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

[Blue]

@dnd4vr , can you tell us what you mean by swinginess. Preferably in terms of success/fail and not numbers. What are you trying to minimize?

 

[Esker]

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).

Yep, totally agree. Most level appropriate attack rolls tend to hit on a natural 10, so moving probability mass toward the center will tend to increase the number of hits, despite the fact that the average roll is the same. On the other hand, my sense is that saves vs spells usually fail on a natural 10 (unless targeting a particularly strong save), so if this change is applied to saves, you are likely to wind up with more failed saves overall.

 

[Esker]

@dnd4vr , can you tell us what you mean by swinginess. Preferably in terms of success/fail and not numbers. What are you trying to minimize?

I think by swinginess he just means high variance of the roll, which means luck plays too great a role in the outcome.

 

[DND_Reborn]

@dnd4vr , can you tell us what you mean by swinginess. Preferably in terms of success/fail and not numbers. What are you trying to minimize?

Sure, glad to.

Think of the result of a typical person's effort at something, even when trying their best. Most often, their "best" will be typical of their skill. Rarely, the perform beyond their norm. Sometimes, they falter, but that is not common either.

With a flat d20, you are just as likely to roll a 1 as a 20 as a 10. In other words, you are just as likely to get worst effort, normal effort, or best effort.

Now, I see why due to combat being a series of rolls (typically not just a swing or two), the linear nature of the d20 sort of works to become non-linear. It still bugs me a little, but not so much as to worry about it right now.

For contested skill checks, for example, a person with a high bonus, say +11 (maximum normal sans expertise), will still lose to someone with a no modifier (+0) 9% of the time and 2.25% they will tie. I've never liked that as it seems pretty bad that someone with high skill and ability would not win over 10% of the time. I had another thread on this a while back.

Now, if I change to using 2d10, it drops to only 3.3% will no modifier win or tie against +11. 3d6 is actually even more extreme, lowering it the chance to only 0.45%! These actually works more towards my concept than 3d20 take middle, actually. My biggest like of 3d20 was there would be no extra math (yeah, not a huge deal but one player in particular has issues even with simple math).

So, ultimately I want skill to matter more than luck and with a flat d20, there is too much luck in rolling a high or low roll, resulting in a great performance or poor one. Results should be more typical. By switching to 2d10, for instance, the high and low rolls are less common, meaning performance beyond normal or well below are less likely. Thus, a higher bonus makes a greater difference towards getting higher results than just a lucky die roll.

Hopefully, that makes sense.

 

[DEFCON 1]

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.

I do not, no. Attacks and saves are just PCs versus a flat number result, a pass/fail situation against a neutral DC. So in that regard having a bell curve doesn't matter to me. Whereas for skill checks... since I use many of them as "knowledge" types of checks (whether it be magic trivia, nature trivia, religion trivia, perceiving things, investigating things etc.)... more often that not it is a bunch of the PC really competing against each other to see who reaches the DCs to get the info. Yes, its supposed to be everybody against the DC, but since only one of them usually needs to reach it to get the info for the party, the question we really end up asking is who is getting the info.

So with that in mind... I found that skill checks rolling 1d20 put much less emphasis on the abilities and proficiencies of characters and more on the randomness of fate, especially when multiple characters were all rolling a check together. The PC with a +1 could regularly beat the PC with the +6 enough times that it felt wrong. By going to the 2d20, when all the PC would then roll "against" each other to reach DCs for knowledge results... the higher ability/proficient characters would succeed noticeably more often against the ones who didn't. Which is what we wanted with the switch.

 

[Esker]

In case anyone is wondering, the probability formula for this system is:

P(Result = k) = 6 * (k-1)/20 * (1/20) * (20-k)/20 + 3 * (1/20)^2 * (19/20) + 1 * (1/20)^3

That is, the chance that middle die is k with all three dice being different (with each combination of values having 3x2x1 possible permutations), plus the chance two dice are equal to k and the other one is anything else (with 3 choices for which die is the odd one out), plus the chance that all three dice are equal to k (only one way that can happen).

 

[DND_Reborn]

I do not, no. Attacks and saves are just PCs versus a flat number result, a pass/fail situation against a neutral DC. So in that regard having a bell curve doesn't matter to me. Whereas for skill checks... since I use many of them as "knowledge" types of checks (whether it be magic trivia, nature trivia, religion trivia, perceiving things, investigating things etc.)... more often that not it is a bunch of the PC really competing against each other to see who reaches the DCs to get the info. Yes, its supposed to be everybody against the DC, but since only one of them usually needs to reach it to get the info for the party, the question we really end up asking is who is getting the info.

So with that in mind... I found that skill checks rolling 1d20 put much less emphasis on the abilities and proficiencies of characters and more on the randomness of fate, especially when multiple characters were all rolling a check together. The PC with a +1 could regularly beat the PC with the +6 enough times that it felt wrong. By going to the 2d20, when all the PC would then roll "against" each other to reach DCs for knowledge results... the higher ability/proficient characters would succeed noticeably more often against the ones who didn't. Which is what we wanted with the switch.

Yeah, I think on further thought I probably wouldn't use it for saves either but I am still debating it. Most saves have a DC of 20 or less (after all DC 8 + modifier caps around 19 for PCs), and rarely in the lower 20's. Still, without proficiency, hitting DCs in the higher teens is already hard.

Yep, the commonness of a low modifier resulting in better than a higher one annoys me as well.

 

[Esker]

The formula for the probability that the result is equal to or greater than k (which is what we really care about):

P(result >= k) = 3 * ((20 - k + 1)/20)^2 * (k-1)/20 + ((20-k+1)/20)^3

This is the probability that exactly two dice are equal to k or greater plus the probability that all three dice are equal to k or greater.

Here's how that compares to just rolling a single d20:

 

[DND_Reborn]

The formula for the probability that the result is equal to or greater than k (which is what we really care about):

P(result >= k) = 3 * ((20 - k + 1)/20)^2 * (k-1)/20 + ((20-k+1)/20)^3

This is the probability that exactly two dice are equal to k or greater plus the probability that all three dice are equal to k or greater.

Here's how that compares to just rolling a single d20:

LOL if you had asked I could have saved you all the effort since I had most of this in my earlier spreadsheet.

 

[jmucchiello]

The only issue I see here is while 10-11 is the "expected" outcome of a 1d20 roll, the DCs you usually see in the game generally require a roll of 12-13 to succeed. So I would think that turns the die rolls into a curve rather than being linear would cause combats to bog down. The need to "get lucky" would become more pronounced.

No empirical data so that's just a hunch.