Power Attack & Strength Damage[edit source]

Remember that PA and high str don't help much with TWF and Master Thrower respectively, since Weak Spot (which lets you do touch attacks) stops you from adding str damage to every attack, and Power Attack only gives a 1:1 bonus on main hand attacks, and no benefit on off-hand attacks when TWF. Also, Distracting Ember has to be within 30' of you and disappears in one round, so it's not the most reliable of powers. Lastly, you're going through Iron Heart powers like crazy--how much damage does this do, taking into account how often you need to refresh your maneuvers? --Ghostwheel 19:43, June 8, 2010 (UTC)

Power Attack and Strength 15 are prerequisites for Roundabout Kick. Distracting Ember doesn't even last an entire round, it only lasts for your turn. I didn't even consider using the Iron Heart powers with martial throw (one of them is ineligible, the other gives +4 to one attack, -4 AC) they are just prerequisites for Bloodstorm Blade and fodder for Blade Storm. Assuming we start with Strongheart Halfling and 15 dex, Dump a stat point into dex, get gloves of dexterity +4, at level 9 our dex is 22 for a +6 bonus, so our standard attack inside 10' is 16 = 7 +6 (dex) +1 (size) +1 (halfling) +1 (point blank). We hit a 25 AC foe about half the time, and an AC 15 ember on everything but a natural one. We summon an ember next to a foe, and toss our scimitar at it, ricocheting off with booomerang ricochet to hit the foe next to it. 37% of the time we accomplish nothing, 2% of the time we get a +1 bonus, 17% we hit once, 3% we hit once and get a +1 bonus, 2% we hit twice (or once and crit once), 4% we hit twice and get a +1 bonus, and 1% we get +2, 3% of the time we hit thrice, getting a +1 bonus, and 1% we get a +2. We hit four times 3% of the time, getting a +1-3 bonus 1% each. We hit 5 times 2% of the time, gaining a +2-3 bonus, and likewise with 6. We hit 7 times about 2% of the time, getting a +3 or +4 bonus. That covers the first 78% of the results. The 80% mark is 9 hits with 3 bonuses and 85% is 15 hits with 7 bonuses. At 88%, so one 8th of the time, we hit 20+ times garnering 8+ bonuses with anywhere between 1 and 22 attacks still to be made in the same round. (I terminated my rollout at 20 hits). The truncated average is 5 attacks left to make, 19 hits and crits made, and a +10 bonus acquired. That's round one. The finite tail diverges, and so our round one attack diverges., but this isn't important in actual play. On round two we make a somewhat weak normal throw and recharge distracting ember as a swift action, then we repeat on round 3, this time with more bonuses. Once we hit level 12 things get really crazy because we don't need to overcome the foe's AC before exploding and have slightly increased opportunities to roll well, and thus do so much more of the time. -Cedges 23:23, June 8, 2010 (UTC)
And at level 20 vs. AC 40? Touch AC, say... 25? And you need to "spend" iron heart maneuvers to activate most of the Bloodstorm Blade maneuvers. The Ember comes from the swordsage level, and you need to regain actions from each seperately much of the time, which means 2 rounds regaining maneuvers before you can repeat your shtick. Taking that into account, what's DPR look like? --Ghostwheel 00:45, June 9, 2010 (UTC)
The ember doesn't come from swordsage levels, see martial study. The swordsage was only used for blood in the water. This needs reworking to find a different approach or a different crit-buddy than the ember. If it had worked, damage per round would have been non-finite, but that doesn't mean much practically. It's like trying to figure out the damage per round of Otto's Irresistible Dance. -Cedges 01:16, June 9, 2010 (UTC)
Irresistible Dance has a DPR of 0. It does not damage. --TK 10:08, June 9, 2010 (UTC)
Exactly, which says very little about how useful it is. That hypothetical but impossible build had an average damage per round of . -Cedges 12:08, June 9, 2010 (UTC)
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. -- 12:46, June 9, 2010 (UTC)
Math time: Not all series are convergent. Consider the mean (average) of discrete events, where the set of possible events is countable. As you can see, it is common in mathematics to use the symbol for series that fail to converge, or diverge, by going towards infinity. It is true that while performing an individual experiment with such a process you are never guaranteed that it will continue forever, but the mean of such experiments can still be infinite. In this case, there is a 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. -Cedges 13:39, June 9, 2010 (UTC)

Incomplete[edit source]

Please remove the incomplete rating. There is more than enough synergy here. At level 9, for every attack you make, you are granted extra attacks with the following probabilities:

  • 6/20 Critical threat on Ember from Lightning Mace
  • 6/20*19/20 Critical hit on Ember from Roundabout Kick

You also get criticals off of your enemies, struck with a -2 ricochet from Boomerang Ricochet. There's only 19/20 chance to make this attack due to natural ones vs the ember.

