I have updated the OP with links to a few of the explanatory posts.
EDIT: I've been wondering whether the "target artifact" combos like Arcum Dagsson or Goblin Trashmaster could be made to work after all. They would certainly go infinite in the old version of the combo, but in this new version we have a lot of new moving parts, and maybe those can't be refreshed as easily as the artifacts. But I'm not sure.
If it still goes infinite, then I think we can still make it work by getting rid of Mirrorworks. Just replace Mirror of Fate and Mirrorworks with Izzet Guildmage and Pull from Eternity, I think. That resolves the problem of requiring more Psychic Battle triggers of our stage artifact, since we will need lots of mana for the stage transition and one copy of Mana Vault and a Keyrune won't be enough. However, we may have the Muzzio problem of being able to bring a copy of whatever we are using to target/sacrifice an artifact below the hyperstage transition, and getting an extra use out of them. Stakfish, do you know an artifact combo that would be safe from this happening?
EDIT: It just occurred to me that getting rid of Mirrorworks can also solve the problem we had with the Soul Foundry deck. That deck also used Muzzio, so we have to switch that out as well, but perhaps we can squeeze out an extra stage or two with that deck.
Very nice summary. I will definitely link it in the OP when I have time, right now I am abroad without a lot of time, and unsure of how to copy post links on mobile. But putting important posts in the OP is something I definitely should have been doing a long time ago.
Skull of Orm looks like a good cut! As for fetching Academy Rector, we can just use Misery Charm, can we not? That will allow the fifth stage back in, getting us to w^4 + w5 + 4.
Concerning the problem FireRogue517 mentioned, there was indeed an error with the early setup, which came about because I was greedy and tried to squeeze in another couple of copies of Dual Nature by having Copy Enchantment copy Dual Nature at strategic points. The additional Dual Nature means one more Dual Nature token is created, but when we bounce the Copy Enchantment (which is copying Dual Nature) card, we trigger the Dual Nature destruction abilities. I believe there was one point where doing this is okay, but there was another point where it was not. That problem could be easily fixed by simply not having Copy Enchantment copy Dual Nature at the wrong time; this will cost us a Dual Nature token, but not a big deal. Of course, the gigastage deck doesn't currently have Dual Nature in it, although perhaps we should keep an eye for its possible inclusion whenever it may become legal, since it may be more efficient.
Oh phooey... I guess being able to save Muzzio through the hyper stage transition is what causes the infinite. So there's currently no other setup for the main stage other than Metallurgeon?
If not, then it looks like the best we can do is to remove the Merfolk stage and end with World at War, getting to w^4+w4+4. I'm not seeing any cuts, although the need for both Salvaging Station and Goblin Welder is driving me nuts.
Heh, the ultracombo article. When I started writing it, I had every intention of finishing it. But, as the gigastage deck started coalescing, I lost the motivation to complete a description of what would (perhaps) become an outdated deck. Maybe if this deck never quite comes together, I will write up the older version.
As for this version, we haven't started writing up anything for it, as it is still in the development stages. I can summarize it briefly I suppose.
The setup is a little different from the previous version. Like before, the basic mechanic is to generate more and more Psychic Battle and Bloodbond March enchantments, and the number of these enchantments are basically our "current number" throughout the combo. However, in this version we removed Dual Nature, since it causes certain problems (currently the problem is with Child of Alara I think). So to get lots of copies of enchantments, we destroy them (using Psychatog in the above deck), and then imprint them on a Mimic Vat to generate a token copy. Then we use Skull of Orm to bring the enchantment back so we can sacrifice it again. This is less efficient then Dual Nature, but that won't affect the final estimate.
The primary stage is similar to the previous version - we have an artifact creature (either Metallurgeon or Rust Tick) that functions as our stage resource, and the stage is built up with alternating Psychic Battle and Bloodbond March groups of triggers.
The hyperstage is the biggest difference in the new version. In the previous version, we had Spellweaver Volute in the hyperstage andSpellweaver Helix in the megastage - in this version, those two cards are bumped up to the megastage and gigastage respectively, and the hyperstage is what's new here. The new spell triggerer is Goblin Dark-Dwellers, which can cast an instant or sorcery of CMC 3 or less when it enters the battlefield. With Panharmonicon, it can cast multiple spells. So we use Battle Cry, or Goryo's Vengeance couple with Muzzio, Visionary Architect, to get lots of Metallurgeons or Rust Ticks; we use Rebuild to regain our hyperstage resource, but at the cost of losing all our stage creatures.
