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

[clearstream]

[Edited] Among the responses to his blog Chris eventually says...

My major beef with the d20 is that, taken unmodified, its swing in results doesn’t resemble real life at all. It resembles arbitrary randomness. Skilled folks aren’t so subject that much to luck. The modifiers built into the game offset the d20’s swing for sure, though.

...and I guess he had that in the back of his mind when he made the design move that he did. Switching from a line to a curve was never a great solution to his initial problem (low hit chances), but could it be a reasonable solution to that completely different problem (emulating real-life)?

I agree with Chris that real-life doesn't feel linear. Most attempts to model real-life use curves of one sort or another. Setting aside the obvious question of how much you care about emulating real-life in your game, there is another objection to be made, and that is that D&D already uses multiple dice rolls to resolve actions.

To resolve a fight, you will roll many dice. You will roll a d20 followed by (most commonly) d8s or d6s; and then if the fight isn't over, you'll roll more dice. Your overall probability of winning will plot neatly onto a curve that will be bellish looking. Still, what about single rolls for skills? 4ed introduced skill challenges: and, of course, they use multiple rolls.

Hmm... but this leads around in a circle. Was Chris' issue really just missing too often?

-vk

Side note: I do have a mild dislike of using multiple dice for core determination, entirely related to the issue that +1 means different things depending on where you started from. That discomforts me when I consider buffs and debuffs, such as aid another, fighting defensively, combat advantage, and magic: I believe it results in a narrowing of mechanically good options for play.

 

[Pseudopsyche]

That's a little misleading. Admittedly, I'm close to reductio ad absurdum here, but if you are inflating specific points on the curve to make your point, I can just as easily say "If I needed a 17 and I roll a 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, or 18 that +1 is meaningless." After all, that +1 only has a visible effect when it makes or breaks the roll, which only happens when you're one short.

Yes, but when you use more than one die, the probability of being one short depends on the DC.

The shift of the curve as a whole is what's actually relevant to game experience over time. +1 will shift the mean by, well... 1. That's very predictable.

Consider this fact: in a d20 system, a +1 bonus to the attack roll increases the expected damage by a constant, 0.05*E[W], where E[W] is the expected damage on a hit. If you are using 3d6, the increase in expected damage due to a +1 bonus depends on the target number. In particular, it depends on the probability of being one short.

 

[Jeremy Ackerman-Yost]

Right, but that's irrelevant to actual play except in specific cases. Sure, you can pull out corner cases, but the distribution of results over time is what really matters, and a 3d6 is a normal distribution.

Maybe this is the biologist in me talking, but a normal distribution is great. It's true to many aspects of life and awesomely predictable over time without giving up outliers for variety's sake.

When I find something in real life that is a nice, straightforward normal distribution, I'm thrilled.

Hand me the graph of the distribution and the relevant modifiers and I'll set you a DC that will give you exactly the percentage of positive and negative outcomes you want.

I'll concede that the average gamer might have a harder time doing that than with a d20 roll, but the system does that for them to a large extent. All of that is further under the hood than I've ever seen anyone not on an internet forum actually go.

 

[clearstream]

Right, but that's irrelevant to actual play except in specific cases. Sure, you can pull out corner cases, but the distribution of results over time is what really matters, and a 3d6 is a normal distribution.

Maybe this is the biologist in me talking, but a normal distribution is great. It's true to many aspects of life and awesomely predictable over time without giving up outliers for variety's sake.

The outcome of a given encounter is typically a normal distribution. Most encounters are not resolved with a single dice roll: at the least two are rolled (the attack, and the damage). Ignoring that and trying to inject your distribution in a new place is kind of silly tbph. It's like worrying about the distribution on each of those d6, taken alone.

Hand me the graph of the distribution and the relevant modifiers and I'll set you a DC that will give you exactly the percentage of positive and negative outcomes you want.

I'll concede that the average gamer might have a harder time doing that than with a d20 roll, but the system does that for them to a large extent. All of that is further under the hood than I've ever seen anyone not on an internet forum actually go.

