I think that, if our only blue sorceries are cards that would reset everything (Worldpurge, for instance, would be safe), then you would have to immediately cast the sorcery once you exile/draw it: it would be the only way to repeatedly trigger Spellweaver Volute, and necessary for the transition, so you could never bank it in between.
We also need to make sure the next hyperstage down is actually necessary to keep the combo going, so we have to use up a trigger from below for... Something. There's still a ways to go before it can be slotted in.
Deathrite feels hard to replace...
Edit: Tezzeret's Gatebreaker also grabs an artifact, which means we can use a Psychic Battle trigger to kill Metallurgeon, imprint it on the Vat, make a hasty token, shuffle it back in, use the next psychic Battle trigger to bounce and replay Gatebreaker, use the trigger to get Metallurgeon, and replay Metallurgeon without using up a Bloodbond March trigger. No good. That and the Helix pretty conclusively rules out Deathrite as an option.
So, our creature needs to have: 2 or fewer toughness ideally (we could go higher, at the cost of reducing space for further layers later on), a tap ability that lets us, in some way, recast a sorcery to trigger Volute, and some search space we can hit with Rebuild.
That deck looks pretty good. My only thought is that it feels like we're leaving the realm of "tokens as an n-stage resource" too early: clearing Mana pools and life totals is hard, but removing multiple kinds of tokens seems easier.
My first thought is that we're constantly making bajilions of useless token copies of our tap creatures with Dual Nature. That means that mass-haste-granting abilities can generate lots of untapped hasty tokens, as well as untap effects. If we could set up an interventing delete-all-I stage before the life megastage, based on giving creatures haste, that could bump what we already have up to a gigastage. Something like:
Input resource 1 red mana
Output resource: lots of hasty copies of a creature that can tap to cast a sorcery (need not be deep reconnaissance) for free. We would have to change around the original hyperstage to use this token instead of green Mana, and I'm not entirely sure how.
Goblin Bushwhacker, to let us turn 1 red Mana into X triggers that would each give all our not-hasty Dual Nature token copies of the above creature haste, to create a new hyperstage.
A way to bounce Goblin Bushwhacker and our red-producer, almost certainly Simian Spirit Guide, as well as all our tokens, to hand. Engulf the Shore seems like a good choice, as long as we can get 2 and only 2 islands down, and our linking creature has 2 or fewer toughness.
From there, we can just replace Deconstruct with Rite of Flame, and I think we'd have a gigastage. All that's left is to find a creature which can tap to give us a sorcery cast. I think that, if we could find a sorcery that we could cheaply draw from library, without allowing us to draw any cards from higher up the chain, we could use Deathrite Shaman as the chaining creature: we would need to keep green Mana unavailable to preserve the current megastage, and prevent the killing of lands, and allow for black Mana production, but we could use its ability to exile some sorcery, use a Mirror to reshuffle it, and then redraw the sorcery somehow. We could do it by limiting color, for instance.
Additionally, we could remove Deep Reconnaissance, and would have to replace Mox Emerald with... Engineered Explosives? That's the hardest part: we need an artifact, where we can't make tokens or the tokend are useless, that we can reuse with Rebuild to kill Deathrite Shaman, putting it on Mimic Vat.
Edit: could we maybe allow the storing of Mana, where the Mana can be used to kill Deathrite Shaman? Then we could use Mox Sapphire as the rebuild target, and use it to pay for the ability on something like Escape Routes, Homarid Shaman, or King Crab, to kill Deathrite with Horobi and then put it on the Vat.
I actually used Mirage
Mirror in my standard megacombo for a while: you'd top up on alternating triggers between targeting Treasure Map and a creature you can untap with Rallying Roar, then blinking it with Aethergeode Miner to turn just 2 energy into a lot of Mana of any color. I had to drop it when I switched to Cogwork Assembler because letting it make copies of any permanent is super unsafe.
Yeah, it seems like my approach to an extensible n-stage framework may not be tenable. I still believe there's a better way than to force delete all of a resource, but for in the meantime, your configuration is probably still the best.
What I mean by that is, there's never a transition between, say, an NL and an SF trigger: you go from SF up to NL, but never down the other way around. Each new extension is always preceded by a PB/BM stage, because we're using the same stage to fuel every new n-stage beyond it. So if we can find a way to safely lock the input resource of that one stage, the rest of the extensions should fall in precisely as needed.
I guess what we could do is start with a deletion-based hyperstage, and then try to build extensions on top of that: because we're only ever using the same bottom trigger for each new extension, and that trigger is eventually generated by the same resource, we'd only need a way to use one delete-all-I for every hyperstage and beyond, right?
Hmmm, right. What if we worked by toggling between two resources in two stages, and using the intervening layer to convert between the two? It would mimic the effect of "delete all I", because you wouldn't be able to save your resource for the next stage down of that type, but it would also keep the stage structured properly.
