Here is the "World Record Damage: Multiple dirty tricks for insane synergy!" thread original post and latest number. I believe that it was created by psly4mne. Here it is.
On the Nasty Gentlemen thread (LoP's dirty trick #4), we discussed ways of achieving world record damage by combining three Dirty Tricks - Attack of the Clones, Perpetual Damage Machine, and of course the Nasty Gentlemen. The number started at 10^21, then grew in fits and bounds. Eventually, it grew beyond the realm of calculation. Consequently, calculating the damage is getting difficult.
EDIT: I updated and simplified the routine. The damage is now much more. I am leaving this post as the original for reference, but the latest number is HERE. Last change: Used Reciprocal Gyre for higher seed damage, 2/18/06.
First, the builds. These are not that important, so don't focus on them. They just include the few necessary elements and a bunch of fluff.
Abe: DaelkyrHalfBlood Wiz5 / Incantatrix10 / ImpurePrince5
Bee: Warforged Egoist17
Cecil: Human Artificer14 / Cleric1 / Chameleon2
Equipment used: 2 staves of Body Outside Body, 1 staff of Blood of the Martyr, 1 staff of Delayed Blast Fireball at CL 20, 4096 Shadow Siblings. Only one or two charges on each staff are needed - Power Surge will take care of the rest.
Preparation:
Bee manifests Fusion with Cecil, then with Abe. Then the cloning begins. First, Abe/Bee/Cecil infuses the staff with Metamagic Item three times (for Repeat, Twin, and Persistent). Abe/Bee/Cecil casts Body Outside Body from one staff. The clone takes the second staff, infuses it with Power Surge, and clones himself. This process continues for a long time (and starts long before the routine begins), so clone supply is effectively limitless.
Whenever, a Fusion or an infusion needs to be replaced, the clones can take care of it. Whenever a Fusion on the main character (ABC) ends, a clone replaces it with a twinned Fusion targeting the two parts of ABC (so ABC is fused all day). This also replenishes ABC's power points. At the beginning of the day, a bunch of clones change their Chameleon feats to various metamagics, divine metamagics, and extra turnings. One changes its feat to Mental Resistance and one takes Snowcasting,Metamagic Item, and Cooperative Metamagic take care of all the metamagic.
All spells are Twinned, Repeated, Persisted (if applicable), and Quickened (if listed as a swift action). They are also shared with the symbionts, with the exception of the Shapechange.
Now, for the explanation of the routine. In the first round, all the necessary preparatory spells are cast. Clones repeatedly infuse ABC with Construct Essence to take care of ability damage for attaching symbionts. The symbiont clones attach in between Body Outside Body castings, so the results of the Body Outside Body castings multiply.
Next, ABC alternates manifesting extended Affinity Field and extended Fate Links. The Fate Links target ABC (who is under the effect of Affinity Field) and a clone who maintains an Affinity Field. This gives everyone within 20 feet (in particular, ABC and a lot of symbionts) a Fate Link to everyone else within 20 feet. This does not create an infinite loop because Fate Link cannot target the same creature twice.
Now, move within 20 feet of the bad guy. ABC changes into a Jovoc for the retributive aura ability. Then a clone uses a readied action to blast ABC with a heavily metamagicked Sphere of Ultimate Destruction. The Fate Links throw a lot of damage around. The only thing keeping the damage finite is the Mental Resistances damping the feedback with DR 3/-.
There are 14400 rounds in the duration of a Persistent spell.
