On the virtue of 3d6

[crayzz]

or "Why I stopped worrying about high AC and learned to love advantage"

The d20 system is really swingy. You have an equal chance to your actual best, your worst, and your average. This is by design: D&D is supposed to be a partially luck based game. You're supposed to have decent chance to completely screw up no matter what, and a decent chance to land a solid crit on a superior opponent. A rogue with +11 to stealth can't just rest on their laurels: a 1 or a 2 will still get them caught. A fighter with a -3 to stealth can still try to be stealthy if they're really desperate: an 18 or 19 might still do the trick. You always have to weigh the risk vs the reward, because there's always that risk, and always that chance of reward, no matter how small.

There's no real sense of reliablity in the system, unless your bonus is gigantic enough to obviate all risk. 5e changed even that by following the bounded accuracy design philosphy: no more gigantic bonuses, and DCs and ACs were modified to a tighter range to reflect that.

If you like this and don't want it to change, then this post isn't for you because I'm going to throw it out the window.

Why 3d6

3d6 has a rough "normal distribution" quality to it. The tendency is towards the mean; the mean, median, and mode are all the same; etc. It brings in a sense of reliability (most of your roles tend to be in the 9 to 12 range) without completely eliminating bad or good roles (about 25% of roles will be 8 or less, another 25% of roles 13 or higher).

Note that 3d6 has a lower maximum role: you could make it 3d6+2, but I don't think that's a good idea, for two reasons. One is that 3d6 also has a lower minimum role, which also serves to make even bad roles more reliable: someone with a +7 on a skill, common by level 5, will auto succeed on any skill checks under 11. The other reason, and a more important one in my opinion, is that reliability is a huge boost in many cases. It hurts more to do really bad than it helps to do really well in most cases (this was an explicit design philosophy in 3.5e, where e.g. DMs were advised to go easier on parties that roll for HP at each level rather than taking the average). Someone with a +7 attack bonus is going to be hitting AC16 considerably more often using 3d6 vs 1d20. The cost of that is hitting AC 19 less often. I think that's a fair trade.

That might seem bad to you, but 5e also introduced a mechanic I've been personally fascinated with since I heard about it: advantage.

Advantage is way better in a 3d6 system

Advantage in 5e is a bit of a kludge. Because of bounded accuracy, the system hands out bonuses like Ebenezer Scrooge hands out shillings. Instead, the usual reward is advantage. The issue is that advantange doesn't stack, and lots of things give advantage. That means a lot of player options get obviated pretty quickly. It's a good thing advantage doesn't stack, too, since 3d20k1 becomes pretty powerful, and it gets worse from their.

At the same time, I really like it as a tool. It makes characters do well more reliably without making them do better than they could normally, which makes absolute sense in a lot of situations. A barbarian recklessly attacking something shouldn't necessarily be able to hit things she couldn't hit without being reckless, but by being reckless and ignoring defense she can attack well more often. It's an interesting mechanic.

In a 3d6 system, advantage becomes a bit more nuanced, and you can do a little more with it. Someone with advantage would instead role 4d6k3, which is a minor but substantial boost, somewhat worse than the 2d20k1 advantage (2d20k1 has a mean of ~13 and a median of ~15 whereas 4d6k3 has a mean and median of ~12).

But! Advantage is relatively easy to get, and we can let it stack: it's not as massive a boost as it was with 2d20k1. If you have advantage from 2 different sources (e.g. reckless attack on a prone enemy), you instead roll 5d6k3 (mean of ~13.5 and median of ~14). You can even let it stack a 3rd time, for 6d6k3, though I suspect ways to get 3 different sources of advantage are relatively rare.

Now this does mean advantage isn't quite as good as before, but the converse is also true: disadvantage isn't quite as ruinous. Having disadvantage is brutal in most contexts. Disadvantage where you roll 4d6 keeping the lowest 3? Not as bad. Not great, still sucks, and you're going to have a real hard time pulling off skills or attacks you need to roll a 16 for, but you won't be flubbing relatively easy rolls so often. And since rolling bad is worse than rolling well is good (at least in my opinion), this shakes out to an overall benefit over the old system.

If you have advantage and disadvantage from multiple sources, you can just let them cancel out. A small character using a long bow at long range against an immobilized enemy would roll 4d6 and keep the lowest 3.

Does this make martials worse?

D&D isn't great to martials. 5e is pretty good compared to past systems, but it pays to be careful: martials rely on advantage more than casters, from what I can tell.

Most martials don't rely on advantage in an explicit, class based sense. Advantage is mostly contextual (knocking an enemy prone, flanking them, etc) with the exception of barbarians through reckless attack. I would suggest giving barbarians a +1 to reckless attack at level 7 (they're better at bringing their strength to bear than most), and at level 11 allowing reckless attack to count as 2 levels of advantage. Note that this would mean a barbarian could easily get 3 levels of advantage (e.g. level 11 barbarian recklessly attacking a prone enemy).

For rangers I'd suggest giving advantage on attacking favoured enemies, making that class feature a little less anemic.

For rogues, I'd suggest adding 2d6 sneak attack damage for each level of advantage past the first.

Another idea is to allow characters to have automatic advantage with certain weapons as a feat: a fighter can fight with all weapons, but this fighter really likes his longsword.

What about skills?

So: skill checks. Same deal: if you can gain advantage from multiple sources, let them stack. The other suggestion I have is to let players take their time for advantage.

For example: the PCs break into a well guarded fort to bust out a prisoner. They need to find a key and a record of where the prisoner is actually being kept. The rogue finds their way into the officer's chambers and start searching through the records. They can't take as long as they want, because they might get caught: need to make an investigation check.

Under the old system, it's pass or fail. Maybe you have advantage from something, but there isn't a lot of choice the player can make. Instead, let them have a choice: they can take their time if they really want. Maybe they get caught mid search, maybe they don't, but they have the chance to weigh that risk in their head and make a meaningful choice. Maybe they do a thorough search, taking twice as long for advantage. Maybe they're desperate or just willing to take the risk, and they take 5 times as long for double advantage: hugely risky, but they'll probably find what they need if they aren't caught first. You can even do the converse: the rogue just wants to do a quick sweep. They do a rush job at disadvantage.