The initial stage is by far the hardest part of this: I don't think the problem lijil find applies to the extensions. There's no point where you have to generate one resource in the middle of generating another one and resetting the state.
This might be a stretch, but maybe if we paired up two stages?
That way, we could alternate between them. The stage below any given NL layer would not be able to consume the same resource as the stage above it. You could refuel a lower stage, by going another level down, but that would require giving up an entire stage to do it, and I don't think that would be able to go infinite.
Edit: I think the bottom trigger might be the easiest part, in a way: it can be something related to using mimic Vat. Untapping it, say, or generating the generic Mana needed to activate it.
Edit: no, that doesn't work either: we can still bank up the top resources, and just save it as we run through the intervening stage. There has to be a more extensible way to chain these, though.
What if we diffentiated between spending the resource during the stage and building up the stack initially? We'd need a way to make one PB and one BM trigger directly translate into a new stack of PB triggers, rather than making one of the input resource. That way, you can't save input resource from the upper stage to the lower, because you're not actually saving any. It's a /very/ weird structure, but we would probably only have to do it for the stage itself, not for the extensions.
I've been reading through the old posts in this thread, and while I'm not all the way through so this might be completely wrong, but I think there might be a better way to approach greater recursion.
I don't understand how your megastage works, but from reading the hyperstage description, it sounds like you guys are implementing the same set of instructions lijil described in #643. You chain together the same stage by adding 2 instructions: use the new resource L to turn all O into I, and put a dividing trigger M on the stack, and use up all I and an M on the stack to create one L. It's actually the same way I'm implementing my stage in standard, using a kind of state variable to divide an upper level from a lower one. The problem is that it's not nearly as extensible as the stage combo: I could only get one of a lower stage and it looks like you guys have managed... 2?
The problem is the delete-all-I approach to preventing infinites. If you can instead make it so that, once you've made an L, spending an I requires using up an M. That way, you can't use the I you save in the lower stage: you either have to let the lower stage resolve completely and use up an M from below IT to regenerate your stage, which is obviously limited, or you have to spend the L you just generated immediately, at which point it's too late to feed the lower stage with your I.
The best way I can see to enforce that restriction is with an imprint card like mimic Vat: if we only have one vat, generating a new untapped hasty token requires putting something on it, and the only way to put the right thing on mimic Vat to start the next stage is by using a trigger from the level below, I think we can force them to only go one way.
So, let's say you start with a stage:
1. If our nontoken creature I is on the Vat, use one I to push X PB on the stack.
2. Pop one PB off the stack to push X BM on the stack.
3. Pop one BM off the stack to produce X O.
4. Pop one PB off the stack and one BM below it to produce one I.
Then add:
5. If our L-producing creature is on the vat, Use one L to push lots of NL on the stack.
6. Pop one NL off the stack to produce X I.
7. Pop one NL off the stack and one BM below it to produce one L, and imprint our L producing creature on the vat.
8. Pop one NL off the stack to put our I-producing creature back on the vat.
That pretty clearly implements a hyperstage: we build a stack of PB- M stages, separated by NL layers, and each combination of NL/BM lets us rebuild the stage above to Grand effect.
The trick is that, if you add another linked "stage":
9. If our K-producing creature is on the vat, use one K to push X SF on the stack.
10. Pop one SF off the stack to produce X L.
11. Pop one SF off the stack and one BM below it to generate one K, and put our K-producing creature on the vat.
12. Pop one SF off the stack to put our L-producing creature on the vat.
If I'm not mistaken, this implements a megastage: each BM in the stage below a K layer produces another K layer, which in turn corresponds to another L-hyperstage.
As long as we can ensure that each new trigger type can hit itself and the next creature down to put it on the vat, but not any of the ones below it, we can keep chaining these modules together, where each module takes us from f_w^n(x) to f_w^(n+1)(x). If we can get even three such linked stages, we'll probably be able to beat the current combo (I don't see this version taking up nearly as much space as the current hyper/megastags, so more room for subsequent stages and layers). And if we can generalize it such that the old stages can link together this way, we could get up to f_w^25(x)!
Obviously, it would take a lot of retooling, and I haven't the faintest idea how to force Mimic Vat's imprinting to match whatever resource we're consuming, but it seems worth exploring at the very least.
Gotcha, thanks: I think choosing 3 as the base and 2 as the first number works best: I only have one Ackermann combo, which gets up to a 4-chain. I can get up to 2->3->8->3 in the main phase, then use that to fuel an Ajani activation for a final layer, which with that combo would give 2->3->(2->3->8->3)->3, which if I'm not mistaken is just 2->3->3->4, correct?
Thanks so much! I think I also lucked out with this standard format, because Cogwork Assembler+Panharmonicon makes every creature with an ETB ability a potential layer.
