Counting missiles

[Empyreal Dragon]

Short sweet to the point.

Reserves of strength to uncap magic missile by 3 CL for 6 missiles.

Force missile mage for 8 missiles.


Now the hard part.

Let's say I make those missiles twinned and repeating with free metamagic.

Now pack both into an arcane fusion, itself twinned and repeated,

Now pack that fusion, into a greater fusion twinned and repeating, with another missile casting, twinned and repeating.

I can't quite work out the math,

But it should be something like...

Gfuse
Mis 32
Fuse
Mis 128

Gfuse
Mis
Mis
Fuse
Fuse
Mis
Mis
Mis

Etc.

How many missiles do we end up with at the end?

[Xervous]

Arcane fusion = 2m
Twinpeat is 4x, so AF is 8m

GAF is AF+m. So 9m
Twinpeated to 36

M= 8, so 288 missiles

[Darg]

Arcane fusion: = af
m = 1 missile
8m * 4 * 2 = 64m = af

af * 4 + 8m *4 = greater af = gaf = 288m

gaf * 4 = 1,152m

So 1,152 missiles if we follow the OP's formula.

[r2d2go]

Short sweet to the point.

Reserves of strength to uncap magic missile by 3 CL for 6 missiles.

Force missile mage for 8 missiles.


Now the hard part.

Let's say I make those missiles twinned and repeating with free metamagic.

Now pack both into an arcane fusion, itself twinned and repeated,

Now pack that fusion, into a greater fusion twinned and repeating, with another missile casting, twinned and repeating.

Base is 8

Twinned+Repeating makes it 16 now, 16 later

Arcane fusion gives two of those, so 32 now, 32 later

Twin makes it 64 now, 64 later

repeat that makes it 64 now, 128 in a round, 64 more in two rounds (256 total)

Here's the unclear part: Is twinned+repeating free always, or limited use? If you're fusing that with the 32-32 fusion, you get 96-160-64 (320 total), twinned to 192-320-128, repeated to 192-512-448-128 (1280 total).

If you're fusing with another 64-128-64 fusion, you get 256-512-256 repeated, or 256-768-768-256 (2048 total).

[Xervous]

Ah bugger I missed a step, cheers to the hive mind of error checking.

[Doctor Awkward]

Base Missiles = 8

Repeat is at all times equal to the current value of missiles.

Twin Spell = Base*2 = 16

Arcane Fusion(AF) = Twinned*2 = 32

Greater Arcane Fusion(GAF) = AF(32) + Twinned(16) = 48

Round 1: GAF = 48 missiles
Round 2: GAF = 48 Missiles + Repeat round 1(48) = 96
Round 3: Repeat from round 2 = 48

Therefore the total number of missiles fired is N*96 where N is the number of times you cast Greater Arcane Fusion.


Now, if GAF = Twinned AF + Twinned, then that's 64 + 16 so GAF = 80
Twinned GAF = 160

The formula then becomes N*160

[Darg]

Guys. There are 144 casts of MM. 144 * 8 is 1152 missiles.

There are 8 MMs unleashed per AF thanks to twin, repeat, and AF's dual casting. Each AF is twinned and repeated increasing the total to 32. Add the additional MM in the GAF that is twinned and repeated to get the total to 36. Each GAF is also twinned and repeated which multiplies the previous total by 4; which leaves us with 144 Magic Missile spells. Each spell has 8 missiles. This leaves us with 1152 missiles.

[Doctor Awkward]

Went over it again, and we both under-counted.

My problem was that I wasn't nesting the repeated spells correctly. A repeated Arcane Fusion creates something of a recursion that has to unpack itself over the course of several rounds.

Normally a Repeated Magic Missile would cast once on Round 1 and again on Round 2. A Twinned Repeated Magic Missile would cast twice on round 1 and twice again on round 2.

With Arcane Fusion(AF) it looks like this:
Round 1: AF (TR+TR)
Round 2: T + T

Where TR is a Twin Repeating Magic Missile for 16 total missiles. Twinning AF simply doubles the results of that.

However casting a Repeat Arcane Fusion gives us this:
Round 1: RAF = (TR+TR)
Round 2: (T+T) + (TR+TR)
Round 3: (T+T)

The twin missiles from the first round repeat, then a repeated arcane fusion gives more missiles, that must again be repeated on the following round. Once again, Twinning just doubles these results.