The issue is not the difficulty in figuring the odds, the issue is that because any modifier means different things at different points in the range the game can get more swingy and player options can narrow (even down to always using Aid Another, because that makes more difference than having your own attack). Others have made this point repeatedly, pointing out for example that in setting up your character choices between a weapon that does more damage or a weapon that has a mod to hit can easily become non-choices.

The problem isn't just not knowing what +1 means, it is that +1 means different things to every participant. Sometimes a Bless is mandated, othertimes it is pointless. Foes a few levels up the spectrum will be unfightable, a few levels down trivial, narrowing the range for player interaction and reducing fun. The + or - 5 guideline certainly won't hold: so players had better like fighting level + or - 1 for the rest of the campaign!

I had thought the 'it's more like r-l' point might be defensible: but it just doesn't pass. One could no doubt architect a system where 3d6 works well, but to spatchcock it on to 4ed is plain bad design.

-vk

 

[Bluenose]

[Edited] Among the responses to his blog Chris eventually says...

My major beef with the d20 is that, taken unmodified, its swing in results doesn’t resemble real life at all. It resembles arbitrary randomness. Skilled folks aren’t so subject that much to luck. The modifiers built into the game offset the d20’s swing for sure, though.

...and I guess he had that in the back of his mind when he made the design move that he did. Switching from a line to a curve was never a great solution to his initial problem (low hit chances), but could it be a reasonable solution to that completely different problem (emulating real-life)?

Side note: I do have a mild dislike of using multiple dice for core determination, entirely related to the issue that +1 means different things depending on where you started from. That discomforts me when I consider buffs and debuffs, such as aid another, fighting defensively, combat advantage, and magic: I believe it results in a narrowing of mechanically good options for players.

However, I agree with Chris that real-life doesn't feel linear. Most attempts to model real-life use curves of one sort or another. Setting aside the obvious question of how much you care about emulating real-life in your game, there is another point to be made, and this is that D&D already uses multiple dice rolls to resolve actions.

To resolve a fight, you will roll many dice. You will roll d20s, d10s, d8s, d6s, and d4s; d12s too, if you have any sense of style. Your overall probability of winning will plot neatly onto a curve that will be bellish looking. Still, what about single rolls for skills? 4ed introduced skill challenges: and, of course, they use multiple rolls.

Hmm... but this leads around in a circle. Was Chris' issue really just missing too often?

-vk

On the subject of linearity, I wonder if rolling 3d20 and disregarding the highest and lowest would get a result closer to a bell curve? I'd think it should, but I lack the time to model it.

 

[Nymrohd]

The outcome of a given encounter is typically a normal distribution. Most encounters are not resolved with a single dice roll: at the least two are rolled (the attack, and the damage). Ignoring that and trying to inject your distribution in a new place is kind of silly tbph. It's like worrying about the distribution on each of those d6, taken alone.

There is a leap of logic here. Just because there are several dice being rolled in a single fight, this does not mean that it will end up aproximating a normal distribution. It would if the sample truly was large enough, but I am not certain that the central limit theorem is applicable for the number of dice rolls in your average encounter.

 

[clearstream]

There is a leap of logic here. Just because there are several dice being rolled in a single fight, this does not mean that it will end up aproximating a normal distribution. It would if the sample truly was large enough, but I am not certain that the central limit theorem is applicable for the number of dice rolls in your average encounter.

I believe you are correct in characterising my reasoning as a leap, but I feel that does not invalidate it.

Imagine a foe with 27hp, whom you hit on a 9+ dealing 1-8 damage. This foe hits you back on 16+ dealing 1-6 damage. You have 18hp.

Run this fight several dozen times. The graph of fight outcomes, including specifics from who won, to number of turns it took, to end hp of victor, will plot onto a bellish curve. The middle will fall on you winning after about ten turns with about 10hp left. At either end are fights where you win without taking a point, and where you lose without landing a point. The distribution will be lopsided due to the biased setup I have provided.

