@hyp_cos: Yeah, I spent a long time trying to figure out a way to use up all of the Muzzio, Visionary Architect tokens we could generate, but in the end there just wasn't a way I could see, at least before we got into uncomputable land. If you're still thinking about it though, I'd be very interested in any way you might find for that, though!
For the current deck, I think Radiant Fountain is too cheap: whenever we don't need to spend the 2 life to gain 4 (which I think is the majority of cases, since we only have to activate Urborg Siphon-Mage below the hyperstage if we don't have enough instant casts left to set up the hyperstage and computation again), we can just spend that life directly to cast Lingering Souls and reset the computation without needing any of the extra stuff. I may be misunderstanding some other line of the deck, but I think a better angle of attack would be to find a card to replace Urborg Siphon-Mage which does NOT require black mana to gain the life, but still requires discarding Aegis Automaton.
@hyp_cos: It's been a while since I've looked at the Chalice of the Void decks, but I can confirm that at the time I left off on working on them, I did not have a working finite version of the Chalice deck, though I was very close. I think the infinite outlined in your post just now was one of the ones I identified. I do have a list of cards Wizards could print that would make the combo work, all of which seemed like plausible designs, none of which actually wound up existing. The closest one I think was if Metallurgeon didn't cost W to activate. That said, the Chalice Deck's main advantage over the more traditional decks that we were working concurrently on somewhat was space efficiency: it saved I think 5 or 6 card slots off the non-chalice version that in turn translated to an additional 2 or 3 stages. That's a huge improvement to the absolute numbers, but in terms of advancements it's much less so. Even if it worked with no infinites, my best Chalice deck wouldn't be able to match a traditional deck if the traditional deck got the handicap of access to a 15-card sideboard. Now that we have these uncomputable decks that blow everything we created before out of the water, there's not much point trying to fix the CHalice version, so feel free to look at an older and more reliable gigastage deck as a reference for our best computable deck.
That said, I do regret that we never managed to finish a write-up for any of the decks between the SadisticMystic 408-layer deck and the uncomputable decks in vintage. A huge amount of effort and thought went into the peak computable decks, and they really were impressive accomplishments in their own right. We just never quite stabilized for long enough to write one up before finding something new.
Regarding the current deck, I've been thinking about ways to add an extra stage to the list in post 4050. Before Black Lotus, it doesn't look like we have any way of generating abundant Green mana, but it's hard to find something we can't bounce with either Aegis Automaton or Stolen by the Fae: the only options I see are shroud creatures or something like Progenitus. The other option I can see would be to have a green mana stage in between the white and blue mana stages, which would allow us to use any green creature with protection from blue and some way to bounce that creature to hand that is only monocolored. The only kicker is that we can't use a green creature as the converter from green mana into bounce triggers, or we could just bounce that instead.
We use Storm Front to tap Surgespanner, which lets us bounce Karoo Meerkat (we can use Dralnu's Crusade to hack Surgespanner to not be blue, bypassing protection, but can't do so for Stolen by the Fae) to make Bloodbond March triggers, creating the stack. Then at the top we can use it to bounce our blue creatures to generate blue mana. The problem is that since Surgespanner's ability costs a blue on resolution, we're at best breaking even, so we need some way to turn a Surgespanner bounce into large quantities of blue mana, which can't be repeated by Stolen by the Fae. That's where I ran out of ideas.
Hmmmm. Unfortunately, I think we can get one going that way, because we can use Domineering Will to give them the changed cards, with Artificial Evolution still in hand. Darn.
In that case, we either need a new way of replicating artifacts that the opponent can't mimic, a new way of producing blue and black mana which can't be donated, or a different key besides red mana and haste.
Perhaps we could do something similar with White mana and untapping, rather than just haste. If we swapped out Mobilize for something more restrictive, we could swap out Break through the Line for say High Alert, and make the stage key off white mana. Though now I realize that Axgard Armory taps for W as well... Foiled again. We need a land which enters the battlefield tapped, doesn't tap for white, and can tap and sacrifice itself to generate the effect we need. Could we maybe do something with Port of Karfell? That would be difficult to do in a way that can't be replicated by The Scarab God...