I actually have a question about Ackermann combos and expressing them at the end: how do you get numbers for the Conway expression? I know each separate Ackermann combo adds another number to the chain, and each layer adds 1 to the last number in the chain, but how do you figure out what the middle numbers are?
For instance, with 6 Ackermann combos and 4 layers after them, I know it would look like 2->x->x->x->x->5, but what would the values of x be there?
I can only get one Ackermann combo in standard, my method is much less extensible, but I feel bad leaving question marks in the final damage total.
Hey, all. I just wanted to let you guys know that your original article inspired me to try a similar challenge in the standard format, relaxing the turn-1 requirement but nothing else. I got up to 9 layers in my current version, and I'm in the process of writing up one that beats Graham's Number now. I thought you might be interested to see it!
We also need to make sure the next hyperstage down is actually necessary to keep the combo going, so we have to use up a trigger from below for... Something. There's still a ways to go before it can be slotted in.
Deathrite feels hard to replace...
Edit: Tezzeret's Gatebreaker also grabs an artifact, which means we can use a Psychic Battle trigger to kill Metallurgeon, imprint it on the Vat, make a hasty token, shuffle it back in, use the next psychic Battle trigger to bounce and replay Gatebreaker, use the trigger to get Metallurgeon, and replay Metallurgeon without using up a Bloodbond March trigger. No good. That and the Helix pretty conclusively rules out Deathrite as an option.
So, our creature needs to have: 2 or fewer toughness ideally (we could go higher, at the cost of reducing space for further layers later on), a tap ability that lets us, in some way, recast a sorcery to trigger Volute, and some search space we can hit with Rebuild.
Maybe Hana Kami, Kodama's Reach, and a Kitsune Diviner?
My first thought is that we're constantly making bajilions of useless token copies of our tap creatures with Dual Nature. That means that mass-haste-granting abilities can generate lots of untapped hasty tokens, as well as untap effects. If we could set up an interventing delete-all-I stage before the life megastage, based on giving creatures haste, that could bump what we already have up to a gigastage. Something like:
Input resource 1 red mana
Output resource: lots of hasty copies of a creature that can tap to cast a sorcery (need not be deep reconnaissance) for free. We would have to change around the original hyperstage to use this token instead of green Mana, and I'm not entirely sure how.
Goblin Bushwhacker, to let us turn 1 red Mana into X triggers that would each give all our not-hasty Dual Nature token copies of the above creature haste, to create a new hyperstage.
A way to bounce Goblin Bushwhacker and our red-producer, almost certainly Simian Spirit Guide, as well as all our tokens, to hand. Engulf the Shore seems like a good choice, as long as we can get 2 and only 2 islands down, and our linking creature has 2 or fewer toughness.
From there, we can just replace Deconstruct with Rite of Flame, and I think we'd have a gigastage. All that's left is to find a creature which can tap to give us a sorcery cast. I think that, if we could find a sorcery that we could cheaply draw from library, without allowing us to draw any cards from higher up the chain, we could use Deathrite Shaman as the chaining creature: we would need to keep green Mana unavailable to preserve the current megastage, and prevent the killing of lands, and allow for black Mana production, but we could use its ability to exile some sorcery, use a Mirror to reshuffle it, and then redraw the sorcery somehow. We could do it by limiting color, for instance.
So, my initial idea would look like:
Bog Initiate
Deathrite Shaman
Engulf the Shore (we can counter it normally, then exile/draw it with Deathrite, making it both our Volute trigger and our delete-all-I generator later on)
Tezzeret's Gatebreaker (it's an M19 artifact that, on ETB, lets us grab a blue card from the library, not sure if we can card it)
Goblin Bushwhacker
Simian Spirit Guide
Additionally, we could remove Deep Reconnaissance, and would have to replace Mox Emerald with... Engineered Explosives? That's the hardest part: we need an artifact, where we can't make tokens or the tokend are useless, that we can reuse with Rebuild to kill Deathrite Shaman, putting it on Mimic Vat.
Edit: could we maybe allow the storing of Mana, where the Mana can be used to kill Deathrite Shaman? Then we could use Mox Sapphire as the rebuild target, and use it to pay for the ability on something like Escape Routes, Homarid Shaman, or King Crab, to kill Deathrite with Horobi and then put it on the Vat.
Mirror in my standard megacombo for a while: you'd top up on alternating triggers between targeting Treasure Map and a creature you can untap with Rallying Roar, then blinking it with Aethergeode Miner to turn just 2 energy into a lot of Mana of any color. I had to drop it when I switched to Cogwork Assembler because letting it make copies of any permanent is super unsafe.
Yeah, it seems like my approach to an extensible n-stage framework may not be tenable. I still believe there's a better way than to force delete all of a resource, but for in the meantime, your configuration is probably still the best.
