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

[NotAYakk]

Hmmm. Two thoughts:

(1) Generally the complaints people have about d20 are precisely about those crit hit/miss zones, especially something that should require a crit success for a beginner but is straightforward for an expert, like navigating rapids or climbing a reverse-slope cliff.

By crit/miss, I mean literally the stuff in d20 that needs a natural 20 (or a natural 1).

If you scale modifiers (and DCs) as described, you end up with within a few % of the same chance of success/failure with 3d6 vs 1d10 as your core random number generator.

Only in the cases when the d20 only fails on a 1, or succeeds on a 20, does the 3d6 provide additional resolution. But its difficulty for the expert is unchanged; what happens is, 3d6 breaks the "natural 20 to succeed" into "6%, 4%, 2%, 0.5%"-ish steps.

This is similar to saying "natural 20 isn't an auto-success; if you roll a 20, you can add an extra 1d6 to your roll". That is what I'm saying "outside of critical hit/miss mechanics", the rescale of modifiers with 3d6 results in an almost impossible to distinguish success resolution engine compared to using the d20.

When people talk about using 3d6, they do not usually focus on the changes in crit/miss chancesin my experience. If they do talk about it, they talk about working to ensure that the chance is the same or similar with 3d6 as with 1d20, which tells me any difference isn't their goal.

Of course, if I successfully teach people that is the difference, people will claim it is why they wanted it all along. That is an inevitable part of analysing a game system someone wants to use.

(2) Dungeon Fantasy/GURPS gets extra mileage out of the 3d6 bell curve by utilizing margin of success (either directly or via Quick Contests, e.g. for a feint, or resisting a spell). Since the bulk of the probability curve will always be around 9-12, each extra +1 not only boosts your success rate but boosts your average success margin. I don't know whether or not that makes GURPS not strictly "roll over/under" by your definitions, but it does suggest that merely shifting D&D to a 3d6 bell curve without utilizing margins of success will not yield the same benefits you get from Dungeon Fantasy/GURPS.

Thank you especially for insight #2.

The margin of success is just scaled.

Unless the exact amount of margin of success matters significantly more than the actual success, nope.

But, imagine a game where you rolled d20+modifier and what mattered was getting exactly 3 away from 15. Not within 3, not 3 or more higher, but your goal is to be exactly 3 away. That is a case where 3d6's bell curve isn't integrated and smoothed into being nearly the same as a black line.

It isn't a mechanic I'm aware of used in RPGs.

An actual example of a RNG that isn't roll over/under is Greg Stolz's ORE's "find matching pairs of dice from your pool of d10s".

 

[DND_Reborn]

Just to return to the OP, since this thread seems alive again, why bother doing the doubling of modifiers, adjusting AC/DCs, and using a d20 when using 3d6 takes care of the issue? It would seem more like doing all the adjustments to keep the d20 is what would really be pointless, wouldn't it?

I'm not certain what you think most people looking into 3d6 want, but IME it is to make easier things easier and harder things harder... which is what it does and does well IMO.

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).

FWIW, I agree with your analysis in the OP, that doubling things and such would allow you to use a d20 and give you similar results, I just don't see why you would bother when 3d6 does the trick.

 

[Argyle King]

Yes, but it pays to consider what you really want out of it. "Limit extremes" is a means, not an end in and of itself. What things actually happening in your game do you not want to happen?

Note that 5e already comes with bounded accuracy.

Depends on what you mean by "bounded accuracy."

 

[Steampunkette]

3d6 is great if you want character skill to be more important than chance.

1d20 is great if you want chance to be more important than character skill.

That's it. That's the whole thing. G'bye.

 

[Umbran]

Depends on what you mean by "bounded accuracy."

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

 

[NotAYakk]

Just to return to the OP, since this thread seems alive again, why bother doing the doubling of modifiers, adjusting AC/DCs, and using a d20 when using 3d6 takes care of the issue? It would seem more like doing all the adjustments to keep the d20 is what would really be pointless, wouldn't it?

Because people seem to think that the bell curve of the 3d6 does something besides rescalign modifiers.

Like:
Your stat modifier to DCs and d20 rolls is now (stat-10). Same for other stuff that modifies d20 rolls:
Proficiency bonus goes from +4 to +12 (doubled).
Spells and items set your AC to twice as far away from 10 as they used to; plate is AC 26, for example, and shields are +4 AC.
Magic items bonuses to attack rolls and AC go from +2 to +6.
Paladin aura save bonus is (Charisma-10).
Artificer flash of genius modifier is (Intelligence-10).
etc.

At 35/12 variance per d6 and 399/12 variance on a d20 (die size squared minus 1, all over 12), 3d6 has 1/4 the variance of 1d20, so the distribution is about half as wide.

If you want all of those effects, going 3d6 is fine.

I'm not certain what you think most people looking into 3d6 want, but IME it is to make easier things easier and harder things harder... which is what it does and does well IMO.

When people talk about 3d6, they almost universally talk about the impact of the bell curve.

Maybe they mean something besides what they say, but that is what I got.

FWIW, I agree with your analysis in the OP, that doubling things and such would allow you to use a d20 and give you similar results, I just don't see why you would bother when 3d6 does the trick.

Well, do they want magic weapons to range from +2 to +6, plate armor and shield to be AC 30 (42 if enchanted), proficiency bonus to be +4 to +12, and each point of strength to add +1 to hit?

Transforming the 3d6 space to the frankly more understood d20 space lets you understand what you are doing. The degree to which it is mathematically similar was a bit surprising to me when I worked it out.

I'm familiar with what the game looks like when ACs start hitting the 40s and magic weapons are +5 and base attack bonus is +10 or higher, and character stats range from 10 to 30 instead of 10 to 20.

Lots of people are familiar with it and its problems and advantages.

As that is what 3d6 does to the game, you can sit back and think about that.

Or not. I'm not going to stop you from playing with 3d6 just because you feel like it. I'm not the dice police! I just thought people would like to know what it did to the math of the game in a more familiar setting.

 

[Steampunkette]

When people talk about 3d6, they almost universally talk about the impact of the bell curve.

Maybe they mean something besides what they say, but that is what I got.

No, no. That's 100% all it is. The Bell Curve weights things to the center.

On a d20 you've got a 40% chance of rolling between a 7 and a 14. On 3d6 it's an 80% chance for the same range.

So character attributes and skill bonuses matter a lot more than the dice roll, most of the time.

If the DC is 12 and you've got a +5 bonus you've got a 10% chance to fail with 3d6 and a 30% with 1d20.

That's literally all it is. People who like 3d6 like making the game less about random chance and more about character skill.

 

[NotAYakk]

No, no. That's 100% all it is. The Bell Curve weights things to the center.

On a d20 you've got a 40% chance of rolling between a 7 and a 14. On 3d6 it's an 80% chance for the same range.

So character attributes and skill bonuses matter a lot more than the dice roll, most of the time.

If the DC is 12 and you've got a +5 bonus you've got a 10% chance to fail with 3d6 and a 30% with 1d20.

That's literally all it is. People who like 3d6 like making the game less about random chance and more about character skill.

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".

 

[DND_Reborn]

That isn't the Bell Curve that does it.

It is just the lower variance.

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

To repeat myself:

I'm not certain what you think most people looking into 3d6 want, but IME it is to make easier things easier and harder things harder... which is what it does and does well IMO.

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 mean, you obviously have a decent grasp on statistics/probability, so do you see what my quote above is say?

3d6 is less swingy (due to the decreased variance) than d20, it makes getting a more central result likely.

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. ).

 

[Steampunkette]

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".

...uh... huh.

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

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?

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.

I'm very confused, right now.