Math help with alternative Weapon Damage by Size Progression

[Kchaka]

Yo.I'm trying to estimate how weapon damages escalate using the basic idea that all weapons damage dice double if they increase by 2 full sizes, so:

1d6 -> 2d6 -> 4d6 -> 8d6 -> 16d6 -> 32d6 -> 64d6 -> 128d6 -> 256d6 (For every 2 FULL SIZE INCREASES!)

This is true, but this progression's formula only works for every other size increase. If you want to increase it just once, it's normaly a 50% damage dice increase, but after that you can't increase it by 50% again. For a double increase you have to go back to the original formula, or you would get an "error", like for example 2d6 x150% = 3d6, x150% = 4.5d6 or 9d6/2, instead of 4d6 as of the original formula.

What I want to know is exactly what would these intemediary size PROPORTIONAL damage dices whould be (using D6s), if they all followed the original formula. So please, help me fill in this chart (for convenience let's say it's a Greatsword Chart):

1d6/4 -> ??? -> ??? -> ??? -> 1d6/2 -> ??? -> ??? -> ??? -> 1d6 -> ??? -> ??? -> ??? -> 2d6 -> ??? -> ??? -> ??? -> 4d6

4d6 -> ??? -> ??? -> ??? -> 8d6 -> ??? -> ??? -> ??? -> 16d6 -> ??? -> ??? -> ??? -> 32d6 -> ??? -> ??? -> ??? -> 64d6

The idea is, for example, if a Greatsword damage dice increases exponentialy as it's size increases, from 2d6 at Medium to 4d6 at Huge and 8d6 at Gargantuan, what would be it's proportial damage (in D6s) if we "stoped" it's growth at half way between Medium and Large size (Large Bastard Sword), at Large size (Large Greatsword) and half way between Large and Huge size (Huge Bastard Sword)?

Even though we know the official damage of these weapons are;

Large Bastard Sword: 2d8
Large Great Sword: 3d6
Huge Bastard Sword: 3d8

;these are not the proportial damage of weapons of these sizes should have if we were following the original formula, where the damage doubles with every 2 full size increases. I would like to know the real proportional damage according to this formula's curve.

I'm sorry if I'm not beeing clear enough. I belive the final damage dices (in d6s) will be far from round numbers.

[Avoron]

I'm not sure exactly what you're asking.

Mathematically, every step multiplies the number of dice by the square root of 2, if you're using the process of "same proportional increase with each step, doubles every two steps."

But that isn't how the actual scale works.
Basically, the rules themselves give you some of the progression, and once you get to a certain size it works like "double the number of dice every two steps" but NOT like "multiply the number of dice by root 2 every step," because the base values for the beginning steps are already there.

For example, the rules might give you:
2d6-3d6
and you can extrapolate from that:
2d6-3d6-4d6-6d6-8d8-12d6

There's a whole long thread about this, and they've come to a pretty nice consensus near the end about how almost all of the dice progressions work.

Sorry, I explained that rather poorly, and I'm fairly certain I completely missed the purpose of the question.

[Kchaka]

Got it!

The magic number is 1,1892071 ,or roughly 19%.

If you take any weapon damage and multiply by this number and you'll get the next half size increase step, like from a Longsword to a Bastard Sword, and if you keep multiplying, after 4 half size increases you'll get exactly the double of the original value, like:

Huge Greatsword >>> Gargantua Bastard Sword >>> Gargantua Greatsword >>> Colossal Bastard Sword >>> Colossal Greatsword >>>

--------- 4d6 ------- >>> ------------ 4d8 --------------- >>> ----------- 6d6 ----------- >>> ------------ 6d8 ------------ >>> ----------- 8d6 ---------- >>>

--------- 4d6 ------- >>> ------------ 5d6 --------------- >>> ----------- 6d6 ----------- >>> ------------ 7d6 ------------ >>> ----------- 8d6 ---------- >>>

Average x1,1892071

---------- 14 ------- >>> ------------ 16.65 -------------- >>> ----------- 19,8 ---------- >>> ----------- 23,55 ---------- >>> ----------- 28 ----------- >>>

This would be a more accurate progression of what damage weapons of these sizes should have

---------- 4d6 ------ >>> --------- 4d6 +1d4 ------------ >>> -------- 5d6 +1d4 ------- >>> -------- 6d6 +1d4 -------- >>> ---------- 8d6 ----------- >>>