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→Divergence of new build for Attack - AC of -2 vs critical immune foe
:::::: Incorrect. Any build relying on extra attacks per critical hit is not an infinite attack build. It is a potentially infinite attack build, but statistics state that you will eventually reach enough 1s to lose all your attacks. However, you're trying to compare an Dancing Apple against a Boring Orange. Irresistible Dance does not damage, so why would it have a DPR? There are other uses of abilities that go beyond damage; however this build does not. So, asking for the DPR is perfectly reasonable and saying it's infinite is, evidently, statistically impossible. --[[Special:Contributions/87.244.76.182|87.244.76.182]] 12:46, June 9, 2010 (UTC)
::::::: Math time: Not all [http://mathworld.wolfram.com/Series.html series] are [http://mathworld.wolfram.com/ConvergentSeries.html convergent]. Consider the [http://mathworld.wolfram.com/ArithmeticMean.html mean (average)] of discrete events, where the set of possible events is [[wikipedia:Countable set|countable]]. As you can see, it is common in mathematics to use the symbol '''∞''' for series that fail to converge, or [http://mathworld.wolfram.com/DivergentSeries.html diverge], by going towards infinity. It is true that while performing an individual [http://mathworld.wolfram.com/ProbabilisticExperiment.html experiment] with such a [http://en.wikipedia.org/wiki/Stochastic_process process] you are never guaranteed that it will continue forever, but the mean of such experiments can still be [http://mathworld.wolfram.com/Infinity.html infinite]. In this case, there is a [http://mathworld.wolfram.com/RealNumber.html real] probability greater than 0 that an individual experiment will never terminate. Assuming a more powerful viewpoint (one in which such experiments can be played out completely as a finite step), in any of these non-terminating cases you will, with probability approaching one, find arbitrarily large strings of 1s just as you claim. Despite these strings of 1s it still managed to fail to terminate. -[[User:Cedges|Cedges]] 13:39, June 9, 2010 (UTC)
== Incomplete ==
::::: The rules as written 1) don't say that immunity in any way prevents a threat, 2) require that threats happen against immune foes to work, and 3) have been interpreted in the FAQ to have threats happen against immune with no recinding. The current FAQ says that critical immunity negates the critical hit. The critical hit is a consequence of the threat which is a consequence of the attack. Critical immunity, as currently described, negates the threat no more than it negates the attack. -[[User:Cedges|Cedges]] 12:08, June 9, 2010 (UTC)
:::::: Dear lord, would you stop trying to justify your answers with 'THE FAQ'. The FAQ is just simply SOMEONE ELSE interpreting the rules instead of you and, you know what, they interpret them wrong quite a few times. Stating that FAQ says 'x' is not justifiable in Character Optimization. --[[Special:Contributions/87.244.76.182|87.244.76.182]] 12:50, June 9, 2010 (UTC)
I am removing the [[Template:Incomplete]] because, with the new build, this article no longer matches the description for that template. It meets the [[Dungeons_and_Dragons_Wiki:Content Requirements|Content Requirements]] as they are currently written. We do not have an [[:Category:Article management templates|article management template]] for [[wikipedia:Wikipedia:Accuracy_dispute|disputed]] articles or for builds that depend on rule interpretations that do not have a consensus among editors. If we add such a template, it should add a SMW property for being disputed so that pages like [[3.5e Optimized Character Builds]] could exclude or sequester disputed pages from their lists. -[[User:Cedges|Cedges]] 02:42, June 10, 2010 (UTC)
:Ghost, I disagree with your stance of "''you can't exactly "threaten" something with something that's immune to what you're doing/using. If something is immune to crits, you're not going to try to confirm the crit--it's immune to it, so you can't even threaten to crit it.''" Mace of Smiting from the DMG states, "and any critical hit dealt to a construct completely destroys it". However, it's important to note that few things are listed as actually being "immune to criticals" but are instead "not subject to critical hits". Therefore, they can be crit, however are not subject to what that (usually) entails. To me, this means that effects that trigger on a crit or threat of one still function against things like undead, contructs, PCs/NPCs with heavy fortification, etc (after all, the entry on vorpal weapons states that it indeed will decapitate undead and contructs, but that doing so doesn't kill them). Whether or not books and/or errata support this stance, I'm not 100% sure.--[[User:Tavis McCricket|Tavis McCricket]] 03:57, June 21, 2010 (UTC)
== New Build that relies on Threats ==