The hyperstage mechanism is actually pretty complicated, as we couldn't get anything simple to work out. So, Rebuild has to replenish our hyperstage resource (which will turn out to be Moggcatcher tokens). It does this by bringing Engineered Explosives back to our hand, so that it can be cast again with a counter, and sacrificed. (Note that if we just bring Engineered Explosives back from the graveyard to the battlefield, it won't get a counter and we can't use it properly - this is quite handy.) Sacrificing Explosives will destroy Scattershot Archer, which can then be imprinted on a Mimic Vat to create a hasted copy. (Engineered Explosives can be brought back from the graveyard using Muzzio or Salvaging Station, while Scattershot Archer can be brought back using Verdant Succession.) The Scattershot Archer can then be activated to destroy Moggcatcher and Strongarm Thug, with the aid of Dearly Departed, Abzan Falconer, and Gratuitous Violence. The Moggcatcher can be imprinted to create a Moggcatcher token, and our hyperstage resource is renewed; the Strongarm Thug can be imprinted to create a token copy, which along with Panharmonicon can bring back both the Moggcatcher and Strongarm Thug to our hand. The Moggcatcher can then be tapped to bring Goblin Dark-Dwellers from the graveyard, which triggers the casting of our cheap instants, including Rebuild to bring Engineered Explosives back to our hand again.
The megastage, like the hyperstage of our previous version, uses Spellweaver Volute as our spell triggerer, and it triggers on the casting of an sorcery. So we use Acorn Harvest as our sorcery (which has CMC greater than 3, so no conflict with Goblin Dark-Dweller), which we can flashback for mana (which we can get cheaply) and 3 life. So life becomes are megastage resource. The instant that renews our hyperstage resource, and the instant that renews our megstage resource but eliminates all of our hyperstage resource, are combined into one: Smite the Monstrous. When we cast Acorn Harvest, we get many copies of Smite the Monstrous via Thousand-Year Storm. Most of the copies can be used to bounce Goblin Dark-Dwellers, which can then be replayed to cast our cheap instants and build up the hyperstage. (Note: we can't rebuild the hyperstage all at once, rather it gradually gets built as it resolves, with the lower Smite the Monstrous triggers standing as placeholders for hyperstage layers until the eventually get resolved and replaced by Battle Cry/Rebuild.) A few more Smite the Monstrous can be used to bounce large creatures that we need to return to our hand. The last Smite the Monstrous is used to destroy Child of Alara, which destroys all nonland permanents, and therefore all of our hyperstage resources (Moggcatcher tokens), but also destroys Centaur Safeguard, which allows us to gain 3 life, renewing our megastage resource. Note that we can't use multiple copies of Smite the Monstrous to destroy Child of Alara and therefore Centaur Safeguard multiple times, because - hmm, I'm forgetting the exact way that works. Stakfish, could you go over that again?
The gigastage uses Spellweaver Helix to cast sorceries, which can only be triggered by a sorcery we have more than one of, so no flashbacking Acorn Harvest to trigger it. So only Spider Spawning can trigger it, which requires a black mana to cast it via flashback. The we get a Frightshroud Courier stage that produces black mana, and a few stages after that; the last deck gets us to around F_{w^4 + w5 + 4}, assuming it works properly.
As for the challenges the deck presents, there have been many. Having four different stage types in the main combo leads to a lot of possible conflict with one level potentially affecting another in undesirable ways. And the newest hyperstage is partcularly complicated; the more complicated, the greater the chance of a flaw or a hidden infinite. Probably the greatest lingering problem is the potential infinite that can come from the megastage and gigastage transitions potentially renewing lower level resources improperly. For example, the way the megastage transition is supposed to work is that we spend three life, go to a higher hyperstage, and gain three life back; but to do so we need to use up a minimal amount of resources from below the megastage transition so as not to go infinite. (Basically, we need to use a few Metallurgeon/Rust Tick triggers to set up the megastage transition). Unfortunately, passing to the higher hyperstage allows us to bring Engineered Explosives and Goblin Dark-Dwellers back to our hand, and keep them in our hand when we pass back down to the lower hyperstage. This allows us to add a couple Moggcatcher tokens, which more then compensates for a couple of lost Metallurgeons, so that goes infinite. So we need to find a way for the megastage transition to use up those extra uses of Engineered Explosives that we gain, and that has been plaguing us for a while. We may have solved it with the necessity to resolve Verdant Succession to gain certain green creatures back, but I'm not totally sure there isn't a hidden infinite somewhere.
Another problem is that Iijil has left, and he was the best one at finding problems and infinities in our prospective decks.
Stakfish, feel free to point out any further details that are worth mentioning.
Yeah, I also would prefer to use Psychic Battle over Grip of Chaos, so that the probabilities remain "reasonable". I had a discussion with Iijil over this, and he was of the opinion that we should just present the deck that had the maximum possible damage. I guess that makes sense. I think, if our deck winds up favoring Grip of Chaos, we would write up the article about that deck, but include an addendum on how things change if we want to replace Grip of Chaos with Psychic Battle.
