TOB Stance - Aura of Chaos - Min/Max Math Question

[ArcaneGlyph]

I'm not half bad at math, but today my brain is failing me.

If Aura of Chaos stance is used, what would be the optimal weapon damage to aim for?

1d4
2d4
1d6
1d8
1d10
1d12

(I think those are all the base weapon damage types)

I my gut feeling is that 2d4 would give you the best average damage and use of the stance, but I would love to see some mathemagics to confirm or disprove my gut.

O Wizards of Statistics Help Please?

Just in case: it means you add another die each time you hit the max value for that die. Eg. For each 6 you roll on a die 6, roll another die 6 until you don't roll a 6.

[Kazyan]

It involves repeated multiplication, so intuitively, I think you'd get weird behavior around 1d3 (specifically, e = 2.718281828...). "Optimally", aren't bigger dice better regardless of AoC, though?

[Psyren]

1d2 (http://www.myth-weavers.com/showthread.php?t=80909&page=6) actually. Imbued Healing is the more reusable, but more difficult way to do this. Luck Devotion is easier to get but a little wonky.

[AmberVael]

Assuming, however, that you're not going for the crazy d2 crusader cheese...

A quick internet search on exploding dice (the common term for the mechanics of Aura of Chaos, as it is used in other games and areas), gives both the equation used to deduce the probabilities of exploding dice, and the average of exploding dice. I am not the kind of person to do more involved statistics on my own time though, so if you want to analyze it or get an explanation, check here. (http://axiscity.hexamon.net/users/isomage/rpgmath/explode/)

Assuming it's correct (it does seem to be upheld by at least one other source I found), the average die values of exploding dice relevant to your question are as follows:

{table=head]Die|Average Result
d4|3.333...
d6|4.2
d8|5.14
d10|6.11
d12|7.09[/table]

While, as you'd expect, the lower dice benefit more from exploding, it's not enough to make up the difference between it and other dice. So while the 2d4 Falchion might be looking a lot cooler, the Greataxe will still have a slightly better average...
While the Greatsword, with its 2d6, continues to reign supreme.

[ArcaneGlyph]

Awesome! Thanks for the linkage and the analysis :smallsmile:

[demigodus]

for a dX, average roll is X/2 + 0.5 = ave

There is then a 1/X chance of an explosion
1/X^2 chance of a second explosion
1/X^n chance of getting off an nth explosion

so, it would be ave(1 + 1/X + 1/X^2 + ... + X^-n + ...)

which, if I remember correction, comes out to ave(1/(1-1/X)) = ave * (X/(X-1))

[(X+1)/2] * [X/(X-1)]

So, for a dX, the average damage is (X^2+X)/(2X-2)

max damage would be for a d1, cause that would be infinite.
minimum damage would be at the equivalent of a d(1+SQRT(2)), so a d2.41

Whether you increase the dice size, or decrease it, the average damage would increase. Since a d2 would only give an average of 3 damage, unless you can get a d1, you always want the biggest dice.

[docnessuno]

Since a d2 would only give an average of 3 damage, unless you can get a d1, you always want the biggest dice.

Except when multiple dices come ito play:
2d6 > 1d12 > 2d4 > 1d10 > 1d8

[kardar233]

Well, I happen to have time and Python on my hands so let's do some simulations:

1d4 gives us 3.33
1d6 gives us 4.2

So Vael's table looks accurate. Let's try multiple dice:

2d4 gives me 6.66
2d6 gives me 8.4

Looks like it scales linearly. That's to be expected, but I wanted to check. So if you use Vael's modified numbers for die averages you'll get the results you want.

[Aliek]

So.... How about a couple size increases and call it a day with say, 6d6 damage? Seems like a sweet way to increase your average damage if you're rolling tons of dice already.