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

[FormerlyHemlock]

That’s pretty approximate, though I do follow the overall thrust of your post.

Yeah, it works best for the average case. The success rate for 10 and under (50%) is almost exactly twice that for 8 and under (25.9%) which is pretty close if you squint to twice that for 6 and under (9.3%). The closer you get to the ends of the distribution, the more inexact the heuristic gets. Worth mentioning because it's the opposite of the "the difference only matters for criticals" claim that I'm seeing most people make here.

 

[Steampunkette]

I'm not @NotAYakk, but I think you've misunderstood the claim.

NO ONE in this thread thinks that rolling 3d6 and rolling d20 produces the same likelihood of success against a given target number.

Rather, the claim is that there is a simple single-die roll that produces much-the-same likelihood of success against a given target number as 3d6 does. Hence changing the spread of results from a linear distribution (which is what a single-die roll gives) to a curved distribution (which is what 3d6 does) has no real relevance to game play. Because you can get almost identical play with a single die roll.

And if I use a d30 and reroll any value over 20 it's the same, so there's no point to using a d20.

Or you can use 2d10 or 1d100 and round to the nearest 5, divide by 5 and apply modifiers so you get the same result, so there's no point to using a d20.

That doesn't make 3d6 pointless. It doesn't mean people are fools who think "Red paint makes it go faster". It just means there's other ways to reach the same answer.

The fact that you can climb a ladder, take the stairs, chill on the escalator, ride the elevator, or get hucked up by a catapult doesn't mean there's no point to the various other methods of getting where you're going. Just means there's different options.

 

[Willie the Duck]

And clearly I did have to read the thread. Silly me.

I'm not @NotAYakk, but I think you've misunderstood the claim.

NO ONE in this thread thinks that rolling 3d6 and rolling d20 produces the same likelihood of success against a given target number.

Rather, the claim is that there is a simple single-die roll that produces much-the-same likelihood of success against a given target number as 3d6 does. Hence changing the spread of results from a linear distribution (which is what a single-die roll gives) to a curved distribution (which is what 3d6 does) has no real relevance to game play. Because you can get almost identical play with a single die roll.

Just to make this even simpler -- The argument looks to be: 'DC 10 with a -2 penalty (effectively DC12) on 3d6 is 37% chance of success. DC 10 with a -4 penalty (effectively DC14) on 1d20 is 35% chance of success. The difference is trivial, so why use 3d6 instead of 1d20 with doubled bonus/penalties (or certainly talk about switch dice methods to one approximating a bell curve as though it has a huge change?'

Fundamentally, I guess I would say that the OP is right that the difference between the two is minimal, but then why choose one over the other (I doubt highly that mentally adding together 3d6 is significantly different than remembering to double bonuses/penalties). Both methods would have some occasional edge case issues* and maybe are best served for games designed from the start with these assumptions.
*when switching back to 3d6+normal bonuses or 1d20+double bonuses instead of the roll-under method we've been using here, which obviously can run off the edges of the possible outcomes quickly, as the DC 3 example showed

Fundamentally, I just don't see what the OP thinks is such a big deal or what greater point they are showing. There are multiple ways to achieve the same results and some people advocating the 3d6 model may or may not realize this*. What does that show?
*Hypothetical people from discussions in the past are always great in that we can assume what we want about what they know or are thinking.

 

[pemerton]

I guess I would say that the OP is right that the difference between the two is minimal, but then why choose one over the other (I doubt highly that mentally adding together 3d6 is significantly different than remembering to double bonuses/penalties). Both methods would have some occasional edge case issues* and maybe are best served for games designed from the start with these assumptions.

The OP thinks that the doubling would be easier because it can happen out-of-play.

For my part, I spent decades playing Rolemaster (lots of d100 rolls and double- or triple-digit arithmetic) and these days play lots of dice pool games, so I don't have any sort of strong aversion to rolling and/or adding multiple dice!

Fundamentally, I just don't see what the OP thinks is such a big deal or what greater point they are showing.