  • 19/20*(portion of your 6 crit range that hits at -2)/20 Critical threat on foe from Lightning Mace.
  • 19/20*(portion of your 6 crit range that hits at -2)/20*(chance to hit foe) Critical hit on foe from Roundabout Kick.

If a foe has 10 more AC than your attack, these last two become

  • 19/20*6/20 Critical threat on foe from Lightning Mace.
  • 19/20*6/20*1/2 Critical hit on foe from Roundabout Kick.

The total of those four is 20.25/20. On average, when you make 20 attacks against an average foe at your level, you are granted 20.25 FREE attacks. When you make those 20.25 FREE attacks you are granted another 20.5 FREE attacks on average, which grant another 20.76 FREE attacks on average, which when you make them grant another 21.02 FREE attacks. Your average damage is already infinite, or to be more technically accurate, it has diverged. Although your mean damage is limitless, your median damage isn't (yet), and there is a fairly large probability that your attack sequence will be finite, but some of the finite sequences are quite damaging, and, with Blood in the Water, hitting the enemies becomes easier and more damaging with every critical you make.

The next 3 levels focus on overcoming the most obvious counter while increasing the chance that your attacks sequence will diverge by giving more opportunities for critical hits on a critical threat. At that point the build is fairly complete, and the remainder is just its logical conclusion. The next four levels make your attacks hit on touch attacks, which pretty much guarantees critical threats and confirmations on natural rolls of 15 or more. You are still at the mercy of your natural die rolls, needing to get at least a couple 15s or better before winning. To overcome this you make more attacks by using the full round attack action, by investing in feats or using maneuvers that increase attacks per round, or by using the Bloodstorm's full-round abilities. -Cedges 00:31, June 9, 2010 (UTC)

You can't actually threaten a critical on the ember, seeing as it's an elemental and thus is immune to crits. It procs neither Lightning Maces nor Blood in the Water. --Ghostwheel 00:39, June 9, 2010 (UTC)
Eww, didn't think of that; all the good stuff is hidden in the types and subtypes. I'm not sure if you can threaten or not vs. critically immune foes, some feats require a threat and work against immune foes, but it goes below divergence either way, unless two with one blow can threaten twice, and with my reading it doesn't. On other solutions, a non-lethal immune ally like a warforged with Improved Resiliency and Steadfast Determination would do instead of the ember. It'd require a low ac to hit though, and the setup would be even more fragile. How do I move this back to my sandbox correctly? -Cedges 01:08, June 9, 2010 (UTC)
This is a murky area. I've read every mention of critical and threat in the PHB, the PHB errata, and the 3.5 Faq. The DMG burst weapons don't work on critical immune creatures because they require a "successful critical hit", which the FAQ takes to be negated by critical immunity (page 54). The ones in the MIC that do work use the words "vulnerable to extra damage from critical hits". So a "successful critical hit" is one that deals the extra damage from the critical. None of this touches on a threat, which is only defined based on the threat range, what the natural die roll is, and whether or not it hits. The warforged Construct Lock feat (Races of Eberron 119) requires threats to work against immune foes to function. Therefore Lightning Mace works against foes not subject or immune to "critical hit"s or "critical"s. Blood in the Water doesn't work on these foes, as it uses the same "successful critical hit" language. Roundabout Kick says nothing about being successful and only uses the words "score a critical hit", which could go either way with the existing rulings but by caution falls in the doesn't work on immune foes category. -Cedges 04:26, June 9, 2010 (UTC)
I say that it's clear just from the word "threaten"--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. --Ghostwheel 07:48, June 9, 2010 (UTC)
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. -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. -- 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 Content Requirements as they are currently written. We do not have an article management template for 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. -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.--Tavis McCricket 03:57, June 21, 2010 (UTC)

New Build that relies on Threats[edit source]

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 argumentum ad verecundiam, when instead it was meant to present three arguments, the third being from a different source:

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 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 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.

-Cedges 15:47, June 9, 2010 (UTC)

Ricochets and Two with One Blow[edit source]

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. -Cedges 15:47, June 9, 2010 (UTC)

Optimized[edit source]

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. --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. -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. -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). --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. -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. --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. -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. --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. Surgo 19:14, June 19, 2010 (UTC)

Divergence of new build for Attack - AC of -2 vs critical immune foe[edit source]

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. -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. Surgo 14:05, June 21, 2010 (UTC)
Community content is available under CC-BY-SA unless otherwise noted.