5E 3d20 variant for 3d6/2d10 to replace d20. Thoughts?

dnd4vr

Hero
EDIT: Thanks for the feedback. Given the information people have shared/ brought up I think we will probably NOT use this idea for attacks, but might use it for skill checks and saves. If you have any additional input, please still reply to the thread. Thanks to all!

Original Post:

So, I had an idea a while ago, and I am sure others have as well. Like others, I don't like the linear d20 roll for mechanics. People have talked about 3d6 and 2d10, and I even like the 4d6-4 curve.

But, then don't follow the 1-20 range of the standard d20. Thus, my idea is to roll 3d20 and use the middle roll, discarding the high and low rolls. This way, you are just comparing the rolls and not adding them up. Slightly simpler and nice for people who don't want to do the math. I know it isn't too hard, but one guy in our group does struggle with it.

The curve generates "typical" results in the middle, will less likely results at the extremes, which to me is more indicative of most peoples' normal performance at tasks. Here's the distrubtion curve (not a "bell-curve" but still fills the concept):

1573235890777.png


You still add your normal bonuses, and adv/disadv is with 2d10 as normal since that is already non-linear.

I'm just curious for the people who tried the 3d6 or 2d10 variants, what are your thoughts on this idea?

EDIT: a critical hit is scored by the two highest rolls being equal and also a result that succeeds at the task.
 
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Salthorae

Imperial Mountain Dew Taster
Does your table NOT have a variant for something?

I like 2d10 for skills, but that's all I use it for, it smooths the outlier rolls and makes the bonus matter more. Not sure the statistical advantage/disadvantage of 3d20 vs. 2d10 honestly. That math is beyond me.
 

TiwazTyrsfist

Explorer
So my only observation here is that your crit rule seems like it would drastically reduce the number of crits. Which may be something you want, idk, but it's something that should be acknowledged upfront.

Under 1d20, you have a 5% chance to Crit.
Under your rule, you have a 5% chance to MATCH the top two dice, BUT what are your odds of that matching number being a success? If you need a 20 to hit, your chance of critting is now like 1 in 400. Even if you only need a 10+ I think your odds of a Crit are 1 in 40? (50% odds of success and 5% odds of matching means 2.5% odds of a crit if I'm doing probability correctly)
 

Blue

Orcus on a bad hair day
But, then don't follow the 1-20 range of the standard d20. Thus, my idea is to roll 3d20 and use the middle roll, discarding the high and low rolls. This way, you are just comparing the rolls and not adding them up. Slightly simpler and nice for people who don't want to do the math. I know it isn't too hard, but one guy in our group does struggle with it.
...
EDIT: a critical hit is scored by the two highest rolls being equal and also a result that succeeds at the task.
Due to bounded accuracy we are generally aiming for numbers in the middle. The difference between needing a 10 or an 11 is a hair over 7.5%. So at the number ranges we are dealing with the most a +1 is 50% more valuable than it is with a straight d20. This leads to more variation for common rolls, and also encourages optimization because it rewards it more.

But for all that, that's definitely playable.

It also increasing crits. It breaks down to - is the highest of 3d20 enough to succeed, and does either of the other match it. Again, assumign bounded accuracy and assuming an 11 or higher on the die is the average for success, that occurs 87.5% of the time for the highest. you then have a 5% chance the second die matches, and a 95%+5% chance the third die matches and the second does not. (The case of all three matching is already in first and second die matching.) So that's 87.5% * (5% + 4.75%) = 8.53%. So crits are about 70% more likely to happen. That's actually closer to the crit rate with advantage than the standard d20 crit rate.

What's the plan for things like champion's increased crit rate?
 

NotAYakk

Adventurer
Blue that isn't right; if your highest roll is 15, the other die doesn't have a uniform distribution from 1 to 20 (it cannot be > 15 for example).

The actual math looks annoyingly complex; every simplification I've tried runs into issues like that.

For example, if you are rolling 2d20 and using the high roll and get a crit on doubles, the distribution of the high roll not uniform, but the distribution of doubles ends up being a uniform distribution. So you get 0.05 times the 1d20 hit chance (P) crits, and 1-(1-P)^2 hit chance.

On the plus side, there are only 20^3 or 8000 cases. So counting is plausible, you could even do it in a spreadsheet.

Doing so we get:
0.07375
0.073625
0.073125
0.07225
0.071
0.069375
0.067375
0.065
0.06225
0.059125
0.055625
0.05175
0.0475
0.042875
0.037875
0.0325
0.02675
0.020625
0.014125
0.00725
so a 7.4% crit chance if you hit on a 1, and a 0.7% crit chance if you hit on a 20.

The number of ways that the two highest rolls land on N is equal to 3N-2 based on the spreadsheet.
 