Summary

The key here is that advantage and disadvantage aren't quite as good as they were before. You can let them stack, and give them out more freely, which opens up player options in tactics, both in combat and skillchecks. Overall, this sort of approach would be weight towards tactical considerations: you need to find a way to get the upper hand on a high AC opponent, possibly through multiple means, but if you can do that, you'll hit them reliably. It makes everything less swingy, and makes advantage an incremental improvement, opening up your options as a DM and as a player.

Do I actually recommend this?

Not really. I obviously think the idea is cool, seeing as I wrote all this, but I suspect the design basis of 5e wouldn't really support this all that well. Bounded accuracy goes a long way to helping out, but I suspect you'd need to ease up on high AC opponents at the very least. You're just not always going to be able to find multiple ways of getting advantage.

It's too large a change to fit neatly in the system as written, but I strongly suspect a 5e-esque system could make it work beautifully.

[Yakk]

Meh, just double all bonuses on d20s.

Stats grant +1 per point away from 10.

Proficiency bonus is +4 at level 1, and goes up by 1 at every odd level.

Magic weapons start at +2 and go up to +6.

Armor grants 2x the base difference from 10. Dex max on medium armor is +4.

Shields grant +4, elven chain shirt +2.

Etc.

The "curve" of 3d6 is ridiculously tiny compared to the massive change in the standard deviation; d20 has a SD of sqrt( 399/12 ) while 3d6 has a SD of (105/12 ), basically a factor of 2. Rolling 3d6 instead of d20 for the most part just makes bonuses twice as big.

(And please, don't show me a "roll exactly X" chart of 3d6: we aren't trying to hit a target number in D&D, we are trying to roll over/under. Then scale it to account for doubled bonuses in the 1d20 version of the game. I've done this -- the resulting curves are barely separated, except in the critical hit/miss zones; and rolling 3d6 every time just to change how crits work seems like overkill.)

---

Note that this will completely destroy the 5e encounter building system either way. And it will swing "power" towards raw bonuses and further away from cool tricks.

[Lupine]

Very interesting.

I think it would fit D&D 5e better than you would expect. Sure, attacks on dragons will take longer, but that makes higher AC feel more... boss-like. As well as makes your AC feel more rewarding, as a dragon fails its roll against you.

I think the modification would be strangest with crits and critical misses.

I might introduce this at my table, letting players choose, and change their choice on long rest, as an experiment. If after a few sessions, they all end up on one style, then we know :smallsmile:

[Yunru]

A MAJOR weakness you fail to identify is what it does to the probability distribution.

Let's say you have three targets with ACs of 0, 10 and 20.
With 1d20:
A commoner with a +2 to hit has a 100% chance to exceed the first target's AC, a 65% chance to exceed the second's, and a 15% chance to exceed the third.
A 1st level fighter with a sword has a +5 to hit, for a 100% chance against the first, 80% against the second, and 30% chance to exceed the third.

With 3d6:
A commoner with a +2 has 100% chance, 83.8% chance, and a 0.5% chance respectively.
The fighter, meanwhile has a 100%, 98.2%, and 9.3% chance.

EDIT: And that difference only grows as the difference in static modifiers does.

[Rynjin]

I've always been curious as to how a hypothetical 3d6 conversion of a d20 system deals with situations where someone may only hit an attack roll or some such on a 19.

For example if you have a +1 bonus to attacks rolls against AC 20, you previous hit on a 19-20, but now you hit only on an 18 (which presumably counts as a Natural 20 in this system?). That seems like a significantly lower chance to hit in that circumstance, and similar corner cases. And for hitting the top end of the scale at all.

Edit:


A MAJOR weakness you fail to identify is what it does to the probability distribution.

Let's say you have three targets with ACs of 0, 10 and 20.
With 1d20:
A commoner with a +2 to hit has a 100% chance to exceed the first target's AC, a 65% chance to exceed the second's, and a 15% chance to exceed the third.
A 1st level fighter with a sword has a +5 to hit, for a 100% chance against the first, 80% against the second, and 30% chance to exceed the third.

With 3d6:
A commoner with a +2 has 100% chance, 83.8% chance, and a 0.5% chance respectively.
The fighter, meanwhile has a 100%, 98.2%, and 9.3% chance.

Yeah, this. Though minor nitpick, against AC 0 you still only have a 95% chance to hit, because a 1 always misses.

[da newt]

Wouldn't this scheme create far more predictable results and also make many outcomes a foregone conclusion - nearly auto successes or failures, by creating a much tighter and normal distribution of possible results?

In the long run, I'd guess this would generate a game where there is more incentive to Max/Min - Optimize - power game ...

[MaxWilson]

Why 3d6

3d6 has a rough "normal distribution" quality to it. The tendency is towards the mean; the mean, median, and mode are all the same; etc. It brings in a sense of reliability (most of your roles tend to be in the 9 to 12 range) without completely eliminating bad or good roles (about 25% of roles will be 8 or less, another 25% of roles 13 or higher).

Note that 3d6 has a lower maximum role: you could make it 3d6+2, but I don't think that's a good idea, for two reasons. One is that 3d6 also has a lower minimum role, which also serves to make even bad roles more reliable: someone with a +7 on a skill, common by level 5, will auto succeed on any skill checks under 11. The other reason, and a more important one in my opinion, is that reliability is a huge boost in many cases. It hurts more to do really bad than it helps to do really well in most cases (this was an explicit design philosophy in 3.5e, where e.g. DMs were advised to go easier on parties that roll for HP at each level rather than taking the average). Someone with a +7 attack bonus is going to be hitting AC16 considerably more often using 3d6 vs 1d20. The cost of that is hitting AC 19 less often. I think that's a fair trade.

