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Iokare, you have to already be able to construct the probability density function in either a piece-wise or continuous function. For instance, the continuous approximation for the probability density function for advantage is "f(x) = (2x-1)/400". From there you can have Wolfram integrate to find the cumulative density or construct moment generating functions to figure out the expected values, variance, etc. It's a useful tool for someone who's already experienced with programs like Mathematica.

Nov 23, 2012 -- 11:15PM, Jenks wrote:

Nov 23, 2012 -- 11:01PM, Ellyh wrote:

By statistics he means the mathematical science of statistics, no rolling is necessary it is entirely possible to math out all the ramifications using the science of statictics without ever needing to roll a single dice and have an answer that is more accurate that rolling the dice 10,000 times.

It's all to do with the theory of probability.

I firmly believe and have for a while that the developers have a very poor grasp of this branch of math because of the decisions they make which seem foolish if you do understand probability.

I'm curious, indulge me. Give me an example or two

The DC 17 Iron-Banded Door in the bounded accuracy article hailed as a good example of Verisimilitude. An 8 Str character(such as the playtest Elf Wizard) breaks it down 15% of the time, a 16 Str character(such as the playtest Dwarf Fighter without any way of increasing their chance of breaking down the door at the time of the article) 35% of the time.

This is being hailed in the article as an example of being good for verisimilitude, yet the result of the decision in the playtest is absolutely wacky. There's simply no reason in the world that an 8 Str character should ever be that close to a 16 Str character's chance of success. Not only does it feel wrong, but it completely skews the balance in game.

Basically, R&D should discover at some point that a talented PC should have roughly +10 above what an incompetent PC has - if an 8 Str character can break down a door 15% of the time, the high Str character should typically break it down 65% of the time. And the circus strongman type should have roughly +10 above that at max(or 115% of the time in this case)

Doing that lets the DM set DCs in a way that can make combat more exciting - the talented PC might consider doing something in combat that the incompetent would never do, yet at the same time, if the party lacks a PC with that skill, they'll eventually be able to muddle through it once the combat is resolved. Perhaps at some significant cost. At the same time, once you get to Epic, you can make Epic skill challenges without necessarily having to make all the PCs Epic at their skills. The talented PC might eventually break down that Adamantine door after several rounds of straining mightily(and alerting the Archdevil nearby as to the party's presence...), where the superheroic PC could try to do it in combat.

4e has the heroic difference down, the problem is that they eventually by default hand out a +16 to everyone.

Nov 25, 2012 -- 8:54PM, Mommy_was_an_Orc wrote:

The problem, as usual, is each new book inevitably comes out with 3-4 options that blows away the previous ones.

I think that analysis is pretty fair, except this last point. It's not that later options are always mechanically stronger than previous options but that they are mechanically different. For much of 4e few books actually surpassed the first PHB's options for classes, paragon paths, and epic destinies. However, the later books certainly expanded the list of optimized builds and added elements that refined older builds. (Putting aside the math-patch feats, I mean). It actually took the designers some time before they realized that every new epic destiny was always going to be compared to Demigod. I'm not sure they ever quite understood how every striker class was going to be compared to Ranger with twin-strike.

My point is just that with each new feature that designers introduce, the number of possible interactions in the system increases factorially, and even if each new feature is on par (per opportunity cost) with previous elements you'll still usually see a slight increase in optimization within those interactions.  That's because since new content is intentionally mechanically different optimizers have more options for whatever they are specifically choosing to optimize. Frequently what happens is that new features introduce new methods for players to exploit or more efficient and effective means for less popular options. While that's not a guarantee of power creep, it can't decrease optimum power without errata. It's also not an excuse for the bad designs that introduce dramatic powercreep, of course.

tl;dr: Well designed new game options are like expanding your selection of tools, since they don't necessarily make your other tools worse. Even if all of your tools have equal utility, the more tools you have at your selection generally the more efficient you can plan your projects.