looks pretty good, I haven't double checked the math, but one thing that might make things clearer is choosing better types? I'd like if the 'linked' types started with the same letter to make it easier to keep track of.
And for demonstrating the power, this first computation is just to give us enough output to convert into one of the UTMs in that repo, which can then simulate any TM computation we can fit in our remaining budget, and even medium-small TMs have un-computable outputs. Which then goes into the definition of busy beaver and how unimaginably fast it must grow. Even something as small as BB(1919) is provably unknowable. (https://github.com/sorear/metamath-turing-machines/blob/master/sample_out/zf.tm) which halts if and only if it finds a contradiction in ZFC, which we can not prove never halts.
we need at least one yarok in play before playing spellweaver helix
we need to make a token mirror before exiling the fated infatuation, which requires march of the machines.
we need to make a token metalworker to make any mana.
we need to not kill ourselves with the II after worldfire. This looks to require getting pious back after worldfire, which seems tricky.
Well we can't possibly have access to the 17th card before we cast SSA the first time if we want to be able to draw SSA for the 18th and final card.
Also I missed that we need to draw the manland because we can't fetch it before the opponent has some. So we are down to three cards which probably have to be something like fated, abandon the post, worldfire? (maybe volute?)
The issue with casting starlight is that that requires either using one of our few helper slots to draw it, or casting it via helix with an abandon the post (which we would need to draw).
I'm forgetting exactly what the setup requirements for worldfire are, especially with this special one that has the luxury of effectively being both the top and bottom of the stack.
Changing the way we cheat omniscience into play seems unlikely, there just aren't a lot of cards that work to even do that in the first place and making them work with the rest of the combo puts additional serious restrictions on what even works. Its honestly kind of insane that it doesn't take more deckspace.
We cant cast SSA until after we resolve worldfire which clears our hand. So it does no good to draw it before.
ok so an outline something like:
tys
II x3
search x4 all legends except veyran
drake
orrery
helix
abandon the post x5
IIx6
worldfirex7
fails by not being able to setup to recover from worldfire (and by not milling enough cards) and can't cast another spell without making the tys trigger lethal.
well, we definitely can't full combo without drawing those 11 nonlegendary creatures, and we also definitely need an abandon the post for worldfire, so that's 12 cards spoken for already. And we need something like fated to actually make mana, so 13 cards seem pretty locked in to get started.
Now if we could hypothetically draw 12 of those with II and still get started, drawing the 13th with SSA on the 7th II. However, I don't think there's a line with just one cast of fated because it dead ends on trying to make enchantments. Meaning that drawing 14 before drawing SSA is required. I might be wrong though.
Maybe there's a line with different cards left over in the opening hand?
edit: current deck for reference (only difference is spawing pool->ghitu encampment)
Well isn't it better to get like 2 full combos instead of 5 mini ones?
So I guess the question is can we be fully optimal and use those 14 II draws on the non-legendary creatures:
1 Xathrid Necromancer
2 Chancellor of the Annex
3 Martyr of Spores
4 Chromescale Drake
5 Archon of Falling Stars
6 Floodchaser
7 Arboreal Grazer
8 Firebrand Ranger
9 Groundskeeper
10 Ruin Ghost
11 Weathered Wayfarer
Leaving three cards for something like:
Abandon the Post
Spellweaver Volute
Fated Infatuation
And the two other legends we got from Search for glory. Though, that still leaves two unfetched until we cast search again.
Which looks like probably enough to mill everything and fetch our artifacts? Rat+Yarok let fated get a bunch of Chromescale triggers. Though I think we need to be a little careful. We need to get rid of our TYS before resolving a Helix trigger for II.
Hmm the line looks a little tricky actually...
Oh and we can finesse for one more card of slack because II draws 2 cards at a time and we can’t use some of our creatures until after resolving SSA.
If we only care about even doing a computation I think we only need like the first 5 of those, leaving a bunch of draws free to be whatever.
Well if we had that it would break our transitions, so soul foundry is probably what we want. I don't remember the exact line but I think it had to do with cheating an archon through a worldfire?
Oh computation should definitely be possible precombat, II drawing 18 cards is a lot.
Something like
land mox crypt EE -> replenish, omniscience
3 cards in hand
TYS
search x3 (veyran, rat, (phabine? or yarok? or k'rrik?))
II x7
draw 14
I'm not sure where the best way to go from there is.
At the very least we are able to worldfire+rebuild to make red mana and then use the last IIs to draw SSA twice precombat. I think that is enough to theoretically have access to the full deck and combos for those two draws?
Also this annoyance with imprint not using last known information is what actually lets the transitions work because in order for a waiting soul foundry trigger to produce a creature it needs to be unused in the higher stage, eliminating the gains we would have tried to smuggle.