Another option would be something like Mirrorpool, but that has to create an infinite somewhere.
Edit: Actually, Mirrorpool has some potential if it somehow doesn't break the hyperstage wide open (I'm quite sure it's safe in the calculation itself, since we definitely have no way to keep it around or donate it). If the only way we could get back Guardian Zendikon were with something like Wargate or Genesis Wave set to X=3, we wouldn't be able to get it back with Spellweaver Helix, but we could with Mirrorpool. It would even be much more efficient by cards. Adding the decklist again because it helps me think:
edit: Is Thousand-Year Storm and the like also unsafe? In the Mirrorpool deck I just outlined I think an effect that can copy higher-cost sorceries is a necessity, but without Dual Nature I think we're limited to just one Temple Garden in a red mana deck, which wouldn't generate N green mana on its own from a Mobilize.
Wow, this combo is REALLY restrictive. Can they also interfere with just their own basic lands, or do they need access to large quantities?
Also, I'm assuming March of the Machines goes infinite in some way that I'm missing, but on the off chance it doesn't, We could maybe give them the cards we need with Domineering Will, without letting them get Mox Sapphire. That would still leave unresolved the issue of generating black mana for The Scarab God, though.
On the bright side, this accounts for both blue and black mana, though we may still need Mox Sapphire for the start. That would get us a decklist like this:
You're right. Here's a simple thought: how about Earthcraft and a basic land like Swamp or Plains? We can just tap the creatures we get back to generate mana.
Hmm, you're right. I misread that Sacrifice to be based on power, not mana value. In that case, we need a more involved regeneration process. Maybe we can find something else that keys off power?
As for giving Master Transmuter haste, it should innately get it from Thopter Engineer, which would give the Transmuter haste but not any of our other creatures.
Edit: How about Vile Redeemer? I know tokens are dying in the computation, but if we could find a creature that repeatedly dies and reanimates whenever some part of the computation happens, we could tie the computation to nontoken creatures dying and build a huge number of spawns.
Edit: How about Solemnity and an inoffensive creature with undying, like Young Wolf. It would constantly die and reanimate, but I guess it would probably break the Turing Machine model...
Hello, all! I'm still getting caught up on all of the changes that have been made to the deck, but in the meantime I've been thinking about how we could add a stage to the current deck and I may have found a good line of attack.
We know we can generalize all or most stages into five instructions across two states:
1. Use 1 resource I to push X trigger A.
2. Iff the state is unlocked, pop one Trigger A to push X trigger B and lock the state.
3. Pop 1 trigger B to generate X resource O.
4. Pop 1 trigger B to unlock the state.
5. Iff the state is unlocked, pop 1 trigger A to generate 1 resource I and lock the state.
Traditionally, the state has been "this creature is not in the graveyard" in vintage, but it doesn't have to be. If we can find a new State tracker and free up a resource (white mana through Safe Passage or red mana, maybe by using Sacrifice and Coat of Arms to store our progress), and some linking triggers that don't get wrecked by Temur Sabertooth.
I've done some digging, and I think we can get some mileage out of taplands with a sacrifice ability and an aura which animates them. Because they come in tapped, we have to animate them with our one aura to untap them with Mobilize. If their activation cost requires we spend mana of our input resource, we can make it too expensive to activate them without leaving them a creature and using something like Primal Beyond. And when they activate, the aura falls off and goes to the graveyard, locking the state since we currently have no way to revive an aura from there.
We spend a red mana to grant Axgard Armory (enchanted) haste, untap it, and activate it, each time grabbing Viridian Harvest to gain life. Then, when it comes time to regenerate red mana, we put the Zendikon on Tinder Farm, give it haste, untap it, sac it for an R, and use an Axgard trigger below to get back the Zendikon. We could move the Zendikon after untapping Tinder Farm but before sacrificing it, but without Zendikon bouncing it back to hand we'd have no way to rebuy it later, and the stage would fizzle.
I can only imagine this has an infinite somewhere earlier in the chain, but I can't find it with my still limited understanding and either way this should hopefully be a good starting point for a stage discussion!
Edit: putting a full decklist here sans final layers as a point of reference, since it doesn't look like there's a full list on this page of the thread.