Bell curves are nice, but IMO the biggest reason not to switch to 3d6 is: it's a lot more addition/subtraction and more opportunities to mess up your mental math. If I roll 12 attacks for 6 Githyanki Warriors, eight against the AC 17 Barbarian and four against the AC 15 Rogue, it's easy: I roll 12 dice and count how many of the first eight are 13+ and how many of the second four are 11+.

Doing the same thing with 3d6 would be a nightmare.

I do like bell curves and I'm looking for ways to import bell curves into my AD&D game, and for ability checks it's straightforward (3d6 absolutely does make sense, does a better job of modelling nonweapon proficiencies, makes 3d6-in-order ability score rolling very intuitive, and also makes psionic powers more reliable and psionic power modifiers more meaningful: +0 is a LOT more reliable than -2 even if your ability score is a 16!). But I feel that switching combat rolls to 3d6 would be too GURPish and not AD&D-ish enough. The same is true of 5E: there's got to be a better solution.

[pragma]

The "curve" of 3d6 is ridiculously tiny compared to the massive change in the standard deviation; d20 has a SD of sqrt( 399/12 ) while 3d6 has a SD of (105/12 ), basically a factor of 2. Rolling 3d6 instead of d20 for the most part just makes bonuses twice as big.

(And please, don't show me a "roll exactly X" chart of 3d6: we aren't trying to hit a target number in D&D, we are trying to roll over/under. Then scale it to account for doubled bonuses in the 1d20 version of the game. I've done this -- the resulting curves are barely separated, except in the critical hit/miss zones; and rolling 3d6 every time just to change how crits work seems like overkill.)

---

Note that this will completely destroy the 5e encounter building system either way. And it will swing "power" towards raw bonuses and further away from cool tricks.

1. The change in standard deviation is because of the curved distribution. I'm not sure what you're getting at with your mathematical justification.
2. How do you feel about a plot of chance to roll over a number? This link -- https://anydice.com/program/18d81 -- will show cumulative distributions when you click the "graph" and "at least" buttons. The 3d6 cumulative distribution is quite different from a 1d20 cumulative distribution, and shifting those distributions left or right relative to each other to reflect different modifier schemes doesn't help.
3. Monster CRs in 5e are already pretty inaccurate and don't have a fixed scaling with number of monsters, so the fact this change would mess them up doesn't seem like a big loss to me.

[Yunru]

Why not just throw away AC entirely, as it'll have the same effect?
At level 9, with a 20 in your attack stat, you roll a 20 or higher 50% of the time.
For comparison, the highest monster AC in the game is 25.
And your inter-quartile range is 4.

[Kane0]

B-b-but what about 2d10?

[crayzz]

Meh, just double all bonuses on d20s.

Stats grant +1 per point away from 10.

Proficiency bonus is +4 at level 1, and goes up by 1 at every odd level.

Magic weapons start at +2 and go up to +6.

Armor grants 2x the base difference from 10. Dex max on medium armor is +4.

Shields grant +4, elven chain shirt +2.

Etc.

The "curve" of 3d6 is ridiculously tiny compared to the massive change in the standard deviation; d20 has a SD of sqrt( 399/12 ) while 3d6 has a SD of (105/12 ), basically a factor of 2. Rolling 3d6 instead of d20 for the most part just makes bonuses twice as big.

(And please, don't show me a "roll exactly X" chart of 3d6: we aren't trying to hit a target number in D&D, we are trying to roll over/under. Then scale it to account for doubled bonuses in the 1d20 version of the game. I've done this -- the resulting curves are barely separated, except in the critical hit/miss zones; and rolling 3d6 every time just to change how crits work seems like overkill.)

---

Note that this will completely destroy the 5e encounter building system either way. And it will swing "power" towards raw bonuses and further away from cool tricks.

I'm confused about what you mean, here. The SD of 3d6 is roughly half of the SD of 1d20, but that doesn't make bonuses twice as big. It just means the contribution to deviations from the mean in 3d6 are roughly half as in d20, so there's a greater tendency towards the average. But those deviations go in both directions. Doubling all bonuses just shifts everything up, increasing the mean and breaking the bounded accuracy because of the higher ceiling. You could double all negatives as well, but there's less of those, and the bonuses and negatives aren't randomly selected. Characters are built to avoid negatives, meaning the overall effect is a higher mean and a higher ceiling.

I want to keep the mean and ceiling where they are, introduce somewhat less variance without eliminating it entirely, and broaden the design space for advantage.


Very interesting.

I think it would fit D&D 5e better than you would expect. Sure, attacks on dragons will take longer, but that makes higher AC feel more... boss-like. As well as makes your AC feel more rewarding, as a dragon fails its roll against you.

I think the modification would be strangest with crits and critical misses.

I might introduce this at my table, letting players choose, and change their choice on long rest, as an experiment. If after a few sessions, they all end up on one style, then we know

For crits, I'd suggest taking a page out of GURPS and counting 17 and 18s as crits (likewise 3 and 4 for critical failure). That makes crits rarer (only ~2% of the time) but with advantage stacking you have more room to play with making them more likely. And because advantage has a smaller impact, there are times where you won't want to go for advantage: moving from having advantage once to having it twice might not be worth it.

And if you have a really high AC enemy, stacking advantage gives you an out. Stun + flanking + reckless attack gives you a ~18% chance to crit, maybe more if you take my suggestions and boost reckless attack to two levels of advantage and allow automatic advantage on certain weapons as a feat. Advantage stacking gives you more options for making crits more likely, giving you tactical options against even the highest AC opponent.


A MAJOR weakness you fail to identify is what it does to the probability distribution.

Let's say you have three targets with ACs of 0, 10 and 20.
With 1d20:
A commoner with a +2 to hit has a 100% chance to exceed the first target's AC, a 65% chance to exceed the second's, and a 15% chance to exceed the third.
A 1st level fighter with a sword has a +5 to hit, for a 100% chance against the first, 80% against the second, and 30% chance to exceed the third.