The previous incorrect build that relied on critical hits on critical immune creatures was replaced by a new build that relies on making threats towards critical immune creatures. Please give careful thought to whether the new build works. At one point, it included the following text, which I redacted because it comes across as making an [[wikipedia:Argument from Authority|argumentum ad verecundiam]], when instead it was meant to present three arguments, the third being from a different source:
<blockquote>You score a threat when you make a natural attack roll within your weapon's threat range. These threats are used to determine when to roll for critical hits as well as for some other mechanics, such as the Construct Lock feat from Races of Eberron which includes, "If you roll a critical threat against a [[SRD:Construct Type|construct]],...". More importantly, there is no current rule that you do not score threats against foes immune to criticals, and the rules as written say that you do. At one point in time the FAQ extolled that only the critical damage was stopped by critical immunity and that effects such as [[SRD:Flaming_Burst|flaming burst]] still functioned on a confirmed critical hit against a foe immune to criticals, so at the time the official opinion must have been that threats are scored against critical immune foes. The FAQ was revised to indicate that these effects do not work because there was no ''successful'' critical hit due to the immunity negating the critical hit. The revision did not touch on threats, therefore we follow the triple consensus of the rules as written, the rules as needed to work, and the unrevised past opinions of the FAQ.</blockquote>
-[[User:Cedges|Cedges]] 15:47, June 9, 2010 (UTC)
== Ricochets and Two with One Blow ==
The new build combines attack duplicating skills from three sources. I believe that my interpretation of the attack roll interactions from the two ricochets and two with one blow are correct in that the penalty to a specific roll due to one effect is not applied to other rolls made because of other effects. If this is incorrect the penalties are a little higher, more attack bonus is needed to auto-hit the ember on every attack, and divergence doesn't begin until Attack - AC >= -13. -[[User:Cedges|Cedges]] 15:47, June 9, 2010 (UTC)
== Optimized ==
Even if the incomplete template doesn't apply, could you demonstrate DPR vs. AC 40 against, say, a single foe, taking into account having to recharge maneuvers every 3 rounds and not having distracting ember on one of the two rounds during which you're not recharging maneuvers? I'm not seeing this as optimized yet, and would like a demonstration of it actually being optimized. --[[User:Ghostwheel|Ghostwheel]] 02:43, June 11, 2010 (UTC)
: DPR vs AC 40 at level 20: Dexterity 36 = 18 (initial) +2 (race) +5 (levels) +5 (inherent) +6 (enhancement). Attack >= 37 = 18 +13 (dex) +1 (size) +1 (race) +1 (weapon, probably more) +1 (aptitude) +1 (focus) +1 (point blank shot) +any other bonuses. Attack - AC >= -3, so we average 1.36 new original attacks per original attack and the damage per round diverges towards infinity. In short the DPR is ∞. More than half the time we do arbitrarily large damage, killing one enemy and gaining an arbitrarily large bonus to attack and damage if it wasn't immune to criticals (from Blood in the Water). We can do this every-other round, so we kill an AC 40 foe essentially once every 4 rounds. If there is one foe that isn't critical immune our damage from each and every attack becomes arbitrarily large as soon as we do an arbitrary amount of damage to one foe. I have a variant that doesn't rely on threats against immunes, doesn't use an ember, and triggers Blood in the Water even against immune foes. I will be posting it soon. It takes two more feats to develop and depends on weak spot, so doesn't work until level 14 or 15. -[[User:Cedges|Cedges]] 03:22, June 18, 2010 (UTC)
:: That was with a standard attacks with the ember. With a full round attack (with the ember) the arbitrarily large damage is achieved more than 3/4s of the time instead of more than half. If the ember can be placed between opponents the second and possibly third attacks of the round can be against different opponents, killing slightly more opponents per ember round. Also, if you redirect attacks gained from lightning mace (from my memory it's unclear if this would be allowed) you kill everything within range when the attacks diverge instead of only the target. -[[User:Cedges|Cedges]] 03:43, June 18, 2010 (UTC)
::: So please show the actual damage off of three rounds of combat, right after waking up. And no, you can't threaten an attack against something that you can't crit. With that in mind, please show the average DPR off of 3 rounds of combat against enemies (including the round you need to recharge maneuvers). --[[User:Ghostwheel|Ghostwheel]] 04:50, June 18, 2010 (UTC)
:::: The average damage per round for three rounds of combat is the same as for two, or even for one: infinite. Without the ability to threaten things you can't crit this build doesn't work at all (I have a variant that does), but whether or not threats happen against critically immune foes is a separate discussion. -[[User:Cedges|Cedges]] 05:10, June 18, 2010 (UTC)