Now add three other characters and four more foes. That's a lot of dice. Enough dice that expected outcomes become strongly favoured. Still, those outliers are always there.

To feel that the linear nature of the 1d20 you roll to attack means that D&D combat is not like life for reasons of distribution alone (i.e. something that can be solved by using multiple dice for that one roll) would only be true if that single roll also ended the combat. That would make it more like a 3ed SoD/SoL spell where a single saving throw determined the outcome. Even then, you would have to be facing just one foe, and won initiative... another roll.



-vk

EDIT On that, we have to remember that one doesn't really know the value of a +1 unless we also know other details of the encounter. I need to rethink my conclusions (in earlier posts) in that regard.

 

[questing gm]

[ame=http://www.youtube.com/watch?v=sIaIdv79Xz4&feature=related]YouTube - The Gamers (Part 4 of 5)[/ame]

I understand where Chris seems to be coming from and I do agree about the 'swingyness' of the d20 (e.g, the iron bars scene in the video above) that sometimes just seems to award pure chance than proper character building.

I think it's fair to use d20 for combat but 3d6 for skill checks.

 

[Jeremy Ackerman-Yost]

One could no doubt architect a system where 3d6 works well, but to spatchcock it on to 4ed is plain bad design.

-vk

While I'm not certain I can agree to most of what you said, this last has some merit. I'm not enough of a 4e wonk to know how many monsters are going to create some problems here.

But the math itself suggests that the average user is only going to notice those issues at the top end of their performance (i.e. fighting the very toughest defenses). You can mitigate most of that by lopping off the biggest, baddest defenses at the knees to get them within the upper range of expected dice outcomes.

No, that won't be perfect, but it would take a series of corner cases to make it look really different over time. But if you're throwing corner case after corner case at your players, you're probably not within the expected design space, anyway.

 

[Votan]

While I'm not certain I can agree to most of what you said, this last has some merit. I'm not enough of a 4e wonk to know how many monsters are going to create some problems here.

But the math itself suggests that the average user is only going to notice those issues at the top end of their performance (i.e. fighting the very toughest defenses). You can mitigate most of that by lopping off the biggest, baddest defenses at the knees to get them within the upper range of expected dice outcomes.

No, that won't be perfect, but it would take a series of corner cases to make it look really different over time. But if you're throwing corner case after corner case at your players, you're probably not within the expected design space, anyway.

True, but I think that the issue also involves synergy. For example, there are powers that involve infliciting a penalty to hit (Psions, for example) that are low level and easy to use. In the d20 version of the game, a -4 penalty is harsh but still leaves a functional opponent (say if it was hitting on 11+, moving to 15+ is a serious hit but still leaves it as a threat). In 3d6, the same numbers might very well create a helpless opponent.

With 3d6 you are shrinking the variance of every action as well as the whiole fight. All fights will show a normal distribution due to the number of separate rolls that are made (at least so long as you believe in the Central Limit Theorem). Further reducing variance moves the game away from one of chance (as odds of an upset became miniscule) and towards rock, paper, scissors (do you have the right power versus the right weak spot to guarentee victory).

A 3d6 approach works much better in games like GURPS where a fight could be settled by a single hit (due to the penalties, equal to damage IIRC, that the victim takes the next round). So there you want to make sure that luck doesn't dominate because fights are over fast. In a modern world version of GURPS, I recall a rifle that does 7d6 damage (hit points are an ability score with a normal person having 10 and exceptional peopel having 18) that could be used for called shots to the head -- if a character with a gun skill got to aim and fire in any sort of clear setting the opponent was simply dead with a single shot. Here you want to reduce variability because so much depends on one roll.

In 4E, by contrast, there are a lot of rolls. And a lot of penalties. All of which were calibrated on a d20 scale.

In 3E the real killer was saving throws -- high saves turned into immunity (you could never miss them) and low saves turned into hopeless situations. Even worse, spell DC boosts became exceptionally deadly as did targeting a low save.

I think that the 3d6 approach does a lot of damage to the assumptions of the system . . .