With 3d6:
A commoner with a +2 has 100% chance, 83.8% chance, and a 0.5% chance respectively.
The fighter, meanwhile has a 100%, 98.2%, and 9.3% chance.

EDIT: And that difference only grows as the difference in static modifiers does.

I don't think those are reasonable numbers to choose from. AC 0 is practically non existent, most things are going to be between 10 and 25.

These are the results (https://anydice.com/program/18d86) (note I'm counting 17 and 18 as a critical hits and ignoring critical failures):



Bonus
Dice system
AC 10
AC 15
AC 20
AC 25


+2
1d20
65%
40%
25%
5%


+5
1d20
80%
55%
30%
5%


+2
3d6
84%
26%
2%
2%


+5
3d6
98%
62.5%
9%
2%



They're not wildly different, but the +5 has a much better chance at moderate to high ACs since your ability to hit an AC drops off faster as it increases. I think that's fairly reasonable.


Wouldn't this scheme create far more predictable results and also make many outcomes a foregone conclusion - nearly auto successes or failures, by creating a much tighter and normal distribution of possible results?

In the long run, I'd guess this would generate a game where there is more incentive to Max/Min - Optimize - power game ...

It does: it makes easy things easier and hard things harder.

I don't think I've ever seen a D&D system that wasn't rife with MinMaxing. Maybe 4e? I'm not too familiar with that one.


Bell curves are nice, but IMO the biggest reason not to switch to 3d6 is: it's a lot more addition/subtraction and more opportunities to mess up your mental math. If I roll 12 attacks for 6 Githyanki Warriors, eight against the AC 17 Barbarian and four against the AC 15 Rogue, it's easy: I roll 12 dice and count how many of the first eight are 13+ and how many of the second four are 11+.

Doing the same thing with 3d6 would be a nightmare.

I do like bell curves and I'm looking for ways to import bell curves into my AD&D game, and for ability checks it's straightforward (3d6 absolutely does make sense, does a better job of modelling nonweapon proficiencies, makes 3d6-in-order ability score rolling very intuitive, and also makes psionic powers more reliable and psionic power modifiers more meaningful: +0 is a LOT more reliable than -2 even if your ability score is a 16!). But I feel that switching combat rolls to 3d6 would be too GURPish and not AD&D-ish enough. The same is true of 5E: there's got to be a better solution.

I kinda like GURPS :(

(ok, I like it aesthetically, I've never actually played it)

I think AD&D would actually be a really good fit for this, actually. AC runs from 10 to -10, really -5 unless you hit god like levels. In low to mid levels where your AC is mostly 5 to -5, 3d6 works nicely IMO.


Why not just throw away AC entirely, as it'll have the same effect?
At level 9, with a 20 in your attack stat, you roll a 20 or higher 50% of the time.
For comparison, the highest monster AC in the game is 25.
And your inter-quartile range is 4.

I'm sorry, I don't understand what you're getting at.


B-b-but what about 2d10?

You could use 2d10! It would probably fit better with 5e than 3d6 anyway.

Advantage is, well, more advantageous the larger die size you use. You can't really let advantage stack with d20: it's too big a benefit, and would dwarf all other mechanics. You probably could let advantage stack somewhat with 2d10, but I'd probably cap it off after two or three advantages. Plus, because it's a larger benefit, you have to be more careful about how you give it away.

2d10 would probably slide more nicely into 5e than 3d6, but I think the design space and set of player options ends up being narrower.

[Yunru]

I'm sorry, I don't understand what you're getting at.

Clearly.
With 3d6, a +9 modifier (I.E. by level 9) has a 50% chance of hitting the highest common AC (20), and 25% chance of only failing by up to 2 (so well within Bless, Precise Attack, etc.). At that point you've irreparably broken bounded accuracy.
(For comparison, with a d20, in order to only have a 25% chance of missing by more than 2, you'd need a +12 attack modifier.)

Long story short: Bell curves are bad in a system built around flat distribution, m'kay?

[MaxWilson]

For crits, I'd suggest taking a page out of GURPS
*snip*

I kinda like GURPS :(

(ok, I like it aesthetically, I've never actually played it)

I think AD&D would actually be a really good fit for this, actually. AC runs from 10 to -10, really -5 unless you hit god like levels. In low to mid levels where your AC is mostly 5 to -5, 3d6 works nicely IMO.

I like GURPS too! I especially love GURPS weapons-based combat. Playing a warrior in GURPS w/ GURPS: Martial Arts (3E or 4E) is super fun. (A)D&D's magic system is more to my taste though, and I have never found a satisfactory way to retrofit Fireballs and Explosive Runes and the like onto a GURPS chassis.

I'm definitely not knocking GURPS, just saying that I haven't found a good way to make bell curves idiomatic for AD&D. "GURPS-ish" is not a pejorative.

To unpack that further: AD&D even more than 5E still has its roots in wargaming, and AD&D will absolutely do things like throw 2-12 Trolls at you as a single encounter, each with 3 attacks. In AD&D it's very important to resolve those 36 attacks in a few seconds. GURPS is much more focused on individual combatants--no sane GURPS warrior would ever fight 12 trolls at once if he could help it--and even then GURPS combat tends to drag sometimes. I blame the 3d6s for part of that, and I think that's one of the reasons my gut is telling me that AD&D needs a better solution for bell-curving.

The best notion I have right now is to say that bell curves matter most at the ends of the curve, and that maybe I should count up situational bonuses (prone enemy, higher ground) or penalties (like being blinded or at long range) and convert those to the defender's choice of advantage or numerical bonuses, at a rate of something like +1 extra dice per +/- 3 modifier. One of my major goals is to ensure that a 9th level Dex 14 Fighter and a blind, drunken, Dex 3 wizard shooting a longbow he's not proficient in no longer have the same 5% chance to hit an Ancient Red Shadow Dragon, even if the wizard is at extreme range. I want situational modifiers to matter, and bell curves can give me that... but I need to do some more math first to see if "defender chooses, +/- 3 per extra d20" gives reasonable-looking curves for all the situational bonuses and penalties.

