transformation of the modifiers and target numbers from a proportion of the variance to a curve, with the highest slope near the normal target numbers and the lowest slope at the extremes. Thus, even small differences become large ones, but very large differences are only slightly more meanginful than large differences. The 3d6 is more predictable but also more stratified, with the extreme values being fatter strata.

Even though 3d6 is more mathematically predictable, the high shifts in probably that come from situational modifiers are not predictable. As long as there are no modifiers to the rolls, the 3d6 is a lot more predictable. But if the situation is such that you may get +1, +2, or no bonus from round to round, the probability will actually swing wider. Further, you will want to compare the usual range of skill or attack modifiers to the usual range of DCs, and compare the shift in % between d20 and 3d6 within those values to see if perhaps you are making high, but fairly common DCs out of reach.

 

[Dark Mistress]

My group has been using 2d10 on skill checks and most other things other than combat stuff.

 

[Nifft]

While each of the 20 rolls is a an even distribution, the actual die roll is not meaningful. There are actually only two results, hit or miss, and they are not the same probability in every scenario. The idea of normalizing attack bonuses and defenses in 4e is actually a way of creating a more bell-like distribution.

No, it's not. It's shifting a point on a uniform distribution. There is no bell.

The bell curve was not invented to model 3d6 or a dice pool or whatever. It's what happens when you sample multiple times from a random distribution. Even though many things in nature, like the d20, begin as a completely random distribution, as the results are aggregated, the bell curve magically appears.

No. If you plot a lot of d20 rolls, you get a flat line, because you are sampling a uniform distribution. Each result from 1 to 20 is equally likely, so each result's bucket will hold about the same number of samples, given a large enough number of samples.

Using a 3d6 does not create a "bell curve."

Adding multiple independent uniform probability density functions creates a more normal probability density function (where "more normal" is jargon that means "more bell-shaped").

So... yeah, it does.

I hope I'm reading you correctly.

Cheers, -- N