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

[DND_Reborn]

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):

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.

 

[Salthorae]

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]

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]

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]

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.

 

[CleverNickName]

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]

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.

 

[DND_Reborn]

Does your table NOT have a variant for something?

Very little. I love to tinker with RPGs and 5E is ripe for it.

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]

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.

 

[DND_Reborn]

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:

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.