[crayzz]

Clearly.
With 3d6, a +9 modifier (I.E. by level 9) has a 50% chance of hitting the highest common AC (20), and 25% chance of only failing by up to 2 (so well within Bless, Precise Attack, etc.). At that point you've irreparably broken bounded accuracy.

Long story short: Bell curves are bad in a system built around flat distribution, m'kay?

No I get that, but I think you're being a bit dramatic when you say "why not throw away AC."

With +9 using a d20, you have a 45% chance to hit AC 20, and a 55% chance of getting at least 18.

But conversely, using a d20, you have a 30% chance of hitting 22, and a 40% chance of hitting at least 20, which shakes out to more reliable than 3d6. 3d6 is good around 10+your bonus and lower, but moving higher than that and it becomes considerably worse.

Capping AC at 25 was a design mistake anyway, imo. It's too easy to get +10 at low levels. Being a little looser with the upper bounds would be better.

[Yunru]

But conversely, using a d20, you have a 30% chance of hitting 22, and a 40% chance of hitting at least 20, which shakes out to more reliable than 3d6. 3d6 is good around 10+your bonus and lower, but moving higher than that and it becomes considerably worse.
Except the problem is there's hardly any AC higher than 20. 20/22 is the standard highest AC. So being bad at rolling higher doesn't matter when you're already rolling high enough.

[MaxWilson]

Capping AC at 25 was a design mistake anyway, imo. It's too easy to get +10 at low levels. Being a little looser with the upper bounds would be better.

It's not really capped at 25 anyway. An Ancient Red Dragon with a Darkness spell up and the Shield spell is AC 27 with disadvantage to attackers. (Frightful Presence can also impose disadvantage even without Darkness.)

Even CR 4 Couatls are AC 24 after factoring in Shield 3/day.

[Fable Wright]

I don't think I've ever seen a D&D system that wasn't rife with MinMaxing. Maybe 4e? I'm not too familiar with that one.

4E required you to optimize or you would be inordinately punished. There was basically no room for quality waste if you wanted to be able to fight at level enemies.

[Yunru]

It's not really capped at 25 anyway. An Ancient Red Dragon with a Darkness spell up and the Shield spell is AC 27 with disadvantage to attackers. (Frightful Presence can also impose disadvantage even without Darkness.)

Even CR 4 Couatls are AC 24 after factoring in Shield 3/day.

Counterpoint: Most things aren't spellcasters.

EDIT: Although that does raise another point: Shield becomes so much more powerful now.

[MaxWilson]

Counterpoint: Most things aren't spellcasters.

EDIT: Although that does raise another point: Shield becomes so much more powerful now.

Counter-counterpoint: "cap" is about maximum, not mode.

[NorthernPhoenix]

Counter-counterpoint: "cap" is about maximum, not mode.

I don't know if there is a "hard max" for AC in the rules, but if there is or if there was, i'd assume it'd be 30 like the other stats. They've simply chosen not to give any statted out creature this value yet.

[Fable Wright]

I don't know if there is a "hard max" for AC in the rules, but if there is or if there was, i'd assume it'd be 30 like the other stats. They've simply chosen not to give any statted out creature this value yet.

The highest ACs I can find offhand are Tiamat (AC 25), the Tarrasque (AC 25), Sul Khatesh (AC 22 + at-will Shield for 27).

Though this, of course, raises a criticism:

At level 12, my Warforged Fighter 2/Battle Smith 10 in Full Plate with a Defensive Fighting Style has a base armor class of 20 (+2 Plate) + 4 (+2 shield) + 1 (Defensive fighting style) +1 (Warforged) and can cast Shield (+5) to get an AC of 31. If buffed up with Shield of Faith and Haste, that's AC 35.

It is extremely difficult for a dragon to hit to hit him at AC 31 (requires a 14+ on a d20, so a 35% chance). Under this variant, the dragon instead has a 16.2% chance of hitting. So my dude takes half damage from what he usually would.

Whereas my regularly tanky fighter who came in expecting a regular ol' game, strutting around with his AC of 23 from his defensive fighting style and nonmagical shield, is hit 91.75% of the time, up from the only 70% chance of a hit he already had. In other words, his defensive investment (which, let's be clear, is not insignificant at all), matters less than 10% of the time under this variant, whereas it mattered 30% of the time normally. When he dodges a dragon's blow, that's because of his defensive investment, and that actually does feel rewarding.

In other words, using the 3d6 distribution makes minor investments in something (like AC) almost completely unworthwhile (all his Fighting style and shield and so on got him was about a 5% less chance to be hit), while major investments make you nearly untouchable.

That kind of polarizing thing is exactly what 5e was supposed to prevent, since absolutely no one liked it in 3.5e.

Mark me in the camp against the 3d6 curve.

[Duff]

Go 4d6-3 and you have a better match for d20 possible range. Or 3d8-2 or 3.

[Yakk]

I'm confused about what you mean, here. The SD of 3d6 is roughly half of the SD of 1d20, but that doesn't make bonuses twice as big. It just means the contribution to deviations from the mean in 3d6 are roughly half as in d20, so there's a greater tendency towards the average. But those deviations go in both directions. Doubling all bonuses just shifts everything up, increasing the mean and breaking the bounded accuracy because of the higher ceiling. You could double all negatives as well, but there's less of those, and the bonuses and negatives aren't randomly selected. Characters are built to avoid negatives, meaning the overall effect is a higher mean and a higher ceiling.

https://anydice.com/program/18d95

Use at most and graph. The curves are right on top of each other.

I doubled 3d6 and subtracted 10; this is similar to halving d20 and adding 5, or rolling 1d10+5.

Look at the overlapped graphs. Their difference is *small*.