::::: That isn't so, since A. you're only critting on a 15 or higher, B. you need to confirm the crit for BitW, C. you can't threaten a crit on the Ember, D. you need to spend a round to regain the ember after you've used it, E. you're not necessarily going to hit on every single attack, F. enemies aren't necessarily going to be adjacent to each other, G. Two With One Blow, Chakram Richoet, and Boomerang Ricochet all give penalties to attack making the chance of hitting (and confirming) lower than usual. Might have missed a few things, but those are a few of the reasons why you're not necessarily going to auto-kill every single thing you're attacking. --[[User:Ghostwheel|Ghostwheel]] 09:50, June 18, 2010 (UTC)
:::::: I've told you the average damage per round, infinite (which as I said previously isn't terribly useful for this type of thing), and the chance of "auto-kill"ing, about once every 4 rounds. Let me address your points. A: Already included in hits/attack calculation. B: I didn't include the bonus from confirming crits in hits/attack, and thus it is an under-estimate against crit vulnerable foes. C: The numbers without this behaviour are so bad as to be unworth mentioning; it is a separate discussion. D. Yes, that's why the frequency of "auto-kill" is half that of doing so with a single attack. E: Already included in calculations. F: That's what the ember is for, see C. G: These were included in the calculation. You are correct, this does not "auto-kill" every attack. Against your benchmark AC of 40 it does so half of every-other round with standard action attacks, and over 3/4s of every-other round with full round attacks. -[[User:Cedges|Cedges]] 15:13, June 18, 2010 (UTC)
::::::: Better find some better concrete proof then that you can even threaten something with a critical that can't be affected by critical hits (burden of proof, etc etc etc), or else it sounds like the whole idea's kaput. --[[User:Ghostwheel|Ghostwheel]] 15:31, June 18, 2010 (UTC)
:::::::: Cedges, could you please actually provide a proof that this series is divergent? You keep saying it, but that's a statement that actually requires a rigorous proof. It will certainly lay that argument to rest; alternatively, you could talk about the ''mean'' and ''median'' damage per round -- show that the calculation of such leads to an infinite number (countable or otherwise). Plus, you cannot threaten a creature with criticals who is immune to criticals. That is complete nonsense. [[User:Surgo|Surgo]] 19:14, June 19, 2010 (UTC)
=== Divergence of new build for Attack - AC of -2 vs critical immune foe ===
This is a random walk beginning at 1 and terminating when 0 is reached. The position represents the number of remaining attacks. It is decreased by one each time step, and increased by one for each granted attack.
At each step, there are the following possible outcomes, with change in number of pending attacks (including making this attack), and the probability that they happen
* -1 1/20 Natural one on Two with One Blow
* -1 4/20 No threat, miss foe
* Varies 9/20 No threat, hit foe, resulting in Chakram ricochet against ally
** -1 1/20*9/20 Natural one vs ally
** -1 13/20*9/20 Hit ally with no threat
** Varies 6/20*9/20 Threaten ally on ricochet
*** 0 1/20*6/20*9/20 fail to confirm vs. ally
*** 1 19/20*6/20*9/20 confirm crit vs ally
* Varies 6/20 threat, hit foe resulting in chakram ricochet against ally
** Varies 1/20*6/20 fail to confirm TwOB threat, continue with ricochet:
*** 0 1/20*1/20*6/20 Natural one vs ally
*** 0 13/20*1/20*6/20 ally with no threat
*** Varies 6/20*1/20*6/20 Threaten ally on ricochet
**** 1 1/20*6/20*1/20*6/20 fail to confirm vs. ally
**** 2 19/20*6/20*1/20*6/20 confirm crit vs ally
** Varies 19/20*6/20 confirm TwOB threat, continue with ricochet:
*** 1 1/20*19/20*6/20 Natural one vs ally
*** 1 13/20*19/20*6/20 ally with no threat
*** Varies 6/20*19/20*6/20 Threaten ally on ricochet
**** 2 1/20*6/20*19/20*6/20 fail to confirm vs. ally
**** 3 19/20*6/20*19/20*6/20 confirm crit vs ally
This results in the following total probabilities for the 5 outcomes: -1: 113/200, 0: 69/4000, 1: 13119/40000, 2: 171/20000, 3: 3249/40000. In 40000ths they are -1: 22600, 0: 690, 1: 13119, 2: 342, 3: 3249. The average drift each step is (-22600+0*690+13119+2*342+3*3249)/40000, or 950/40000, or 19/800. This is a random walk with bias or wind, the bias is away from zero in the same direction as the initial condition, and the step sizes don't increase. Therefore the average number of time steps until zero-crossing diverges. I need to find or write a proof of this obvious and simple property for walks with more than just a left or right step, failing that I'll work out the whole darned stochastic process. -[[User:Cedges|Cedges]] 03:34, June 21, 2010 (UTC)
:I'm not up to date on Markov processes; the result that the time steps until zero-crossings diverge is good enough for me. Provided the result is written down somewhere (so it is obvious), I find the above more than sufficient. Thanks for satisfying this! You should copy/paste this into the page (with perhaps a citation for the walks with more than two steps) to lay to rest any arguments from randoms who come and look at it. [[User:Surgo|Surgo]] 14:05, June 21, 2010 (UTC)