Change of Heart isn't a problem here because Cowardice is gone, otherwise it would absolutely be an issue. Living Twister, on the other hand, definitely is. I'm not sure about Raff Capashen, Ship's Mage... Are there any historic spells in the deck which can interact with the combo?
Re the new list: that looks good, besides the Living Twister thing (we can also spend a W to bounce Living Twister with Aegis Automaton, giving us the R we need to activate the extra ability), but we might still be able to find a different way around it. I don't think Sealed Fate works here without Recoup, though: we can just use a sorcery with a B flashback cost.
That's fair, especially given how close we seem now (though you just know at some point someone's going to figure out how to stack a second UTM on top of the one in our list and we'll have to figure out some new notation: perhaps a new ordinal in the fast-growing hierarchy representing Busy Beaver itself, added by fiat?).
Looking at the options with K'rrik, Son of Yawgmoth, just replacing Desolation Giant as the destroy effect won't be enough: we'll also need a second trigger to replace its Bloodbond March triggers. Right now, it also breaks Seismic Smite since we can recoup it to get lots of Thousand-Year Storm triggers and get {r}{r} per trigger, but we might be able to use that to our advantage by making it harder for us to get back the land. Though the fact that Recoup, Seismic Smite, AND all the destroy-all-your-creatures sorceries cost {r} is a big problem. Damn.
What if we combined that with Petrahydrox as the red-producer, and a red sorcery to set things off? That way, you could produce red each time by targeting Petrahydrox when you cast an instant via Spellweaver Volute and bounce it to hand, where it can tap for an {r} via Chrome Mox and get brought back by a Bloodbond March below, and since the red spell you'd use at the topmost layer is still a sorcery, it would still let you bounce it. Or no, Petrahydrox is blue and would let us flashback Worldpurge.
Actually, we can't use Recoup and the Worldpurge hyperstage at all: we have to hardcast Omniscience to rebuild after a Worldpurge, which means we NEED the easy blue access that would let us flashback Worldpurge with Recoup in the first place. Damn.
@jfb1337: Out of curiosity, has there been any discussion of actually submitting this new deck to a journal? I'm struck by the Abstract section and formality of the language around the lemmas
The write-up was actually very helpful, and answers pretty much all of my questions on the math side. I'm a lot more confident now that the above hyperstage works. I would like to suggest that when we all next reach a short stopping point, we freeze the decklist for any improvements, besides maybe a megastage or a proof of the Flooding variant: there's basically always some improvement in efficiency or search space to make for a higher damage total on the output, and the delta between where we are now and where someone just reading the finished write-ups would be is gigantic (and far more so than it was just a few months ago, kudos again to you guys!).
I've also put some thought into cutting Cowardice from the hyperstage, but I'm honestly not sure it's possible in a way that still enables other stages: at the end of the day, we HAVE to be able to bounce Desolation Giant, and I can't find any way that would bounce it but not the other stage creatures in the above construction. We might be able to explore a trick similar to the Muldrotha, the Gravetide or Repeated Reverberation shenanigans we used for the standard decks, of course.
We could also switch to one of the other ways to destroy all our creatures, and just have something like Petrahydrox as our red producer. But then we still need to find a way to recur the new creature wipe.
Re negative life: It's not so much the principle of the change I'm worried about, it's the ability to use combat damage to start the computation instead of killing Goblin Boom Keg, which would let us keep Vedalken Orrery out mid-computation and potentially interrupt a non-halting execution for arbitrary damage. If we keep the conceit that the opponent will die if dropped to 0 life, then we can't deal arbitrary damage in a computation like that because they'd die before we could get arbitrary value out of it.
Re the combo: I mostly get the execution, but I'm not that well practiced with it so I'm unclear on what outputs it gives us on its own when we run it. I also have no idea about the math behind waterclocks, etc., so I'm slightly hazy on the details of how big we're getting (I assume from the fact we're iterating on it our number of states isn't capped by unique creature types, but I don't and may never understand exactly WHY).