The tails, where there is a difference, are in the "crit hit/miss" extremes. The vast majority of experience at the table - hit, miss - comes from the shape of the middle of the graph.

3d6 D&D is almost identical to 1d20 D&D with modifiers (and DC distance from 10) doubled.

[Theodoxus]

I haven't put any thought into this, but since you can replicate a d20 roll with a d10 and a control die (typically a d6 for simplicity), it seems like there could be interesting rider effects you could incorporate...

Kinda like Craps for D&D, certain dice combinations (10 and 6 being the most obvious, but not necessarily the most interesting) might have added or alternate effects. You could even theoretically have each player have their 'special' combination. Say, I wanted 8 and 4; if I roll that on an attack, and the 18 + mod hits the target, I get my 'signature move' added to the attack (whatever it might be - a kick to the face for extra damage; a contested roll to knock prone; the People's Elbow - whatever. Like I said, zero thought has been given, just stream of consciousness as I type - but it would open up a new realm of possibilities without altering the math one iota and still give the general "feel" of manipulating probability by rolling multiple dice (and since 2d10 (using different colors or designating the 10s die as your controller) works just as well as 1d10 & 1d6, it even works for folks who hate rolling different polyhedrons at the same time. :smallwink:)

[Jerrykhor]

No way, i like my nat20 crits, tyvm.

[MaxWilson]

The highest ACs I can find offhand are Tiamat (AC 25), the Tarrasque (AC 25), Sul Khatesh (AC 22 + at-will Shield for 27).

And Sul Khatesh also has Foresight! AC 27 with disadvantage is not easy to hit. : )

[BigOunce]

No way, i like my nat20 crits, tyvm.

Just in case anyone was wondering what this looks like;

You have a 5% chance of rolling a 20 to crit on a d20. With disadvantage this becomes a 0.25% chance.

You have a 0.46% chance of rolling a triple 6 to crit on 3d6. Even with single advantage, that's only a 1.62% chance. Double advantage is (napkin math) still below that of a single d20 roll.

That's the natural result of moving probability to a bell curve - the extremes become considerably rarer. And I like my crits too.

[DMJosh]

I like the "feel" of a natural 20 too much to change the core mechanic of a d20 game. Yes, it's possible to get a similar feeling from a different crit mechanic, but there's just something iconic about the good ol' d20. It ain't perfect, but I like it.

On a more practical note, given that I play often with younger players and people unaccustomed to RPGs, I'd never switch to 3d6 just because it adds an extra counting step to every roll. It might be only a half a second a roll, but that adds up over a multi-hour session. Not quite as noticeable as when the game slows while your wizard counts fireball damage or your rogue counts sneak attack damage, but still...

[Mr Adventurer]

GURPS uses 3d6 and has alternative critical rules - 18 is an automatic crit, 16 or 17 is a crit if it is also a hit. IIRC.

[KorvinStarmast]

The "curve" of 3d6 is ridiculously tiny compared to the massive change in the standard deviation; d20 has a SD of sqrt( 399/12 ) while 3d6 has a SD of (105/12 ), basically a factor of 2. Rolling 3d6 instead of d20 for the most part just makes bonuses twice as big.
{snip}
Rolling 3d6 every time just to change how crits work seems like overkill.) This is a point I think often lost on those trying to fiddle with the d20 system (which is swingy).

[Cikomyr]

GURPS uses 3d6 and has alternative critical rules - 18 is an automatic crit, 16 or 17 is a crit if it is also a hit. IIRC.

I have an alternative silly idea.

Instead of "oh, make 18, 17 and maybe 16 crits", how about "if you roll triples, you crit"

The only difference between a crit hit and crit miss is if the crit.. Hit or miss.

So triple 3s could be a crit hit from someone skilled, and a crit fail from anyone else. You can even flourish the narrative, saying that any triple digit is "the character takes a cool chance"

[Diego]

GURPS uses 3d6 and has alternative critical rules - 18 is an automatic crit, 16 or 17 is a crit if it is also a hit. IIRC.
I grew up playing GURPS so I get excited every time it comes up.

GURPS is 3d6, roll under.
3 was critical success always, 18 was critical failure always
4 was crit success unless you needed a 5 or less, 17 was crit failure unless you needed a 16+ or less
5 and 6 were crit success if you needed 15/16 or less, 15 and 16 were crit failure if you needed or less.

The standard cases of 3 & 4 / 17 & 18 worked out to about 2% chance for crit success, 2% for crit failure. Compare to 5% of natural 20.

[crayzz]

I have an alternative silly idea.

Instead of "oh, make 18, 17 and maybe 16 crits", how about "if you roll triples, you crit"

The only difference between a crit hit and crit miss is if the crit.. Hit or miss.

So triple 3s could be a crit hit from someone skilled, and a crit fail from anyone else. You can even flourish the narrative, saying that any triple digit is "the character takes a cool chance"

If you're gonna go that route, make it double 6s and double 1s. Each has a 16/216 chance, putting them a bit higher than crits on a d20, making you less beholden to the probability curve.

[Mr Adventurer]

I grew up playing GURPS so I get excited every time it comes up.

GURPS is 3d6, roll under.
3 was critical success always, 18 was critical failure always
4 was crit success unless you needed a 5 or less, 17 was crit failure unless you needed a 16+ or less
5 and 6 were crit success if you needed 15/16 or less, 15 and 16 were crit failure if you needed or less.

The standard cases of 3 & 4 / 17 & 18 worked out to about 2% chance for crit success, 2% for crit failure. Compare to 5% of natural 20.

Whoops, got the numbers the wrong way up, thanks. That's it.

I would actually like to play a game of 5e trying out a 2d10 curve - I think 3d6 is a bit of a narrow curve as others are suggesting.

[GreyBlack]

Nah, brah. Everything should be rolled with percentile dice, and your success should be determined in percents.

Obviously.