Setting a Twin Repeating Arcane Fusion + a Twin Repeating Magic Missile inside of a Greater Arcane Fusion gets us:
Round 1: [(TR+TR) + (TR+TR)] + TR
Round 2: (T+T)+(T+T) + (TR+TR)+(TR+TR) + T
Round 3: (T+T)+(T+T)

Each instance of R that appears translates to another T that is resolved on the subsequent round. Repeating Greater Arcane Fusion ends up with this:
Round 1: [(TR+TR) + (TR+TR)] + TR
Round 2: [(T+T)+(T+T) + (TR+TR)+(TR+TR) + T] + [(TR+TR) + (TR+TR)] + TR]
Round 3: (T+T)+(T+T) + (T+T)+(T+T) + [(T+T)+(T+T) + (TR+TR)+(TR+TR) + T]
Round 4: (T+T)+(T+T) + (T+T)+(T+T)

The repeated Greater Arcane Fusion from the first round gives another layer on the second round that must be unpacked the third, as the first one is just finishing, resulting in four total rounds before all of the castings are finished. Once again, Twinning the Repeat Greater Arcane Fusion simply doubles the results.

As instance of "T" in that diagram is a Twinned Magic Missile for 16 projectiles, that equals 44*16 for 704. So a Twinned Repeating Greater Arcane Fusion that casts a Twinned Repeating Arcane Fusion of two Twinned Repeating Magic Missiles plus a third Twinned Repeating Magic Missile from a caster that creates 8 missiles per casting results in 1,408 total missiles over four rounds. The total average damage would be about 4,928.

[Hish]

My math matches Darg's, and I can't really follow anyone else's reasoning.

What is the plan for actually reducing metamagic that far? Arcane thesis & a bunch of +0 metamagics? The only other thing I can think of is DMM and an absurd Cha mod.

[Darg]

I think they are thinking it would be over multiple rounds. However the OP only ever mentioned one round of casting.

[Hish]

I tried working it out by hand instead of using algebra, and I got the same answer. I'll try to copy down my work as clearly as I can. This also shows the round by round breakdown.

Spoiler: lengthy work

Show

G = G. Arcane Fusion
A = Arcane Fusion
M = Magic Missile
T = Twinned
R = Repeated

Round 1:
TRG = TG (add TG to rd 2) = 2G = 2(TRA + TRM) = 2TRM + 2TRA = 2TM + 2TA (add 2TM + 2TA to rd 2) = 2(2M) + 2(2A) = 4M + 4(TRM + TRM) = 8TRM + 4M = 8TM (add 8TM to rd 2) + 4M = 16M + 4M = 20M
Round 2:
TG + 2TM + 2TA + 8TM = 2G + 2(2A) + 10TM = 2(TRA + TRM) + 4(TRM + TRM) + 10(2M) = 2TRA + 2TRM + 4TRM + 4TRM + 20M = 2TA + 2TM + 4TM + 4TM (add 2TA + 10TM to rd 3) + 20M = 2(2A) + 10(2M) + 20M = 4(TRM + TRM) + 40M = 8TRM + 40M = 8TM (add 8TM to rd 3) + 40M = 8(2M) + 40M = 56M
Round 3:
2TA + 10TM + 8TM = 4A + 36M = 4(TRM + TRM) + 36M = 8TRM + 36M = 8TM (add 8TM to rd 4) + 36M = 16M + 36M = 52M
Round 4:
8TM = 16M

Total: 144 castings of magic missile, for 1152 missiles in total.

I notice that the distribution over the four rounds is almost a 1:3:3:1 ratio, like Pascal's triangle. 16:48:48:16 would match that ratio perfectly, and the discrepancy of 4, 8, 4, 0 can be explained by the spare castings of twinpeat MM from GAF.

Spoiler: Excessive detail

Show

In the first round, the MM from GAF is double twinned, once because of GAF being twinned and once because it is twinned itself. Double twin equals four extra castings. This carries into the second round because of repeat, but the same thing happens then, so you get 8 extra castings of MM. Four of these repeat in the next round, and none carry into round four.

[RNightstalker]

My math matches Darg's, and I can't really follow anyone else's reasoning.

What is the plan for actually reducing metamagic that far? Arcane thesis & a bunch of +0 metamagics? The only other thing I can think of is DMM and an absurd Cha mod.

Incantatrix has improved metamagic that will reduce the cost of metamagic feats...though I don't know if that was explicitly stated or understood in the OP.