Re the hyperstage: it needs some fixes, and in an edit in a few minutes I'll put the new version in this comment. Primarily, it needs a way to turn mana from Mana Echoes and/or generic computation output into Thousand-Year Storm count, and switch to green mana. Beyond that, I'm pretty sure it actually works
Re the layers: Heliod's Intervention can be used to kill a Goblin Boom Keg without killing Vedalken Orrery, allowing us to potentially interrupt a non-halting computation and deal arbitrary damage. Talon of Pain, however, can't, which is cool: we can only activate it when neither card is a creature, and with no Psychic Battle we can't change the target after playing March of the Machines and loop it back to the Boom Keg. Stream of Life will work, but I think we have to use green mana in the hyperstage or we'll be able to first resolve Worldpurge, then resolve Inner Fire, leaving the hyperstage with 7 R left to work with.
Edit: Is Hive Mind too dangerous for the computation, or would we be okay with giving our opponents copies? If so, we could use Sanguine Sacrament to give our opponents the life, which tucks itself on bottom and would let us draw cards safely.
That's about as far as a strategy like that can get, since there aren't any UW bounce spells (besides Time Wipe and Worldpurge, which bring their own problems), but 3 stages is still better than 0 and it fits fairly easily into the already-existing framework.
Private Mod Note
():
Rollback Post to RevisionRollBack
To post a comment, please login or register a new account.
For the current deck, I think Radiant Fountain is too cheap: whenever we don't need to spend the 2 life to gain 4 (which I think is the majority of cases, since we only have to activate Urborg Siphon-Mage below the hyperstage if we don't have enough instant casts left to set up the hyperstage and computation again), we can just spend that life directly to cast Lingering Souls and reset the computation without needing any of the extra stuff. I may be misunderstanding some other line of the deck, but I think a better angle of attack would be to find a card to replace Urborg Siphon-Mage which does NOT require black mana to gain the life, but still requires discarding Aegis Automaton.
@hyp_cos: It's been a while since I've looked at the Chalice of the Void decks, but I can confirm that at the time I left off on working on them, I did not have a working finite version of the Chalice deck, though I was very close. I think the infinite outlined in your post just now was one of the ones I identified. I do have a list of cards Wizards could print that would make the combo work, all of which seemed like plausible designs, none of which actually wound up existing. The closest one I think was if Metallurgeon didn't cost W to activate. That said, the Chalice Deck's main advantage over the more traditional decks that we were working concurrently on somewhat was space efficiency: it saved I think 5 or 6 card slots off the non-chalice version that in turn translated to an additional 2 or 3 stages. That's a huge improvement to the absolute numbers, but in terms of advancements it's much less so. Even if it worked with no infinites, my best Chalice deck wouldn't be able to match a traditional deck if the traditional deck got the handicap of access to a 15-card sideboard. Now that we have these uncomputable decks that blow everything we created before out of the water, there's not much point trying to fix the CHalice version, so feel free to look at an older and more reliable gigastage deck as a reference for our best computable deck.
That said, I do regret that we never managed to finish a write-up for any of the decks between the SadisticMystic 408-layer deck and the uncomputable decks in vintage. A huge amount of effort and thought went into the peak computable decks, and they really were impressive accomplishments in their own right. We just never quite stabilized for long enough to write one up before finding something new.
Regarding the current deck, I've been thinking about ways to add an extra stage to the list in post 4050. Before Black Lotus, it doesn't look like we have any way of generating abundant Green mana, but it's hard to find something we can't bounce with either Aegis Automaton or Stolen by the Fae: the only options I see are shroud creatures or something like Progenitus. The other option I can see would be to have a green mana stage in between the white and blue mana stages, which would allow us to use any green creature with protection from blue and some way to bounce that creature to hand that is only monocolored. The only kicker is that we can't use a green creature as the converter from green mana into bounce triggers, or we could just bounce that instead.