It does mean that sometimes the very top transition gets to be slightly more efficient, but its less of an effect than being able to hide cards on the stack for the top transition, which has already been shown to be safe.
I'm really not sure what the optimal line for the start is, Ratadrabrik has some odd consequences.
It seems like we can easily make the 53 rabines and lot of mind's eyes. I'm a bit lost as to what the absolute best way to do that is.
The opponent can regenerate spawning pool via k'rrik then let it die to interrupt computation.
Edit: Also looking into it a bit yeah Ratadrabik is way better than harmonic prodigy, we do need to be a little careful with it. But the interaction with bloodbond march is kinda hilarious and actually lets the foundry stage do useful work.
The two slots that seem to be doing the least are: twinning glass is just used for the rebuild after worldfire, mainly for orrery. But we do need something for that, master transmuter is too expensive for that and so is something like casting omniscience. Faerie conclave This is solely to give the opponent a single land so that we can activate weathered wayfarer. It has to be a land they can't get mana from.
Edit: I guess ghitu encampment is safe now that we cant get it in combat for first strike to matter, though that's a pretty minor improvement.
As an unoptimized proof of concept something like:
crypt, ruby, snow island, epic experiment -> resurgent belief, omniscience
3 cards in hand
TYS
Caress (x3)-> 10 cards in hand
1 veyran
2 search for glory (x7) (yarok, phabine, krrik, ashnod, etc)
3 chromescale drake for 6 (metalworker, orrery, helix, mind's eye, )
4 opalescence
5 march
6 fated (x9 TYS)
7 volute
8 lingering souls ->volute fated (1+10TYS*2veyran*6spells = 121 = enough chromescale drakes to mill and draw what it can, some metalworkers, and a bunch of mind's eyes) each metalworker taps for 16 (orrery, helix, coat of arms, keg, twinning glass, mirror, transmuter, furnace) then cast artifacts
9 wrong turn (get rid of TYS)
10 abandon the post triggers helix for caress + lingering souls + starlight + whatever else
Caress targeting opponent gives us 50+ mind eye triggers and we have the mana to draw our deck.
setup for worldfire
worldfire
resolve setup
ruby
SSA
fullcombo precombat limited by posion, though we don't want to caress them more because phabine is more efficient
enter combat, get ~50 phabine triggers, fullcombo with those.
not infinite because even though the opponent could refill their library, we run out of attack triggers.
I might be missing something with Dihada, but I don't see a way to get the 53 phabines (or 7 phabines + 7 harmonic prodigies + 7x AE) we would want. And the first chunk of those triggers are just gonna be drawing the creatures we need. Losing II and search for glory makes getting additional cards pretty difficult.
And for demonstrating the power, this first computation is just to give us enough output to convert into one of the UTMs in that repo, which can then simulate any TM computation we can fit in our remaining budget, and even medium-small TMs have un-computable outputs. Which then goes into the definition of busy beaver and how unimaginably fast it must grow. Even something as small as BB(1919) is provably unknowable. (https://github.com/sorear/metamath-turing-machines/blob/master/sample_out/zf.tm) which halts if and only if it finds a contradiction in ZFC, which we can not prove never halts.
we need at least one yarok in play before playing spellweaver helix
we need to make a token mirror before exiling the fated infatuation, which requires march of the machines.
we need to make a token metalworker to make any mana.
we need to not kill ourselves with the II after worldfire. This looks to require getting pious back after worldfire, which seems tricky.
Also I missed that we need to draw the manland because we can't fetch it before the opponent has some. So we are down to three cards which probably have to be something like fated, abandon the post, worldfire? (maybe volute?)
The issue with casting starlight is that that requires either using one of our few helper slots to draw it, or casting it via helix with an abandon the post (which we would need to draw).
I'm forgetting exactly what the setup requirements for worldfire are, especially with this special one that has the luxury of effectively being both the top and bottom of the stack.
Artifacts like astral cornucopia can be found with chromescale drake.
Changing the way we cheat omniscience into play seems unlikely, there just aren't a lot of cards that work to even do that in the first place and making them work with the rest of the combo puts additional serious restrictions on what even works. Its honestly kind of insane that it doesn't take more deckspace.
ok so an outline something like:
tys
II x3
search x4 all legends except veyran
drake
orrery
helix
abandon the post x5
IIx6
worldfirex7
fails by not being able to setup to recover from worldfire (and by not milling enough cards) and can't cast another spell without making the tys trigger lethal.
Now if we could hypothetically draw 12 of those with II and still get started, drawing the 13th with SSA on the 7th II. However, I don't think there's a line with just one cast of fated because it dead ends on trying to make enchantments. Meaning that drawing 14 before drawing SSA is required. I might be wrong though.