The OP thinks that they are showing that moving from a linear distribution (single die) to a curved distribution (sum-of-dice) doesn't, in itself, make much difference provided that what we care about is meeting or exceeding a target number, rather than rolling a particular number exactly.

@FormerlyHemlock has made an interesting counter-point: I'll summarise it as once you consider the roll of modifiers in changing the target number, the difference between the two dice-roll methods increases enough to become interesting.

One thing I like about rolling 2d6 in Classic Traveller is that it tends to make ties more likely, and ties are interesting. But this doesn't contradict the OP, because ties are all about rolling an exact number rather than meeting or exceeding a target number.

And my personal favourite resolution method is dice pools where you count successes, because it allows for a chance of failure no matter how many dice are rolled, and also - assuming pools of reasonable size - tends to make ties more likely.

 

[Willie the Duck]

The OP thinks that...

The OP thinks that...

Thank you. It's not a great week for me (work-wise) to try to keep up on all the One D&D threads along with other lots-of-text threads like this one, so you likely saved me from having to abandon the endeavor. I guess it's all personal preference, but I also don't find adding 3d6 at the table that burdensome, and would dislike needing a binder of updated modifiers and target numbers. Regardless, we're back to it not making that much difference -- there are two ways to alter the game which would have similar effects (cue gasps).

@FormerlyHemlock has made an interesting counter-point: I'll summarise it as once you consider the roll of modifiers in changing the target number, the difference between the two dice-roll methods increases enough to become interesting.

One thing I like about rolling 2d6 in Classic Traveller is that it tends to make ties more likely, and ties are interesting. But this doesn't contradict the OP, because ties are all about rolling an exact number rather than meeting or exceeding a target number.

And my personal favourite resolution method is dice pools where you count successes, because it allows for a chance of failure no matter how many dice are rolled, and also - assuming pools of reasonable size - tends to make ties more likely.

Interesting. If FomerlyHemlock is who I think they are, I'm sure they've done their homework. Personally, I'm not overly convinced that simply changing around chances of success is all that interesting until the difference is big enough to routinely change behavior -- ex: PCs will not leap across fatal-distance-drop gaps unless the chance of failure is very low, so changing fail chances from 7% to 3% is actually interesting. Chance of ties--now that is definitely a big deal (and yes, is tangential to OP) ! If you start messing around with the chance of ties, suddenly what happens on a tie gets a lot more important (does one or the other side win? Does it re-test? If so, does it delay a round? etc.).

 

[Deset Gled]

I guess I'm joining this conversation late, but the first thing that struck me in the OP's analysis was this:

Why this works is because the mean of 3d6 is 10.5, just like 1d20. The standard deviation of 1d20 is sqrt( 399/12 ) and the standard deviation of 3d6 is sqrt( 3 * 35/12 ) = sqrt( 105/12 ). Which means SD(1d20) = 2 * SD(3d6).

When we double the modifiers on 1d20 rolls, we in effect halve its standard distribution. The resulting distributions have the same first and second moments. The difference -- the third moment -- is far smaller than you'd naively expect from looking at the "roll exactly" curves.

This change in standard deviation is played off like its no big deal. But to me, it's jaw dropping. Putting in into decimal, standard deviation of a d20 is ~5.766. Standard deviation of 3d6 is ~2.958. That not trivial, that's huge! Insanely huge, IMNSHO, considering the numbers we see in D&D. I don't know how you can simply handwave that difference away.

The second (and very closely related) issue is that changing to 3d6 makes bonuses all sorts of wonky. In standard d20 gaming, a mod of +/- 1 means changing the odds by 5%. It's flat across the board; you know what your bonus is getting you. In a 3d6 world, that +/- 1 will mean a change of <0.5% if you're near the limits of what is possible. Or it will be a change of >12% if you're right near the average. You have to know the target DC exactly (and all modifiers) to know if a +1 bonus is game changing or meaningless. And, frankly, that seems terrible to me.

 

[pemerton]

This change in standard deviation is played off like its no big deal. But to me, it's jaw dropping. Putting in into decimal, standard deviation of a d20 is ~5.766. Standard deviation of 3d6 is ~2.958. That not trivial, that's huge! Insanely huge, IMNSHO, considering the numbers we see in D&D. I don't know how you can simply handwave that difference away.