I guess what we could do is start with a deletion-based hyperstage, and then try to build extensions on top of that: because we're only ever using the same bottom trigger for each new extension, and that trigger is eventually generated by the same resource, we'd only need a way to use one delete-all-I for every hyperstage and beyond, right?
The initial stage is by far the hardest part of this: I don't think the problem lijil find applies to the extensions. There's no point where you have to generate one resource in the middle of generating another one and resetting the state.
That way, we could alternate between them. The stage below any given NL layer would not be able to consume the same resource as the stage above it. You could refuel a lower stage, by going another level down, but that would require giving up an entire stage to do it, and I don't think that would be able to go infinite.
Edit: I think the bottom trigger might be the easiest part, in a way: it can be something related to using mimic Vat. Untapping it, say, or generating the generic Mana needed to activate it.
Edit: no, that doesn't work either: we can still bank up the top resources, and just save it as we run through the intervening stage. There has to be a more extensible way to chain these, though.
What if we diffentiated between spending the resource during the stage and building up the stack initially? We'd need a way to make one PB and one BM trigger directly translate into a new stack of PB triggers, rather than making one of the input resource. That way, you can't save input resource from the upper stage to the lower, because you're not actually saving any. It's a /very/ weird structure, but we would probably only have to do it for the stage itself, not for the extensions.
I don't understand how your megastage works, but from reading the hyperstage description, it sounds like you guys are implementing the same set of instructions lijil described in #643. You chain together the same stage by adding 2 instructions: use the new resource L to turn all O into I, and put a dividing trigger M on the stack, and use up all I and an M on the stack to create one L. It's actually the same way I'm implementing my stage in standard, using a kind of state variable to divide an upper level from a lower one. The problem is that it's not nearly as extensible as the stage combo: I could only get one of a lower stage and it looks like you guys have managed... 2?
The problem is the delete-all-I approach to preventing infinites. If you can instead make it so that, once you've made an L, spending an I requires using up an M. That way, you can't use the I you save in the lower stage: you either have to let the lower stage resolve completely and use up an M from below IT to regenerate your stage, which is obviously limited, or you have to spend the L you just generated immediately, at which point it's too late to feed the lower stage with your I.
The best way I can see to enforce that restriction is with an imprint card like mimic Vat: if we only have one vat, generating a new untapped hasty token requires putting something on it, and the only way to put the right thing on mimic Vat to start the next stage is by using a trigger from the level below, I think we can force them to only go one way.
So, let's say you start with a stage:
1. If our nontoken creature I is on the Vat, use one I to push X PB on the stack.
2. Pop one PB off the stack to push X BM on the stack.
3. Pop one BM off the stack to produce X O.
4. Pop one PB off the stack and one BM below it to produce one I.
Then add:
5. If our L-producing creature is on the vat, Use one L to push lots of NL on the stack.
6. Pop one NL off the stack to produce X I.
7. Pop one NL off the stack and one BM below it to produce one L, and imprint our L producing creature on the vat.
8. Pop one NL off the stack to put our I-producing creature back on the vat.
That pretty clearly implements a hyperstage: we build a stack of PB- M stages, separated by NL layers, and each combination of NL/BM lets us rebuild the stage above to Grand effect.
The trick is that, if you add another linked "stage":
9. If our K-producing creature is on the vat, use one K to push X SF on the stack.
10. Pop one SF off the stack to produce X L.
11. Pop one SF off the stack and one BM below it to generate one K, and put our K-producing creature on the vat.
12. Pop one SF off the stack to put our L-producing creature on the vat.
If I'm not mistaken, this implements a megastage: each BM in the stage below a K layer produces another K layer, which in turn corresponds to another L-hyperstage.
As long as we can ensure that each new trigger type can hit itself and the next creature down to put it on the vat, but not any of the ones below it, we can keep chaining these modules together, where each module takes us from f_w^n(x) to f_w^(n+1)(x). If we can get even three such linked stages, we'll probably be able to beat the current combo (I don't see this version taking up nearly as much space as the current hyper/megastags, so more room for subsequent stages and layers). And if we can generalize it such that the old stages can link together this way, we could get up to f_w^25(x)!
Obviously, it would take a lot of retooling, and I haven't the faintest idea how to force Mimic Vat's imprinting to match whatever resource we're consuming, but it seems worth exploring at the very least.
I actually have a question about Ackermann combos and expressing them at the end: how do you get numbers for the Conway expression? I know each separate Ackermann combo adds another number to the chain, and each layer adds 1 to the last number in the chain, but how do you figure out what the middle numbers are?
For instance, with 6 Ackermann combos and 4 layers after them, I know it would look like 2->x->x->x->x->5, but what would the values of x be there?
I can only get one Ackermann combo in standard, my method is much less extensible, but I feel bad leaving question marks in the final damage total.
http://alex.shankland.org/index.php/2018/06/11/megacombo-1/