So long as Grip of Chaos is not in the deck, there is really nothing that requires chance other than card drawing, and with Mirror of Fate we can arrange the library however we want to. So the probability of getting the combo off only includes the cards we draw up until we start using Mirror of Fate, so really it can be no worse (and in fact will be much better than) 1 in 60!, which I would consider firmly in "imaginable numbers".
About your question: Yes, any possible infinite damage combo is prohibited; I'm not sure what you mean by "optimal luck" never reaching that state, could you clarify?
I played around certain times with combos that would be finite if the opponent always acted in a way to keep the maximum damage down, rather than cooperate to go infinite; but Iijil and Stakfish seem to like the rules as they are.
Yes, the fast-growing hierarchy is consistent with the definition of ordinals. Now, F_w (64) is not greater than F_m (64) for all finite ordinals m, and cannot possibly be, since F_m (64) can be arbitrarily large. But, F_w (n), as a function of n, is faster growing than F_m (n) for any fixed m; we have F_w (n) = F_n (n) < F_m (n) for n < m, but once n passes m we have F_w (n) = F_n (n) > F_m (n). So past a certain point F_w (n) will always be greater. More generally, if we have two ordinals a < b < epsilon_0, then F_b will be a faster growing function than F_a. So the ordinals match up orderwise with their corresponding functions.
This might strike one as an academic point, since F_w (n) = F_n (n) doesn't seem like a major leap forward from the finite ordinals. But really it is. To see the big difference, look at what happens with F_{w+1} (n). For example, take F_{w+1} (4). This is equal to F_w (F_w (F_w (F_w (4)))). First we have F_w (4) = F_4 (4) ~ an exponential stack of 10's of height an exponential stack of 10's of height an exponential stack of 10's of height about 10^10^10^21. Big, but not that big given F_m on finite ordinals. But then we go to F_w (F_w (4)) = F_{F_4 (4)) (F_4 (4)) - now, that big number we just described goes into both the variable and the subscript of F, so now we are at an extremely high level in the finite hierarchy. Then we plug the extremely big result of that into the next F_w, so the extremely big result goes into both the variable and the subscript again. Then we plug that value into F_w one final time. Clearly, this is much bigger than an F_m (n) that we can easily describe without this iteration process. That's the power of diagonalization at limit ordinals.
Well, we are hoping to get our omega^4 deck working with no fake cards needed - I'm pretty sure there's a way. Getting to omega^5 seems quite difficult at this point, it might require several made up cards to make it work smoothly, although I haven't really put much thought into it.
As I said earlier in a discussion on the potential limits, I don't really know how to construct an omega^omega structure, at least not using the stack. I did however just think of a way to create an omega^omega structure using creatures on the battlefield, with +0/+X counters for various X.
So, we will make use of Thousand-Year Storm to keep increasing the number of times an instant or sorcery gets copied. So we will have an instant/sorcery that says something like:
"As an additional cost to cast this spell, remove a +0/+X counter from target creature you control, where X is at least 2."
"Put a +0/+(X-1) counter on that creature."
and an instant sorcery that says something like:
"As an additional cost to cast this spell, remove a +0/+1 counter from target creature you control."
"Create a token copy of that creature. For each counter on that creature, put a counter of the same type on the token copy."
And then, we create a deck that has the ability to cast those above two instants/sorceries as many times as we want, as long as we have creatures with +0/+X counters on them. Also, we need to be able to put a +0/+X counter on a creature for some relatively large X, but only a finite number of times.
This gets us to omega^omega in the fast-growing hierarchy. When you have a X creatures with one +0/+1 counter each (and no other counters on them), and the Thousand-Year Storm counter is at Y, we can cast the second spell X times, taking the counter from Y to Y+X. If we have one creature with two +0/+1 counters on it, then casting the second spell gets us about Y creatures with one +0/+1 counter each, so we can cast Y more spells and take the TYS counter from Y to about 2Y. So a creature with three +0/+1 counters will take Y to f_2(Y), a creature with four counters will take Y to f_3(Y) and so on. Next, for a creature with a single +0/+2 counter we cast the first spell, creating a creature with Y +0/+1 counters, so we get about f_Y(Y), or f_omega(Y). Then a creature with one +0/+2 counter and one +0/+1 counter can be targeted by the second spell to create Y creatures with one +0/+2 counter each, so we get f_{omega+1}(Y). Continuing in the fashion, a creature with two +0/+2 counters will take Y to f_{omega*2}(Y), a creature with one +0/+3 counter will take Y to f_{omega^2}(Y), a creature with one +0/+4 counter will take Y to f_{omega^3}(Y), and so on. So the whole structure is at the omega^omega level, and if we can recurse over that structure (say by having an ability that creatures a +0/+X counter, where X is say the number of creatures), we can get f_{omega^omega + alpha}(Y) for some smaller alpha.