After some poking around, I think one option that we can at least explore is something like:
Surgespanner
Storm Front
Shiv's Embrace (or any other card to grant Surgespanner flying)
Karoo Meerkat
Karoo Meerkat
We use Storm Front to tap Surgespanner, which lets us bounce Karoo Meerkat (we can use Dralnu's Crusade to hack Surgespanner to not be blue, bypassing protection, but can't do so for Stolen by the Fae) to make Bloodbond March triggers, creating the stack. Then at the top we can use it to bounce our blue creatures to generate blue mana. The problem is that since Surgespanner's ability costs a blue on resolution, we're at best breaking even, so we need some way to turn a Surgespanner bounce into large quantities of blue mana, which can't be repeated by Stolen by the Fae. That's where I ran out of ideas.
In that case, we either need a new way of replicating artifacts that the opponent can't mimic, a new way of producing blue and black mana which can't be donated, or a different key besides red mana and haste.
Perhaps we could do something similar with White mana and untapping, rather than just haste. If we swapped out Mobilize for something more restrictive, we could swap out Break through the Line for say High Alert, and make the stage key off white mana. Though now I realize that Axgard Armory taps for W as well... Foiled again. We need a land which enters the battlefield tapped, doesn't tap for white, and can tap and sacrifice itself to generate the effect we need. Could we maybe do something with Port of Karfell? That would be difficult to do in a way that can't be replicated by The Scarab God...
Another option would be something like Mirrorpool, but that has to create an infinite somewhere.
Edit: Actually, Mirrorpool has some potential if it somehow doesn't break the hyperstage wide open (I'm quite sure it's safe in the calculation itself, since we definitely have no way to keep it around or donate it). If the only way we could get back Guardian Zendikon were with something like Wargate or Genesis Wave set to X=3, we wouldn't be able to get it back with Spellweaver Helix, but we could with Mirrorpool. It would even be much more efficient by cards. Adding the decklist again because it helps me think:
2 Opalescence
3 Dual Nature
4 Vedalken Orrery
5 Riftsweeper
6 Gravebreaker Lamia
7 Marchesa's Smuggler
8 Coat of Arms
9 Rotlung Reanimator
10 Dralnu's Crusade
11 Arcbond
12 Arcbond
13 Fractured Identity
14 Artificial Evolution
15 Sea Gate Stormcaller
16 Kaervek's Spite
17 Safe Passage
18 Goblin Boom Keg
20 Mirrorworks
21 Master Transmuter
22 Mox Sapphire
23 Bloodbond March
24 The Scarab God
25 Rings of Brighthearth
26 Temur Sabertooth
27 Elvish Spirit Guide
28 Hunting Wilds
29 Ambush Commander
30 Worldfire
31 Worldpurge
32 Acorn Harvest
33 Acorn Harvest
34 Radiant Fountain
35 Akoum Refuge
36 Eureka
38 Everbark Shaman
39 Burnt Offering
40 Panharmonicon
41 Spellweaver Helix
42 Wormfang Behemoth
43 Deathgrip
44 Mystical Teachings
45 Overgrown Tomb
46 Mana Crypt
47 Tolarian Academy
48 Channel
49 High Alert
50 Mirrorpool
51 Wargate
52 Guardian Zendikon
53 Tinder Farm
edit: Is Thousand-Year Storm and the like also unsafe? In the Mirrorpool deck I just outlined I think an effect that can copy higher-cost sorceries is a necessity, but without Dual Nature I think we're limited to just one Temple Garden in a red mana deck, which wouldn't generate N green mana on its own from a Mobilize.
Edit: question answered. Arcbond is rough.
Also, I'm assuming March of the Machines goes infinite in some way that I'm missing, but on the off chance it doesn't, We could maybe give them the cards we need with Domineering Will, without letting them get Mox Sapphire. That would still leave unresolved the issue of generating black mana for The Scarab God, though.
Cryptic Trilobite
Immaculate Magistrate
Dimir Signet
and Rage Weaver in addition to Thopter Engineer
We can use Coat of Arms/Rotlung Reanimator shenanigans to generate plentiful elf tokens on our side, then give an Immaculate Magistrate haste, put that many counters on Cryptic Trilobite, and from there we can filter the colorless mana through Dimir Signet to generate blue and black. To keep doing so, we need more Immaculate Magistrates, which means reshuffling them back into the library and milling them, which requires some green mana input to bounce Riftsweeper and Gravebreaker Lamia.