In all seriousness, the debates on how to roll for success has been going on since literally OD&D. There used to be many different ways to roll for success, including but not limited to rolling a d6, d20, 3d6, or d100. I wouldn't mind seeing less unified mechanics in the game, but that's not the game 5e was designed to be. I'd even argue that 5e actively resists against that as unnecessary complexity.

In short: Good idea, Simpson's did it.

[Mr Adventurer]

Nah, brah. Everything should be rolled with percentile dice, and your success should be determined in percents.

Obviously.


Well, I mean, Warhammer Fantasy Roleplay...

[gkathellar]

An excellent little essay with some interesting ideas.

[Zigludo]

With regard to attack rolls and saving throws, I don't really approve of using 3d6. I considered it for a long time, and then I realized that it was going to mess with a whole lot of combat math. For instance Archery fighting style was going to get a lot stronger (it's already probably the best), Bless gets a lot stronger as does Bane, Precision Attack, Bardic Inspiration and Cutting Words, +1 weapons and armor, Shield of Faith... basically everything that affected accuracy or saves was made more powerful. Basically, the metagame of optimal play shifts heavily towards buffs. And in the meantime enemies with high AC got buffed and PCs stacking AC also became much stronger (a goblin swinging against a level 1 fighter with 19 AC gets his damage output cut by 66%.) So I started drawing up a bunch of conversion rules and tables and eventually... I realized that I was basically just converting the rules back into the same probability curves that the d20 attack roll is generating in the first place. And that if I just wanted more consistency for player actions I could usually achieve that result by fiddling with individual ACs and DCs and saving throws, with a lot less effort than rehauling the entire die roll system.

For ability checks though! I actually have been meaning to test that system out for quite some time now, with no changes to the rules, because the knock-off effects that it would have are actually desirable to me -- making the difference in aptitude / expected chance of success drastically different for different PCs, making proficiency and magical bonuses more powerful, etc etc. I haven't actually tested that one yet though :smallbiggrin:

[crayzz]

Nah, brah. Everything should be rolled with percentile dice, and your success should be determined in percents.

Obviously.

In all seriousness, the debates on how to roll for success has been going on since literally OD&D. There used to be many different ways to roll for success, including but not limited to rolling a d6, d20, 3d6, or d100. I wouldn't mind seeing less unified mechanics in the game, but that's not the game 5e was designed to be. I'd even argue that 5e actively resists against that as unnecessary complexity.

In short: Good idea, Simpson's did it.

You jest, but I'd absolutely enjoy that.


An excellent little essay with some interesting ideas.

Thank you!


With regard to attack rolls and saving throws, I don't really approve of using 3d6. I considered it for a long time, and then I realized that it was going to mess with a whole lot of combat math. For instance Archery fighting style was going to get a lot stronger (it's already probably the best), Bless gets a lot stronger as does Bane, Precision Attack, Bardic Inspiration and Cutting Words, +1 weapons and armor, Shield of Faith... basically everything that affected accuracy or saves was made more powerful. Basically, the metagame of optimal play shifts heavily towards buffs. And in the meantime enemies with high AC got buffed and PCs stacking AC also became much stronger (a goblin swinging against a level 1 fighter with 19 AC gets his damage output cut by 66%.) So I started drawing up a bunch of conversion rules and tables and eventually... I realized that I was basically just converting the rules back into the same probability curves that the d20 attack roll is generating in the first place. And that if I just wanted more consistency for player actions I could usually achieve that result by fiddling with individual ACs and DCs and saving throws, with a lot less effort than rehauling the entire die roll system.

For ability checks though! I actually have been meaning to test that system out for quite some time now, with no changes to the rules, because the knock-off effects that it would have are actually desirable to me -- making the difference in aptitude / expected chance of success drastically different for different PCs, making proficiency and magical bonuses more powerful, etc etc. I haven't actually tested that one yet though :smallbiggrin:

Yeah, that's roughly where I sit too. For combat it's too big a change and undermines too many assumptions. 3d6 fits better with skills, especially if you allow players to take their time for extra advantage. I never liked the lack of granularity is resolving skills in 5e. You either roll, or the DM just decides you can do it, but things my character can definitely do eventually but maybe not fast enough doesn't fit into that system very well. Letting players choose how "hard" they try and how much time they take gives them a few more options.

The sorcerer wants to convince some politician to make some deal at a state dinner: do they spend the whole evening trying their absolute hardest to convince this guy, or do they do a cold sell, and if he doesn't buy into it move on to someone else? You don't have as many options for differentiating those two scenarios mechanically, but 3d6 lets you be a little bit more nuanced through multiple levels of advantage.

[FilthyLucre]

I'd be interested in percentile dice rolls if it could be kept simple.

[Theodoxus]

I wouldn't mind seeing less unified mechanics in the game, but that's not the game 5e was designed to be. I'd even argue that 5e actively resists against that as unnecessary complexity.

Don't even get me started on the bait and switch WotC played us for between the PHB release and the DMG. They hyped up the fact that there'd be all kinds of dials and tweaks we have; options to make the game as simplistic or complex as we wanted.

And then the DMG came out, and there were just some variant rules that didn't do anything they had promised...

[Cikomyr]

The one thing that I struggle with is how you translate any "19-20" critical hit range.

[Fable Wright]

The one thing that I struggle with is how you translate any "19-20" critical hit range.

You go from critting on a 16+ (about a 5% chance) to critting on a 15+ (about a 10% chance).

[PoeticallyPsyco]

Hmm, it seems like most of the complaints about balance deal with combat, while it's skills that suffer the worst cognitive dissonance from the swinginess of d20 rolls (why does my supposedly hypercompetent [X] fail so often?).

Why not keep d20s for combat and use 3d6 for skills?