Maybe there's a line with different cards left over in the opening hand?
edit: current deck for reference (only difference is spawing pool->ghitu encampment)
1 Coat of Arms
2 Xathrid Necromancer
3 Artificial Evolution
4 Arcbond
5 Comeuppance
6 Dralnu's Crusade
Starting a Computation
7 Opalescence
8 Wrong Turn
9 Kaervek's Spite
10 Goblin Boom Keg
11 March of the Machines
Utility
12 Vedalken Orrery
13 Metalworker
14 Twinning Glass
15 Thousand-Year Storm
16 Bloodbond March
17 Chancellor of the Annex
Foundry Stage
18 Martyr of Spores
19 Soul Foundry
20 Phabine, Boss's Confidant
21 Cowardice
22 Mirror of Fate
23 Chromescale Drake
24 Ashnod the Uncaring
25 Ratadrabik of Urborg
26 Spellweaver Volute
27 Veyran, Voice of Duality
28 Fated Infatuation
29 Lingering Souls
30 K'rrik, Son of Yawgmoth
31 Archon of Falling Stars
32 Pious Interdiction
Helix Megastage
33 Spellweaver Helix
34 Worldfire
35 Starlight
36 Abandon the Post
37 Abandon the Post
38 Mox Ruby
39 Yarok, the Desecrated
Blue Mana Stage
40 Master Transmuter
41 Floodchaser
42 Great Furnace
43 Brutal Suppression
44 Search for Glory
45 Snow-Covered Island
46 Arboreal Grazer
47 Firebrand Ranger
48 Groundskeeper
49 Forest
White Mana Stage
50 Ruin Ghost
51 Weathered Wayfarer
52 Archaeological Dig
53 Ghitu Encampment
Start
54 Mana Crypt
55 Epic Experiment
56 Resurgent Belief
57 Omniscience
58 Infectious Inquiry
End Layers
59 Mind's Eye
60 Smoke Spirits' Aid
So I guess the question is can we be fully optimal and use those 14 II draws on the non-legendary creatures:
1 Xathrid Necromancer
2 Chancellor of the Annex
3 Martyr of Spores
4 Chromescale Drake
5 Archon of Falling Stars
6 Floodchaser
7 Arboreal Grazer
8 Firebrand Ranger
9 Groundskeeper
10 Ruin Ghost
11 Weathered Wayfarer
Leaving three cards for something like:
Abandon the Post
Spellweaver Volute
Fated Infatuation
And the two other legends we got from Search for glory. Though, that still leaves two unfetched until we cast search again.
Which looks like probably enough to mill everything and fetch our artifacts? Rat+Yarok let fated get a bunch of Chromescale triggers. Though I think we need to be a little careful. We need to get rid of our TYS before resolving a Helix trigger for II.
Hmm the line looks a little tricky actually...
Oh and we can finesse for one more card of slack because II draws 2 cards at a time and we can’t use some of our creatures until after resolving SSA.
If we only care about even doing a computation I think we only need like the first 5 of those, leaving a bunch of draws free to be whatever.
Oh computation should definitely be possible precombat, II drawing 18 cards is a lot.
Something like
land mox crypt EE -> replenish, omniscience
3 cards in hand
TYS
search x3 (veyran, rat, (phabine? or yarok? or k'rrik?))
II x7
draw 14
I'm not sure where the best way to go from there is.
At the very least we are able to worldfire+rebuild to make red mana and then use the last IIs to draw SSA twice precombat. I think that is enough to theoretically have access to the full deck and combos for those two draws?
It does mean that sometimes the very top transition gets to be slightly more efficient, but its less of an effect than being able to hide cards on the stack for the top transition, which has already been shown to be safe.
I'm really not sure what the optimal line for the start is, Ratadrabrik has some odd consequences.
It seems like we can easily make the 53 rabines and lot of mind's eyes. I'm a bit lost as to what the absolute best way to do that is.
Edit: Also looking into it a bit yeah Ratadrabik is way better than harmonic prodigy, we do need to be a little careful with it. But the interaction with bloodbond march is kinda hilarious and actually lets the foundry stage do useful work.
Otherwise we would just want to cut it for a second volute again to save the card slot.
Its difficult to see where improvement could come from.