On the bright side, this accounts for both blue and black mana, though we may still need Mox Sapphire for the start. That would get us a decklist like this:
2 Opalescence
3 Dual Nature
4 Vedalken Orrery
5 Riftsweeper
6 Gravebreaker Lamia
7 Thopter Engineer
8 Coat of Arms
9 Rotlung Reanimator
10 Dralnu's Crusade
11 Arcbond
12 Arcbond
13 Fractured Identity
14 Artificial Evolution
15 Sea Gate Stormcaller
16 Kaervek's Spite
17 Avacyn, Guardian Angel
18 Goblin Boom Keg
20 Immaculate Magistrate
21 Dimir Signet
22 Rage Weaver
23 Mirrorworks
24 Master Transmuter
25 Mox Sapphire
26 Bloodbond March
27 The Scarab God
28 Rings of Brighthearth
29 Temur Sabertooth
30 Elvish Spirit Guide
31 Mobilize
32 Ambush Commander
33 Worldfire
34 Worldpurge
35 Acorn Harvest
36 Acorn Harvest
37 Radiant Fountain
38 Akoum Refuge
39 Eureka
41 Wood Elves
42 Panharmonicon
43 Spellweaver Helix
44 Wormfang Behemoth
45 Deathgrip
46 Mystical Teachings
47 Temple Garden
48 Mana Crypt
49 Tolarian Academy
50 Channel
51 Break through the Line
52 Primal Beyond
53 Guardian Zendikon
54 Axgard Armory
55 Tinder Farm
56 Viridian Harvest
How do we break this?
As for giving Master Transmuter haste, it should innately get it from Thopter Engineer, which would give the Transmuter haste but not any of our other creatures.
Edit: How about Vile Redeemer? I know tokens are dying in the computation, but if we could find a creature that repeatedly dies and reanimates whenever some part of the computation happens, we could tie the computation to nontoken creatures dying and build a huge number of spawns.
Edit: How about Solemnity and an inoffensive creature with undying, like Young Wolf. It would constantly die and reanimate, but I guess it would probably break the Turing Machine model...
We know we can generalize all or most stages into five instructions across two states:
1. Use 1 resource I to push X trigger A.
2. Iff the state is unlocked, pop one Trigger A to push X trigger B and lock the state.
3. Pop 1 trigger B to generate X resource O.
4. Pop 1 trigger B to unlock the state.
5. Iff the state is unlocked, pop 1 trigger A to generate 1 resource I and lock the state.
Traditionally, the state has been "this creature is not in the graveyard" in vintage, but it doesn't have to be. If we can find a new State tracker and free up a resource (white mana through Safe Passage or red mana, maybe by using Sacrifice and Coat of Arms to store our progress), and some linking triggers that don't get wrecked by Temur Sabertooth.
I've done some digging, and I think we can get some mileage out of taplands with a sacrifice ability and an aura which animates them. Because they come in tapped, we have to animate them with our one aura to untap them with Mobilize. If their activation cost requires we spend mana of our input resource, we can make it too expensive to activate them without leaving them a creature and using something like Primal Beyond. And when they activate, the aura falls off and goes to the graveyard, locking the state since we currently have no way to revive an aura from there.
Putting it all together, I get the following:
Break through the Line
Primal Beyond
Guardian Zendikon
Axgard Armory
Tinder Farm
Viridian Harvest
Additionally, we replace Marchesa's Smuggler with Thopter Engineer, and swap our red rituals for Sacrifice.
We spend a red mana to grant Axgard Armory (enchanted) haste, untap it, and activate it, each time grabbing Viridian Harvest to gain life. Then, when it comes time to regenerate red mana, we put the Zendikon on Tinder Farm, give it haste, untap it, sac it for an R, and use an Axgard trigger below to get back the Zendikon. We could move the Zendikon after untapping Tinder Farm but before sacrificing it, but without Zendikon bouncing it back to hand we'd have no way to rebuy it later, and the stage would fizzle.
I can only imagine this has an infinite somewhere earlier in the chain, but I can't find it with my still limited understanding and either way this should hopefully be a good starting point for a stage discussion!
Edit: putting a full decklist here sans final layers as a point of reference, since it doesn't look like there's a full list on this page of the thread.