For the example of how long you want to spend searching a room, this is kind of an aside, but I'm seriously tempted to steal from Shadowrun's long-term skill challenges (can't remember what they're actually called). Not quite the same, but here's my idea: every [appropriate unit of time] you spend, you get to roll a d6. You find what you're looking for when the best three rolls meet or exceed the DC, however long that takes. You could actually generalize that to a lot of the exploration pillar to make it more immersive: every meaningful contribution your character makes to the goal nets them another d6 (advantage). For instance, uh... setting up a watch for camp. Just staying awake in a spot with a good view gives you your standard 3d6, but if you also set up trip wires with cans to make noise you roll 4d6k3, if your innocuous animal companion also patrols around (Aid Another action) that goes up to 5d6k3, etc..

[Fable Wright]

Why not keep d20s for combat and use 3d6 for skills?

"I have Expertise (Athletics), and I'd like to Grapple and Shove the target prone..."

Do I do this as a Skill roll, or an Attack roll? It's already one of the most powerful combat options out there, but whether you use a d20 or 3d6, it's an outlier and messes with system cohesiveness.

[Lucas Yew]

I'd support 3d6 over 1d20, 'cause not only I prefer the benefits of a bell curve to a flat probability, but that the cubic d6's are way more physically available compared to the other Platonic dice types (including d10s and d%s) where I live. Shame I can't acquire those crystal clear Harras casino dice, I lost my only set I acquired 20 years ago during a family tour to Las Vegas...

[MoiMagnus]

The d20 system is designed for the attack rolls.
In combat, you definitely don't want "skill-full almost always hit, skill-less almost always miss", because it transforms your game into a math problem where you have to use each of your action optimally. (I mean, I love fire emblem, but as a single player game)
The high variance is compensated by the fact that you make multiple attack rolls so it kind of averages out on a battle.

The d20 system start breaking out with save rolls. When the issue of a fight is determined by a single save roll, I find it kind of boring. But you could put the blame on spell design rather than on the d20 system itself, as a lot of spells do not have this problem.

The place where I find that replacing the d20 system by 3d6 make the most sense is skill tests. In 5e, the problems of the d20 system are kind of pushed under the carpet since the DM is only supposed to call for a skill test when he judge there is a relevant chance of success and a relevant chance of failure (otherwise, he is supposed to grant automatic success or automatic failure). But the need for that kind of DM hand-waving shows that the d20 system is used here for the sake of uniformity rather than because it is an adequate system.

[crayzz]

The d20 system is designed for the attack rolls.
In combat, you definitely don't want "skill-full almost always hit, skill-less almost always miss", because it transforms your game into a math problem where you have to use each of your action optimally. (I mean, I love fire emblem, but as a single player game)
The high variance is compensated by the fact that you make multiple attack rolls so it kind of averages out on a battle.



I think that's probably the strongest criticism of using 3d6.

Bell curve distributions happens when the result is a linear combination of variables with flat distributions. Attack rolls don't really fit that description very well, they're a one off action. Every individual attack is already being modeled. You get a bell curve esque result anyway as a result of all that rolling, making each attack fit to a bell curve distribution could tend to make things a forgone conclusion.

But certain actions aren't one off attempts. Part of what got me thinking about this was how to model a game of chess. A chess game could easily go for several dozen rounds. A single roll makes sense for a single one off action, but a lot of actions a play could take are qualitatively different. They're the result of minutes or hours of work, a series of iterative actions that build off each other.

I can imagine a system that breaks actions up into different categories of "iterativeness" and resolves them using different die rolls. Something like a history check should probably be a d20 roll: you either remember it or you don't. Medicine checks might be 2d10: they're more iterative than a one off actions (a lot of injury treatments are multi-step, but overall it boils down to "do you recognize the problem and know how to fix it). A persuasion check might be 3d6: convincing someone of something requires you to repeatedly read their reactions and judge what they need to hear to be convinced.

[Zigludo]

First of all, I want to say that the posts in this thread have been remarkably constructive and erudite. (And furthermore they seem to confirm most of the biases and assumptions I carried with me into this topic which makes them doubly erudite.) Usually by this point in a conversation about alternate dice mechanics and skill rolls at least one person is accusing another of being a bad DM...


"I have Expertise (Athletics), and I'd like to Grapple and Shove the target prone..."

Do I do this as a Skill roll, or an Attack roll? It's already one of the most powerful combat options out there, but whether you use a d20 or 3d6, it's an outlier and messes with system cohesiveness.

Per the rules it's an ability check the same as any other, with the only difference from a normal skill check being that both you and the opponent roll at the same time.

Let's say we're looking at a case where one of these Expertise (Athletics) player characters is trying to grapple a target, and the grappler's Athletics bonus is 6 higher than the target's Athletics/Acrobatics bonus. (I think 6 is a pretty good estimate of the disparity at low to mid levels, but at high levels it can get a lot more out-of-hand when the grappler has up to a +17 to Athletics checks.)


What follows is a little work I did in AnyDice: (link to see the data yourself and check my math. Click on "At least" and the data point you're looking for is at 0): (https://anydice.com/program/18e14)
Using the d20 system, if the grappler doesn't have advantage on the checks, the grappler has a 73.75% chance to successfully grapple. (And a ~54.39% chance to successfully grapple+shove prone combo with extra attack.)
If the grappler does have advantage (ie, raging barbarian, enlarged, whatever), the grappler has an 87.31% chance of success. (And a ~76.23% chance of pulling off the combo.)
Switching to the 3d6 system, the grappler has a 90.35% chance to succeed WITHOUT advantage. (And an 81.63% chance to perform the combo.)
In 3d6, with advantage (using the 4d6 drop 1 method recommended by most 3d6 advocates I've encountered online), that chance of success increases to 95.86%. (And a 91.89% chance of pulling off the combo.)

As expected the 3d6 system makes bonuses to the roll much more important and makes it harder for a contestant at a numerical disadvantage, and due to the contested nature is actually even more meaningful than the effect had when comparing a roll to a static DC. If you use the "roll 3d6 twice, take the highest total" method instead of the "roll 4d6, take highest 3 method", then the effect is even more pronounced. I'd generally recommend sticking to the 4d6D1 method if using a 3d6 system so as not to make Advantage (even) more powerful than intended by the developers.