1 Coat of Arms
2 Xathrid Necromancer
3 Artificial Evolution
4 Arcbond
5 Comeuppance
6 Dralnu's Crusade
Starting a Computation
7 Opalescence
8 Wrong Turn
9 Kaervek's Spite
10 Goblin Boom Keg
11 March of the Machines
Utility
12 Vedalken Orrery
13 Metalworker
14 Twinning Glass
15 Thousand-Year Storm
16 Bloodbond March
17 Chancellor of the Annex
Foundry Stage
18 Martyr of Spores
19 Soul Foundry
20 Phabine, Boss's Confidant
21 Cowardice
22 Mirror of Fate
23 Chromescale Drake
24 Ashnod the Uncaring
25 Harmonic Prodigy
26 Spellweaver Volute
27 Veyran, Voice of Duality
28 Fated Infatuation
29 Lingering Souls
30 K'rrik, Son of Yawgmoth
31 Archon of Falling Stars
32 Pious Interdiction
Helix Megastage
33 Spellweaver Helix
34 Worldfire
35 Starlight
36 Abandon the Post
37 Abandon the Post
38 Mox Ruby
39 Yarok, the Desecrated
Blue Mana Stage
40 Master Transmuter
41 Floodchaser
42 Great Furnace
43 Brutal Suppression
44 Search for Glory
45 Snow-Covered Island
46 Arboreal Grazer
47 Firebrand Ranger
48 Groundskeeper
49 Forest
White Mana Stage
50 Ruin Ghost
51 Weathered Wayfarer
52 Archaeological Dig
53 Faerie Conclave
Start
54 Mana Crypt
55 Epic Experiment
56 Resurgent Belief
57 Omniscience
58 Caress of Phyrexia
End Layers
59 Mind's Eye
60 Smoke Spirits' Aid
The two slots that seem to be doing the least are:
twinning glass is just used for the rebuild after worldfire, mainly for orrery. But we do need something for that, master transmuter is too expensive for that and so is something like casting omniscience.
Faerie conclave This is solely to give the opponent a single land so that we can activate weathered wayfarer. It has to be a land they can't get mana from.
Edit: I guess ghitu encampment is safe now that we cant get it in combat for first strike to matter, though that's a pretty minor improvement.
current state of the deck:
1 Coat of Arms
2 Xathrid Necromancer
3 Artificial Evolution
4 Arcbond
5 Comeuppance
6 Dralnu's Crusade
Starting a Computation
7 Opalescence
8 Wrong Turn
9 Kaervek's Spite
10 Goblin Boom Keg
11 March of the Machines
Utility
12 Vedalken Orrery
13 Metalworker
14 Twinning Glass
15 Thousand-Year Storm
16 Bloodbond March
17 Chancellor of the Annex
Foundry Stage
18 Martyr of Spores
19 Soul Foundry
20 Phabine, Boss's Confidant
21 Cowardice
22 Mirror of Fate
23 Chromescale Drake
24 Ashnod the Uncaring
25 Harmonic Prodigy
26 Spellweaver Volute
27 Veyran, Voice of Duality
28 Fated Infatuation
29 Lingering Souls
30 K'rrik, Son of Yawgmoth
31 Archon of Falling Stars
32 Pious Interdiction
Helix Megastage
33 Spellweaver Helix
34 Worldfire
35 Starlight
36 Abandon the Post
37 Abandon the Post
38 Mox Ruby
39 Yarok, the Desecrated
Blue Mana Stage
40 Master Transmuter
41 Floodchaser
42 Great Furnace
43 Brutal Suppression
44 Search for Glory
45 Snow-Covered Island
46 Arboreal Grazer
47 Firebrand Ranger
48 Groundskeeper
49 Forest
White Mana Stage
50 Ruin Ghost
51 Weathered Wayfarer
52 Archaeological Dig
53 Faerie Conclave
Start
54 Mana Crypt
55 Epic Experiment
56 Resurgent Belief
57 Omniscience
58 Infectious Inquiry
59 ????
60 ??????
where 59 and 60 are some ending layer sequence that also helps with the start somehow now that the first metalworker can't tap for mana.
Edit:
I think we can just use 59: Mind's Eye and 60: smoke spirits' aid and fix the start with Caress of phyrexia getting us a few early mind's eye triggers.
As an unoptimized proof of concept something like:
crypt, ruby, snow island, epic experiment -> resurgent belief, omniscience
3 cards in hand
TYS
Caress (x3)-> 10 cards in hand
1 veyran
2 search for glory (x7) (yarok, phabine, krrik, ashnod, etc)
3 chromescale drake for 6 (metalworker, orrery, helix, mind's eye, )
4 opalescence
5 march
6 fated (x9 TYS)
7 volute
8 lingering souls ->volute fated (1+10TYS*2veyran*6spells = 121 = enough chromescale drakes to mill and draw what it can, some metalworkers, and a bunch of mind's eyes) each metalworker taps for 16 (orrery, helix, coat of arms, keg, twinning glass, mirror, transmuter, furnace) then cast artifacts
9 wrong turn (get rid of TYS)
10 abandon the post triggers helix for caress + lingering souls + starlight + whatever else
Caress targeting opponent gives us 50+ mind eye triggers and we have the mana to draw our deck.
setup for worldfire
worldfire
resolve setup
ruby
SSA
fullcombo precombat limited by posion, though we don't want to caress them more because phabine is more efficient
enter combat, get ~50 phabine triggers, fullcombo with those.
not infinite because even though the opponent could refill their library, we run out of attack triggers.