Math and Game Effects of Bell Curve variant d20? [3.x]

[DodgerH2O]

So lacking the mathematical skills to do the analysis myself (or rather the time to learn the equations and run them) I was wondering how much "Bell Curve" alternate rules (Specifically 3d6, but if there are others, I'm open to them) change the basic assumptions of the d20 system, particularly 3.5 and PF.

Without any calculations, it seems like it makes BAB and AC variance between equal level opponents far more important. When most of the rolls end up between 9 and 12, that extra point that takes you out of the range would make far more than a 5% difference.

Similar logic would apply to skills. Skill ranks and taking 10 would be far more powerful than just hoping for a lucky roll. This makes sense to me from a "realism" standpoint, why can an adventurer who's lucky make a better suit of armor than a smith who has put in decades of practice to learn the art and takes the extra time to be sure it's made just right?

I'm still assembling what will probably be an E6 or E10 homebrew, and given those parameters, would the bell curve distribution have different effects?

I know from a statistical standpoint 3d6 is a pretty bad curve, but anyone with Yahtzee or Shadowrun will have enough. Would, say, 5d4 be better? I know that altering critical threat ranges and such would be a pain, whereas at least 3d6 has already set modifications. How about percentile dice with a gaussian curve in table format?

[gkathellar]

While you're correct on skill ranks being more valuable, things like taking 10 are dramatically less valuable because everyone rolls 10 all the time anyway. Taking 20 (18, I guess), on the other hand, is very much worth it.

As for alternate rolling systems in general: The more dice you add, the more predictable a roll is going to be. One die, on the other hand, will behave strangely on a consistent basis. 3d6 is elegant in that it's predictable and its average (10.5) is that same as that of a d20. Likewise for 2d10 (though that's somewhat more erratic).

5d4 would result in noticeably higher rolls, with an average of 12.5, and would be even more predictable than 3d6, with rolls hitting 12-13 an overwhelming amount of the time.

[Yitzi]

Without any calculations, it seems like it makes BAB and AC variance between equal level opponents far more important. When most of the rolls end up between 9 and 12, that extra point that takes you out of the range would make far more than a 5% difference.

Basically, although it makes things even less relevant when attack rolls tend to be well over AC.


I'm still assembling what will probably be an E6 or E10 homebrew, and given those parameters, would the bell curve distribution have different effects?

Not really.


I know from a statistical standpoint 3d6 is a pretty bad curve

It's actually pretty decent.


Would, say, 5d4 be better?

No, 5d4 would throw off the average (1d20 and 3d6 have 10.5 average, 5d4 has 12.5 average.) 5d4-2 would work, though (it'd have a bit more spread than 3d6, but a lot less than 1d20.). If you don't want constant modifiers, 7d2 works as well, if you can handle rolling that many dice (ok, more likely flipping coins) and don't mind a somewhat narrow range.
If you want the same average and roughly the same effective spread as 1d20, but with a bell curve, 11d6-28 gives a very good approximation to the bell curve.


I know that altering critical threat ranges and such would be a pain, whereas at least 3d6 has already set modifications. How about percentile dice with a gaussian curve in table format?

A bit tricky to do all of them, but if there's a particular roll you'd like an equivalent for, it shouldn't be too hard.