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This gives me an interesting idea. The next time a character fails a save throw against a curse, I'll have them be cursed to roll 3d6 for every occasion where they would roll a d20. Crits will still trigger at 3 and 18.

I'll take notes and report back.
 

prabe

Villager
At one point, I had a system similar to this. A critical success involved rolling a nat 20 and two other successes; a critical failure involved rolling a nat 1 and two other failures. I knew (and know) that makes it more likely to critically succeed at something you're good at (and critically fail at something you're ... not good at); to me this was (and kinda still is) a feature, not a bug. My big problem with using it in 5E is that critical failures are ... not well-supported, and I don't like critical successes without critical failures.
 

dnd4vr

Hero
Does your table NOT have a variant for something?
Very little. I love to tinker with RPGs and 5E is ripe for it. :D

The critical rule was a quick after thought before I went to work. I have to work on it more tomorrow to decide if I like the idea or not. While at work I came up with a couple other ideas, but have to look at the math in the morning.
 

Salthorae

Imperial Mountain Dew Taster
This gives me an interesting idea. The next time a character fails a save throw against a curse, I'll have them be cursed to roll 3d6 for every occasion where they would roll a d20. Crits will still trigger at 3 and 18.

I'll take notes and report back.
what is the goal? Sorry I’m not seeing the point.
 

dnd4vr

Hero
I like 2d10 for skills, but that's all I use it for, it smooths the outlier rolls and makes the bonus matter more. Not sure the statistical advantage/disadvantage of 3d20 vs. 2d10 honestly. That math is beyond me.
Here are the "curves" for 3d20TM and2d10:

1573272798743.png


2d10 will average 11, not 10.5. It has a higher peak so a greater chance of a middle value. The extra probability is taken from the lower numbers due to the minimum result of 2 instead of 1 and the dual-line nature instead of a curve.

The 2d10 variant works well enough, but like I said in the OP I am trying to find a way to accomplish a greater middle result without having to roll dice and add them.
 

Don Durito

Explorer
Just use 3d20 for skills, which can't crit, and then use the basic d20 for attack rolls and saving throws.

Advantage/Disadvantage is more of a problem but I suppose you could role 4 dice and take the 2nd highest or lowest.
 

dnd4vr

Hero
Just use 3d20 for skills, which can't crit, and then use the basic d20 for attack rolls and saving throws.
I would like to try removing some of the swinginess of the linear d20. Even if we try it or something else, who knows if we'll stick with it. I know others have used the 2d10 and 3d6 options and I am curious how they like those and what they thing of this.

Still working on how I want adv/disadv to work, but likely go with RAW and just 2d20, since it already makes it non-linear.
 

Horwath

Explorer
3d6 works great.
Crits can also work very well if you take similar crit mechanics from PF2ndEd:
If you beat the AC/DC( :p ) by 5, it gets critical result(if able)

Advantage would be 5d6(drop 2 lowest), that is little weaker than 2d20 drop 1 lowest, but close enough.

It also leaves room for adding smaller bonus in 4d6 drop 1 lowest(for flanking IE)

opposite goes for disadvantage.

Elven accuracy is close with 8d6 drop 5 lowest, but that is a lot of dice to throw for every advantage.


but with 3d6 and crit being +5 over target, we can get back to small fixed bonuses that now actually means something.

3d6+2(or +3) would work very well as advantage.
 

Don Durito

Explorer
I would like to try removing some of the swinginess of the linear d20. Even if we try it or something else, who knows if we'll stick with it. I know others have used the 2d10 and 3d6 options and I am curious how they like those and what they thing of this.

Still working on how I want adv/disadv to work, but likely go with RAW and just 2d20, since it already makes it non-linear.
Well yeah, but do you find it an issue in combat situations? Surely you already have a non-linear distribution there given that a whole series of multiple roles in used to resolve combat?

Are you finding combat to be swingy?

I suspect that if you introduce a futher bell curve into combat you will be narrowing the range of encounters that are threatening to PCs without being lethal.
 

DEFCON 1

Legend
As a user of the 2d10 for skill checks system (for Adv/Disadv roll 3d10 take higher/lower two), while I can understand the curiosity of something like 3d20 take middle... I personally have no need to make sure 1s and 20s are still on the table. My range goes from 2 to 20 plus modifiers and that I have not seen any reason to go against it. The only advantage a 3d20 take middle might give you is if you wanted to make Nat 1s and Nat 20s much rarer, as they would only occur 1 in 400 times as been said. As I don't feel the need for that in my games, I personally would not use that system.
 

dnd4vr

Hero
Well yeah, but do you find it an issue in combat situations? Surely you already have a non-linear distribution there given that a whole series of multiple roles in used to resolve combat?

