2d10 as Replacement for d20?

[masteraleph]

I will note that it hurst anything that relies on Critical Hits- that might be part of the desired removal of optimization, but it definitely makes Student of Caiphon, Daggermaster, Avengers in general, and anything else that relies on crits particularly less powerful (presuming that a crit becomes a natural 10+10).

 

[Ancalagon]

VERY important note!

2d10 does not result in a bell curve! Instead, it's a pyramid. This is important because it means that the slope is constant.

This results in more predictable odds, and more constant effect of modifiers. The chance of rolling exactly an 11 on a 2d10 is 10/100. The chance to roll 12 is 9/100, the chance to roll 13 is 8/100... all the way down to 1/100 for a 20.

However, if you have 3 dice or more, *then* you have an actual standard deviation curve (or at least something close to it). The progression of the odds isn't so smooth.

 

[Ancalagon]

Interestingly, if the two die aren't the same size (say, 1d12+1d8) the probability curve is shaped like a truncated pyramid...

 

[TheCosmicKid]

Inspired by the PbtA mechanics resolution (roll 2d6, 6 or lower = failure; 7 - 9 = success with cost or complication; 10+ = success), which relies of a bell curve distribution of outcomes rather than sheer randomness, is it possible to implement a variant system in 4E without making any other changes? Rather than the three outcomes, this would still be a success or failure (fail forward, in some cases) on the roll against the set DC or defense score: roll 2d10 + modifiers against the DC/defense instead of d20 + modifiers.

From a mathematically persnickety perspective:

2d10 does not have the same mean as 1d20.
3d6, however, does. (An interesting fact that 1E and 2E took much more advantage of than the d20 System editions.)

Obviously, this decreases the random component of such rolls; consequently, perhaps, it may disincentivize or reduce optimization (or, at least, math fix optimization, like expertise and improved defense feats).

It's important to quantify how exactly the randomness is decreased.

Speaking of 3d6 because of the mean thing...

Imagine a d20 check with a 50% probability of success. A +0 check against DC 11, for absolute simplicity. The probability of success if you switch to 3d6 is still 50%. Half of the results are still above the DC, half below. So the randomness here has changed not at all.

Now give the check a small modifier: +1, still against a DC of 11. The probability of success with a d20 roll becomes 55%. But with 3d6, it's 62.5%. And this gap continues to widen as the modifier increases. By +5, it's 75% for the d20 but over 95% for the 3d6.

So coin tosses are still coin tosses, but modifiers mean more on a bell curve. Or more precisely, differences in modifiers mean more. Characters who are good at a task find the task much more of a "sure thing", while characters who are bad at the task may find it a near-impossibility. If your goal is to reduce the importance of math fix optimization feats, then, I'm sorry to say that I expect this change to have the opposite effect.

 

[darkbard]

Thanks for this feedback, folks. These are precisely the factors that, not having done any of this math in 25 years or so, I have trouble conceptualizing.

 

[AbdulAlhazred]

VERY important note!

2d10 does not result in a bell curve! Instead, it's a pyramid. This is important because it means that the slope is constant.

This results in more predictable odds, and more constant effect of modifiers. The chance of rolling exactly an 11 on a 2d10 is 10/100. The chance to roll 12 is 9/100, the chance to roll 13 is 8/100... all the way down to 1/100 for a 20.

However, if you have 3 dice or more, *then* you have an actual standard deviation curve (or at least something close to it). The progression of the odds isn't so smooth.

It is still a normal distribution, as any distribution of independent measurements is by definition. The 'pyramid' you refer to is merely a result of the fairly high standard deviation and the granularity of the measurement (that there are only 10 discrete values in this case). Obviously if you take more measurements (use more dice) then you will get a steeper curve (smaller standard deviation) and because more different results are possible, it will also be a better fit to the bell curve.

What IS true, even for 2d10, is that getting a +1 when you need a 12 to pass a check is vastly more useful than getting a +1 when you need an 18 to pass a check. As I said before though, given that most checks in 4e fall into a range of requiring an 8-14 to pass them, you're not going to see a massive difference if you use 2d10 vs 1d20. It will be different for specific checks, but its going to mostly come out in the wash.

 

[Ancalagon]

It is still a normal distribution, as any distribution of independent measurements is by definition. The 'pyramid' you refer to is merely a result of the fairly high standard deviation and the granularity of the measurement (that there are only 10 discrete values in this case). Obviously if you take more measurements (use more dice) then you will get a steeper curve (smaller standard deviation) and because more different results are possible, it will also be a better fit to the bell curve.

The pyramid is a property of rolling two dice of the same size - you will get it with 2d4 and 2d1000. 3d4 will look more like a bell curve than 2d100, this is not due to granularity, but the number of dice.

What IS true, even for 2d10, is that getting a +1 when you need a 12 to pass a check is vastly more useful than getting a +1 when you need an 18 to pass a check.

That is correct. a +1 increases your chance by 10/100 when you started at 12 to pass, but only by 4/100 when getting it at 18 to pass.

 

[Garthanos]

I will note that it hurst anything that relies on Critical Hits- that might be part of the desired removal of optimization, but it definitely makes Student of Caiphon, Daggermaster, Avengers in general, and anything else that relies on crits particularly less powerful (presuming that a crit becomes a natural 10+10).

One could make a crit a natural 18-20, this would be 4%

One could even then do something interesting with each of those.

18 == Basic Crit
19 == Advanced Crit
20 == Superior Crit

 

[AbdulAlhazred]

One could make a crit a natural 18-20, this would be 4%

One could even then do something interesting with each of those.

18 == Basic Crit
19 == Advanced Crit
20 == Superior Crit

Yup, this is really the MAIN advantage of using multiple dice, which is that you have some 'slots' that are much lower probability, and some that are a bit higher probability, so you can tune things a bit finer. This can help avoid needing to make secondary checks or other such mechanisms that you might otherwise need in order to regulate things that should be VERY rare.

OTOH one might ask WHY would you want to have results which are such huge outliers? It tends to make your game much more swingy.

 

[Garthanos]

And that's my big response really is 'Meh'. It just isn't going to change the game enough to matter. Not averaged over many encounters of various types. Nobody will really NOTICE a difference, which is the main thing.

i suspect it is a philosophy thing....