D&D 5E Surprisingly, nothing breaks when switching D&D to 2d10 instead of d20

[JiffyPopTart]

I did a heatmap/grid of this crossreferencing a bunch of modifier values with a bunch of target numbers.

As stated earlier the end result is that it amplifies the ease or difficulty of any given roll.

Very Easy turns into Very Very Easy.
Easy turns into Very Easy.
Slightly Easy, Neutral, and Slightly Hard are unchanged.
Hard turns into Very Hard.
Very Hard turns into Very Very Hard.

I haven't tried the change in an actual game as I was worried the end result would be players feeling like going all-in on one thing rather than making a well rounded character would be encouraged with this system.

 

[Li Shenron]

There are advantages to bell curves, but the system has to be designed for it. D&D wasn't. This essentially makes easy stuff easier, and hard stuff harder - potentially much, much harder.

This might actually be a selling point for 2d10.

Yes D&D is designed for the comedy of sometimes dying when doing something easy and sometimes succeeding at something outrageous, but not everyone likes that. The cost of this is the lack of reliability when doing intermediate tasks, especially in the exploration phase. 2d10 increses predictability therefore reliability.

However the matter is more complicated by two aspects beyond the basic math:

- most DMs always skip checks for easy tasks, so how the lower side of the probability distribution looks like might not matter

- the availability of bonuses can vary significantly between groups

 

[Ancalagon]

I would be concerned that people with high stat and expertise would almost never fail a check. It's already rare with a d20 but with the shape of the 2d10 curve...

Oh and btw, if you want to have fun? try 1d8+1d12 - now that's an interesting distribution curve!

 

[clearstream]

I would be concerned that people with high stat and expertise would almost never fail a check. It's already rare with a d20 but with the shape of the 2d10 curve...

Oh and btw, if you want to have fun? try 1d8+1d12 - now that's an interesting distribution curve!

Or d0-9 and d1-10 perhaps?

 

[clearstream]

Bless, Guidance, Etc. become super attractive with 2d10.

Advantage becomes less of an advantage, unless you just add +3/+5 or something rather than rolling 2d10 twice.

I like the idea that bonuses are worth more so when you gain that +1 proficiency bonus or your attribute bonus goes up, it makes a bigger impact.

Pick up and reroll one of the d10s? Could allow naturally stacking up to two levels of (dis)advantage.

 

[tetrasodium]

I would be concerned that people with high stat and expertise would almost never fail a check. It's already rare with a d20 but with the shape of the 2d10 curve...

Oh and btw, if you want to have fun? try 1d8+1d12 - now that's an interesting distribution curve!

that's already the case under normal

 

[NotAYakk]

I would be concerned that people with high stat and expertise would almost never fail a check. It's already rare with a d20 but with the shape of the 2d10 curve...

Oh and btw, if you want to have fun? try 1d8+1d12 - now that's an interesting distribution curve!

You are playing roll-over, not roll exactly. The distribution of 1d8+1d12 (SD 4.1) and 2d10 (SD 4.06) and 1d15+3 (SD 4.3) and 5d6-7 (SD 3.8) are very hard to distinguish in actual play results of "how many times did someone miss or hit a given target number in a game", assuming you have some kind of ~5% auto-hit/auto-miss "crit" mechanics attached.

Like, 100s or 1000s of samples to have any decent chance to tell which is which.

You should roll multiple dice as your core roll-over DC resolution mechanic when
a) You have a mechanic that is more interesting than "add up the total".
b) You intend to do standard-deviation based scaling differently on two parts of the game differently, and this provides a quick shortcut.
c) You consider this a quicker shortcut than somehow boosting the size of modifiers and target numbers would be.
d) You consider rolling more than one die to be intrinsically better for no reason related to its distribution shape.

Take craps, for example: here you are trying to roll a number exactly. Now the shape of the distribution matters more than roll-over systems.

When you play "roll over", you care about the cumulative distribution function, and that is a kind of integration. Integration flattens (or averages, or smooths) the bell curve into a very slightly wavey line (again, outside of the tails, which compass the area of a "crit miss" or "crit hit" mechanic). If you are visual, don't look at the bell curve, compare the roll over/under possibility. And scale the two charts based on mean (average) and standard deviation (a scale on modifiers/target numbers) to isolate the effects of that from the effects of the curve. The two curves end up being ridiculously close to each other.

And often the reason is (d), people might have more fun rolling more dice, or they might have more fun believing a story about how the bell curve makes it a better game, or whatever. If those stories make you feel your game is better, and thus your game is better, yay!

I think, as someone doing (even amateur) game design, you should know the cause of the effects, and not just hand wave "it felt better". That lets you intentionally cause gameplay effects instead of accidentally getting lucky.

 

[Ancalagon]

@NotAYakk you cannot use SD (you mean standard deviation yes?) with a 2d10 or 1d8+1d12 curve. That's not a normal distribution. You need to use non parametric statistics.

Or you now, just look at the shape of the curve and think about how that will impact gameplay.

 

[NotAYakk]

@NotAYakk you cannot use SD (you mean standard deviation yes?) with a 2d10 or 1d8+1d12 curve. That's not a normal distribution. You need to use non parametric statistics.

Or you now, just look at the shape of the curve and think about how that will impact gameplay.

Central limit theorem says "nyaaaa" to that. Yes, it is an abuse of statistics. But I'm abusive towards statistics.

Stop looking at the shape of the curve and look at the shape of the integrated curve. Gameplay in roll-over is the chance you roll X or higher, not the chance you roll X.

And when you graph the chance you roll X or higher, correct for median and standard deviation, you get two curves that are barely separate.

I have done this. I described what I did. I checked my work. Do I have to generate the graph for the 50th time? I find it rarely helps.

The fastest way to do it is to do this. Graph (1d8+1d12) * (SD of 1d20) - average of that roll, against (1d10) * (SD of 1d8+1d12) - average of that roll, both "roll under", on a dice rolling website.

Here we go: AnyDice

The curves are basically on top of each other, outside of the "crit hit/miss" stuff. And I rounded the 1.4ish ratio to 1.5; that is where most of the difference between the curves come from.

What this shows is it compares resolution mechanics of:
(a) d20 game, where modifiers are scaled up by 50% and DCs are scaled 50% further from 10 compared to 5e.
(b) 1d8+1d12 game, where modifiers are left just like 5e.

Once you patch in a "crit miss/hit" mechanic covering the outermost 5%, it becomes nearly impossible to tell which of the two systems you are using from a description of only the hit/miss/success/failure results of the game.

 

[loverdrive]

So nice to see fellow mathematicians out in the internet.