Are you finding combat to be swingy?

I suspect that if you introduce a futher bell curve into combat you will be narrowing the range of encounters that are threatening to PCs without being lethal.
Hmm. Excellent point. Since combat is typically a series of d20 rolls, the average result will resolve over the series of rolls.

As a user of the 2d10 for skill checks system (for Adv/Disadv roll 3d10 take higher/lower two), while I can understand the curiosity of something like 3d20 take middle... I personally have no need to make sure 1s and 20s are still on the table. My range goes from 2 to 20 plus modifiers and that I have not seen any reason to go against it. The only advantage a 3d20 take middle might give you is if you wanted to make Nat 1s and Nat 20s much rarer, as they would only occur 1 in 400 times as been said. As I don't feel the need for that in my games, I personally would not use that system.
Cool. Thanks for your input. Using the 2d10 or 3d6 for skills only introduces the idea of typical performance since only a single roll usually resolves the check.

So, you don't use this for saves though? I think if I suggest we go to 2d10 or 3d6 for skills, I might still also use it for saves as well. Saves aren't nearly as common as attack rolls, and neither are skill checks. Using a d20 variant for those won't be often so the additional complexity also won't be a constant "burden" to the mathematically challenged.
 

Krachek

Adventurer
It change a lot the “swing” factor.
but to give the ability to roll 3d6 instead of a d20 via an item can be an interesting power.
but I won’t make it permanent.
 

Blue

Orcus on a bad hair day
I would like to try removing some of the swinginess of the linear d20. Even if we try it or something else, who knows if we'll stick with it. I know others have used the 2d10 and 3d6 options and I am curious how they like those and what they thing of this.

Still working on how I want adv/disadv to work, but likely go with RAW and just 2d20, since it already makes it non-linear.
Wouldn't you want a curve the other way then?

Because really, you're generating a boolean succeed/fail. So what we're looking for to minimize swinginess (success change to fail and vice versa) is to minimize the change a +1 will make at the ranges you will most likely be rolling at. With bounded accuracy that's closer to the middle of the range.

So you shouldn't care that a 2 and a 3 are close to each other - they are both failures. What minimizes swinginess is if 10 and 11 are close to each other. So that a random +/-1 doesn't make a big difference in the results. So you want a distribution where the ends are common and the middle are rare. That gives you a good pass/fail with minimal amount of swinginess for small variations in your modifiers.

Don't care about the raw number rolled, that is an intermediary step in finding your pass/fail. So if you actually observe too much swinginess, the problem is in pass/fail getting thrown off.
 

Esker

Explorer
Wouldn't you want a curve the other way then?

Because really, you're generating a boolean succeed/fail. So what we're looking for to minimize swinginess (success change to fail and vice versa) is to minimize the change a +1 will make at the ranges you will most likely be rolling at. With bounded accuracy that's closer to the middle of the range.

So you shouldn't care that a 2 and a 3 are close to each other - they are both failures. What minimizes swinginess is if 10 and 11 are close to each other. So that a random +/-1 doesn't make a big difference in the results. So you want a distribution where the ends are common and the middle are rare. That gives you a good pass/fail with minimal amount of swinginess for small variations in your modifiers.

Don't care about the raw number rolled, that is an intermediary step in finding your pass/fail. So if you actually observe too much swinginess, the problem is in pass/fail getting thrown off.
I thought the idea was to make bonuses matter more? This should accomplish that, but with the side effect of making hard DCs harder and easier DCs easier.

As @Blue said, I think the way to analyze a system like this isn't to look at the distribution of individual rolls, but rather to look at the success probability for different DCs at different bonuses. The average outcome on a d20 type roll doesn't mean anything by itself, since you're always comparing to a threshold.

I tend to agree that this system probably isn't appropriate for checks where 1 and 20 are special (i.e. attack rolls). It could be quite nice for skill checks, but I suspect some tweaking of DCs will be needed. Also if you leave advantage and disadvantage alone it makes them relatively more potent, so that will take some consideration.

I'm not sure about saves... I'm sure you could work out an alternative system for setting things like spell DCs, but you wouldn't want to accidentally create a situation where you have effectively no chance of making certain saves if you're not proficient / focused on that ability / have advantage.
 

Blue

Orcus on a bad hair day
As @Blue said, I think the way to analyze a system like this isn't to look at the distribution of individual rolls, but rather to look at the success probability for different DCs at different bonuses. The average outcome on a d20 type roll doesn't mean anything by itself, since you're always comparing to a threshold.
But we do need to do that in the context of bounded accuracy. There is a range of results near the middle of the dice that will end up (after modifiers) to be a success more often than not because of how 5e handles targets (like AC and save DCs) and the modifiers to the die (like attack bonus and save bonus).
 

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