2 Opalescence
3 Dual Nature
4 Vedalken Orrery
5 Riftsweeper
6 Gravebreaker Lamia
7 Thopter Engineer
8 Coat of Arms
9 Rotlung Reanimator
10 Dralnu's Crusade
11 Arcbond
12 Arcbond
13 Fractured Identity
14 Artificial Evolution
15 Sea Gate Stormcaller
16 Kaervek's Spite
17 Avacyn, Guardian Angel
18 Goblin Boom Keg
20 Mirrorworks
21 Master Transmuter
22 Mox Sapphire
23 Bloodbond March
24 The Scarab God
25 Rings of Brighthearth
26 Temur Sabertooth
27 Elvish Spirit Guide
28 Mobilize
29 Ambush Commander
30 Worldfire
31 Worldpurge
32 Acorn Harvest
33 Acorn Harvest
34 Radiant Fountain
35 Akoum Refuge
36 Eureka
38 Wood Elves
39 Panharmonicon
40 Spellweaver Helix
41 Wormfang Behemoth
42 Deathgrip
43 Mystical Teachings
44 Temple Garden
45 Mana Crypt
46 Tolarian Academy
47 Channel
48 Break through the Line
49 Primal Beyond
50 Guardian Zendikon
51 Axgard Armory
52 Tinder Farm
53 Viridian Harvest
After that we'd add layers starting with red mana and/or mana of any color.
Re the new list: that looks good, besides the Living Twister thing (we can also spend a W to bounce Living Twister with Aegis Automaton, giving us the R we need to activate the extra ability), but we might still be able to find a different way around it. I don't think Sealed Fate works here without Recoup, though: we can just use a sorcery with a B flashback cost.
Soulblast isn't safe anymore, because we can give our opponent a Goblin Boom Keg and March of the Machines, ignore our own March of the Machines, and use Soulblast to kill their Boom Keg without killing our Vedalken Orrery. We can just swap it out for either of the other red sorceries.
Petrahydrox+Recoup lets us generate blue mana, which lets us Recoup Worldpurge outside the hyperstage. I'm pretty much blank on how to fix that.
Temur Sabertooth doesn't target, so it can still bounce Voice of Duty.
The first attempt looks like it would work, except that Temur Sabertooth can also return Walker of Secret Ways, and that we can still loop by using Recoup to directly flashback Rude Awakening. I think that if we swap Rude Awakening for Hidden Strings and find a different stage from Walker of Secret Ways (or a Sabertooth equivalent that targets), the first draft is workable!
Looking at the options with K'rrik, Son of Yawgmoth, just replacing Desolation Giant as the destroy effect won't be enough: we'll also need a second trigger to replace its Bloodbond March triggers. Right now, it also breaks Seismic Smite since we can recoup it to get lots of Thousand-Year Storm triggers and get {r}{r} per trigger, but we might be able to use that to our advantage by making it harder for us to get back the land. Though the fact that Recoup, Seismic Smite, AND all the destroy-all-your-creatures sorceries cost {r} is a big problem. Damn.
What if we combined that with Petrahydrox as the red-producer, and a red sorcery to set things off? That way, you could produce red each time by targeting Petrahydrox when you cast an instant via Spellweaver Volute and bounce it to hand, where it can tap for an {r} via Chrome Mox and get brought back by a Bloodbond March below, and since the red spell you'd use at the topmost layer is still a sorcery, it would still let you bounce it. Or no, Petrahydrox is blue and would let us flashback Worldpurge.
Actually, we can't use Recoup and the Worldpurge hyperstage at all: we have to hardcast Omniscience to rebuild after a Worldpurge, which means we NEED the easy blue access that would let us flashback Worldpurge with Recoup in the first place. Damn.
The write-up was actually very helpful, and answers pretty much all of my questions on the math side. I'm a lot more confident now that the above hyperstage works. I would like to suggest that when we all next reach a short stopping point, we freeze the decklist for any improvements, besides maybe a megastage or a proof of the Flooding variant: there's basically always some improvement in efficiency or search space to make for a higher damage total on the output, and the delta between where we are now and where someone just reading the finished write-ups would be is gigantic (and far more so than it was just a few months ago, kudos again to you guys!).