It's not handwaved away. See the sentence that you quoted:

Why this works is because the mean of 3d6 is 10.5, just like 1d20. The standard deviation of 1d20 is sqrt( 399/12 ) and the standard deviation of 3d6 is sqrt( 3 * 35/12 ) = sqrt( 105/12 ). Which means SD(1d20) = 2 * SD(3d6).

When we double the modifiers on 1d20 rolls, we in effect halve its standard distribution.

 

[Garthanos]

It's not handwaved away. See the sentence that you quoted:

I guess I'm joining this conversation late, but the first thing that struck me in the OP's analysis was this:



This change in standard deviation is played off like its no big deal. But to me, it's jaw dropping.

Me too its huge.

Putting in into decimal, standard deviation of a d20 is ~5.766. Standard deviation of 3d6 is ~2.958. That not trivial, that's huge! Insanely huge, IMNSHO, considering the numbers we see in D&D. I don't know how you can simply handwave that difference away.

The second (and very closely related) issue is that changing to 3d6 makes bonuses all sorts of wonky. In standard d20 gaming, a mod of +/- 1 means changing the odds by 5%. It's flat across the board; you know what your bonus is getting you. In a 3d6 world, that +/- 1 will mean a change of <0.5% if you're near the limits of what is possible. Or it will be a change of >12% if you're right near the average.

hovering near that median is likely more common ie normal distributions happen

You have to know the target DC exactly (and all modifiers) to know if a +1 bonus is game changing or meaningless. And, frankly, that seems terrible to me.

For me. Basically target DC differences and your attribute bonuses and stuff which are decided on like getting that d4 from a bard or even the OP +5 from shield are more significant compared to the random factors when using 3d6 than they are using a d20.
Results are less swingy.

 

[pemerton]

The second (and very closely related) issue is that changing to 3d6 makes bonuses all sorts of wonky. In standard d20 gaming, a mod of +/- 1 means changing the odds by 5%. It's flat across the board; you know what your bonus is getting you. In a 3d6 world, that +/- 1 will mean a change of <0.5% if you're near the limits of what is possible. Or it will be a change of >12% if you're right near the average. You have to know the target DC exactly (and all modifiers) to know if a +1 bonus is game changing or meaningless. And, frankly, that seems terrible to me.

Basically target DC differences and your attribute bonuses and stuff which are decided on like getting that d4 from a bard or even the OP +5 from shield are more significant compared to the random factors when using 3d6 than they are using a d20.
Results are less swingy.

I agree with @FormerlyHemlock here: I think the d20 actually significantly changes the effects of bonuses.

Eg if my required roll is 11, then a +1 bonus increases my chance of success by 10% (from 10 in 20 to 11 in 20).

Whereas if my required roll is 16, then a +1 bonus increases my chance of success by 20% (from 5 in 20 to 6 in 20).

And if my require roll is 20, then a +1 bonus doubles my chance of success (from 1 in 20 to 2 in 20).

The fact that the increments are constant (ie a +5% step per bonus) doesn't seem that significant to me, compared to this significant difference in the actual impact it has on my chance of success.

 

[Deset Gled]

Eg if my required roll is 11, then a +1 bonus increases my chance of success by 10% (from 10 in 20 to 11 in 20).

Whereas if my required roll is 16, then a +1 bonus increases my chance of success by 20% (from 5 in 20 to 6 in 20).

...

The fact that the increments are constant (ie a +5% step per bonus) doesn't seem that significant to me, compared to this significant difference in the actual impact it has on my chance of success.

That's a strange way to describe it. Looking at it that way, if your odds change from 0.001% to 0.01% you could say that the chance of success increased by 1000%. Yet both probabilities are too small to even be measured with a d20. Mathematically, what you're describing is basically irrelevant to meaningful calculations like weighted averages. And you haven't demonstrated how the 3d6 method makes anything better.

I won't say your math is wrong, I just have no idea how it is meaningful.