1[standard] Shapechange (into a Chronotyrn)
1[swift] Death Ward
1[dual] Mirror Action (Mental Resistance) not twinned or repeated
1[dual swift] Delay Death
2[standard] Body Outside Body
2[swift] Body Outside Body
2[dual] Body Outside Body
2[dual swift] Body Outside Body
3-10400 Same as 2
10401[standard] Extend Fate Link
10401
focus
10401[dual] Extend Fate Link
10401[dual move] focus
10402-12400 Same as 10401
Except: must lose one Fate Link for an Affinity Field once every 40 rounds (including one in round 10401)
Total 2000/40=50 Fate Links lost
Also: Must lose one Fate Link to target the bad guy
12401[free] Change into a Jovoc with the Shapechange
12401[nonaction] A clone casts Sphere of Ultimate Destuction from the staff (Empowered, Maximized, Enervated, Fiery, Snowcast, Energy Substituted, Admixed, Repeated, and Twinned)
12401[standard] Blood of the Martyr
12401[swift] Blood of the Martyr
12401[dual] Blood of the Martyr
12401[dual swift] Blood of the Martyr
12402-14400 Same as 12401
Total:
Body Outside Body castings: 10399*4*4=166384
Symbionts: 4096*5^166384=1.090e116301
Fate Links among symbionts: 2000*2-51=3949
Damage Reduction: 3
Affinity Fields active at end: 0
Blood of the Martyr castings: 2000*4*4=32000
Initial Damage:
Sphere: 40d6
Enervate: 60d6
Fiery: 60d6+60
Admix: 120d6+120
Empower: 120d6+60d6+180
Max: 900+60d6
Total: 960-1260
960-1260 initial damage. The damage then scales according to the following nonlinear difference equations:
S(i)=0 for i <= u
S(i) = i-u for u < i <= 2u
S(i) = (i-u)+r*(2+a)(i-2u) + r*(n-1)*S(i-u) + n*r*(r+1+a)*S(i-2u) for i>=2u
D(i)=2n*S(i)+2n*(r+2)*S(i-u)+(8i-6u)
T(0)=D(m)
T(i)=D(T(i-1)) for i>0
Total damage = T(b), where
u = amount of damage reduction, here 3
r = number of Fate Links, here 3949
n = number of Symbionts after Body Outside Body cloning, here 1.090e116301
a = number of Affinity Fields active, here 0
m = damage dealt by initial spell (Delayed Blast Fireball in this case), here 900+60d6
b = number of Blood of the Martyrs cast, here 32000
S(i) is an exponential function. D(i) is therefore exponential. T(i) is feedback into an exponential function, which makes it REALLY BIG.
I am not going to solve this now. MAYBE I will be inspired to do it later. If anyone is feeling ambitious, the equation for D(i) can be solved explicitly with diagonalization or generating functions. I think generating functions would be marginally easier.
To give you an idea of what kind of numbers we are talking about, I ran a simulation for u=3, r=200, n=2^20, a=0, m=480, b=0. I could not do b>0 because it would take too long to run and be too big to write down.
The damage was 4.133e1321.
Now, let's look at the new routine, taking into account the change - we can now only have one Fate Link between any two participants. Also, I didn't take into account before that damage the target takes gets sent back through Fate Link (Fate Link is two-way). This matters a lot because the target doesn't have Mental Resistance
Current Routine Starts Here
The big Gyre deals:
Gyre: 25d12
Admix: 50d12
Enervate: 75d12
Empower: 75d12+37d12
Fiery: 75d12+37d12+112
Max: 900+37d12+112 = 1012+37d12
Total: 1049 - 1456
Setup: Similar enough that you can figure it out
Round 1: Same
Rounds 2-9800: 4 BOB castings
Round 9801 before actions: The psion (not fused) has previously manifested Affinity Field and shared it with his psicrystal. He now manifests extended overchanneled Fate Link between himself and his psicrystal. Affinity Field does its thing, and everyone is happy.
Shift into Jovoc, Blast for 1049 - 1456 damage initial.
Round 9801-14400: 4 BotM castings
Total:
u=3
r=1
n=7600 * 5^(9799*16)=1.563*10^109591
a=0
m=1012+37d12
b=4600*16=73600
The system of equations is:
S(i)=B(i)+(n-1)S(i-u)+M(i-u)
B(i)=nS(i-u)+M(i-u)+i
M(i)=S(i)+nS(i-u)+2B(i)
(initial conditions omitted)
Solving these by diagonalization yields (very roughly) S(i)=(2n)^(i/u)
D(i)=nS(i)+M(i)+B(i)
D(i) is very roughly (2n)^(i/u)
T(0)=D(m)
T(i)=D(T(i-1)) (i>0)
So we have:
Total damage > (2.5*10^36530)^^73600, using Knuth's up-arrow notation
Notice that this is more than before. By a lot. This is because stacking Fate Links was a bad idea in the first place - more Bloods of the Martyr are more important once the framework is in place
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Here is the original thread on the WOTC boards in case you want to read the other posts or the upper half of the latest number post.