Re Hive Mind: yeah that makes sense. In that case, we could use Beacon of Immortality to get the same effect.
I've also put some thought into cutting Cowardice from the hyperstage, but I'm honestly not sure it's possible in a way that still enables other stages: at the end of the day, we HAVE to be able to bounce Desolation Giant, and I can't find any way that would bounce it but not the other stage creatures in the above construction. We might be able to explore a trick similar to the Muldrotha, the Gravetide or Repeated Reverberation shenanigans we used for the standard decks, of course.
We could also switch to one of the other ways to destroy all our creatures, and just have something like Petrahydrox as our red producer. But then we still need to find a way to recur the new creature wipe.
Re the combo: I mostly get the execution, but I'm not that well practiced with it so I'm unclear on what outputs it gives us on its own when we run it. I also have no idea about the math behind waterclocks, etc., so I'm slightly hazy on the details of how big we're getting (I assume from the fact we're iterating on it our number of states isn't capped by unique creature types, but I don't and may never understand exactly WHY).
Re the hyperstage: it needs some fixes, and in an edit in a few minutes I'll put the new version in this comment. Primarily, it needs a way to turn mana from Mana Echoes and/or generic computation output into Thousand-Year Storm count, and switch to green mana. Beyond that, I'm pretty sure it actually works
Re the layers: Heliod's Intervention can be used to kill a Goblin Boom Keg without killing Vedalken Orrery, allowing us to potentially interrupt a non-halting computation and deal arbitrary damage. Talon of Pain, however, can't, which is cool: we can only activate it when neither card is a creature, and with no Psychic Battle we can't change the target after playing March of the Machines and loop it back to the Boom Keg. Stream of Life will work, but I think we have to use green mana in the hyperstage or we'll be able to first resolve Worldpurge, then resolve Inner Fire, leaving the hyperstage with 7 R left to work with.
Edit:
2 Xathrid Necromancer
3 Arcbond
4 Artificial Evolution
5 Mirrorweave
6 Dowsing Dagger
7 Dralnu's Crusade
8 Starfield of Nyx
9 Desolation Giant
10 March of the Machines
11 Goblin Boom Keg
12 Vedalken Orrery
14 Pull from Eternity
15 Cowardice
16 Mirrorworks
17 Bloodbond March
18 Cephalid Shrine
19 Thousand-Year Storm
20 Invulnerability
21 Satyr's Cunning
22 Mana Echoes
24 Chrome Mox
25 Spellweaver Helix
26 Seismic Spike
27 Worldpurge
28 Gerrard's Verdict
29 Flash of Defiance
30 Flash of Defiance
31 Panharmonicon
32 Drownyard Temple
We actually don't have to switch to green, and can't: Deconstruct can nuke Goblin Boom Keg, so we use Seismic Spike destroying Drownyard Temple to generate the R.
Edit: Is Hive Mind too dangerous for the computation, or would we be okay with giving our opponents copies? If so, we could use Sanguine Sacrament to give our opponents the life, which tucks itself on bottom and would let us draw cards safely.
2 Bloodbond March
3 Thousand-Year Storm
4 Cephalid Shrine
5 Mirrorworks
6 Recoup
8 Nyxborn Seaguard
9 Nyxborn Seaguard
10 Reduce to Dreams
12 Xathrid Necromancer
13 Aether Mutation
14 Whirling Dervish
We weave together batches of Thousand-Year Storm triggers on the bounce spells and Bloodbond March triggers on the creatures. Reduce to Dreams lets us rebuy the enchantment creatures, netting a red mana to cast Recoup and get our Spellweaver Volute copies of the instants. Deny Reality can rebuy all our enchantment creatures, but also Xathrid Necromancer to generate black mana. Aether Mutation can do the same, but it can also target Whirling Dervish (Deny Reality can't since the Dervish has pro-black) to generate the green mana it needs.
That's about as far as a strategy like that can get, since there aren't any UW bounce spells (besides Time Wipe and Worldpurge, which bring their own problems), but 3 stages is still better than 0 and it fits fairly easily into the already-existing framework.