Then, we could use +X/+0 counters to get up to omega^{omega*2}, or general +X/+Y counters to get to omega^{omega^2}, but it gets more and more complicated and contrived.
Looking at the above spells, the first doesn't generally do anything positive, while the second seems pretty strong. I guess it wouldn't be too hard to balance the spells, say by giving the first spell some positive effect (maybe generating mana or something), while the second can be nerfed by giving it a high mana cost or some drawback. The real problem is that Wizards has gone away from having lots of different +X/+Y counters, and everything is +1/+1 now. So we wouldn't get spells that dealt with general +0/+X counters. Still, the above spells seem like they could fit in a reasonable card game, if not our current state of MtG, rather than being totally contrived cards that are only designed to create a massive function.
As for encoding something at the level of epsilon_0, I have no idea how we would do that. Beklemishev's worms seems like the most likely possibility, since it doesn't rely on a tree structure or complicated arithmetic functions. But I don't know how we would implement the reduction procedure: if we use the stack to represent integer sequences, then the reduction procedure means resolving the stack until we find an ability representing a smaller number than the top ability of the stack; then we need to recreate the part of the stack we just resolved, except with the top ability decremented; then we copy that part of the stack X times where X keeps increasing. I don't really see how we can recreate the stack that we just resolved, unless it gets copied onto the battlefield or something. Or we could represent the integer sequence on the battlefield. But, since the battlefield is unordered, we need something to represent the order, like the toughness of a creature or something like that. But then the reduction procedure seems equally ridiculous. So this remains a pipe dream, for now.
So, I had an interesting idea - let's say we wanted to go back to using Boggart Mob. We can target it using for example Godtoucher, but unfortunately Godtoucher also targets Child of Alara, so we can go through the megastage transition without spending the life. But here's a possibility - we could replace Mimic Vat and Horobi, Death's Wail with Soul Foundry and Brudiclad, Techor Engineer. So, instead of creating tokens by destroying them via Mimic Vat, we use Cowardice to send them back to our hand and imprint them on a Soul Foundry. Now, when we tap Godtoucher, we can target Child of Alara, but we can't destroy it.
It would be nice if we could now get rid of Mimic Vat, but unfortunately I don't see how we are going to create token copies of our enchantments. I had an idea that we could go back to using Splinter Twin and Crown of the Ages, but for now, let's just keep Mimic Vat in the deck.
Hmm, we could throw in a third color, and have to crack an Explosives for 3 to destroy Tajuru Archer, which would waste an Explosives. That would nullify Centaur Safeguard, of course, so we need a replacement, but it could be a good way to solve those two particular problems.
Edit: Okay, so going with Tajuru Archer handles the problem of creating two Moggcatchers with one run through the combo. But, it still doesn't handle the problem of creating an unwanted Metallurgeon token. I believe you can do the same thing as what I described before: Create a stage for Metallurgeon, then each time you sacrifice Engineered Explosives to destroy Beastcaller Savant, you also destroy the original Metallurgeon, and can create a token copy of it, allowing you to extend the Metallurgeon stage. So I don't know how to handle this.
Oh right, we can use Mimic Vat to get two uses of Engineered Explosives. But, don't we run into the danger of using both Explosives to kill Moggcatcher? We just need to bounce Moggcatcher once to create a bank of Bloodbond March triggers.
I'm thinking that Metallurgeon still goes infinite. We can use our Metallurgeon tokens to create a stage, with Bloodbond March triggers on the top. We can then crack an Explosives to destroy both Wirewood Herald and Metallurgeon, creating tokens of both. We use the Wirewood Herald trigger to return it to our hand, and then resolve a Bloodbond March trigger to return Metallurgeon to the battlefield. Use the Metallurgeon token to extend the stage by a couple layers. Cast the Herald to bounce Moggcatcher, sacrifice Goblin Dark-Dwellers, creating a token copy, make the hyperstage transition, get Explosives back with Rebuild, and sacrifice it again to destroy Herald and Metallurgeon again. Create a couple more layers of the Metallurgeon stage, play Moggcatcher for Bloodbond March triggers and destroy it with the Herald, and create a Moggcatcher token. Tap the token to bring back Dark-Dwellers, and get Explosives back, going back to where we started, but with four more layers in the Metallurgeon stage.
Wait, how does Wirewood Herald and Lys Alana Bowmaster handle both the destruction and retrieval of Moggcatcher? Each time we destroy Wirewood Herald, we get to retrieve Wirewood Herald once, and that allows us to cast it once, getting one batch of targetings of Moggcatcher.
We do need a hasted token of Rust Tick to do anything artifact-wise, so we do need to dip into Psychic Battle triggers wherever those are on the stack. The potential problem is that we can use a PB trigger to destory the nontoken Rust Tick, create a Rust Tick token, tap the hasted Muzzio to retrieve the nontoken Rust Tick, target it with the next PB trigger, and create another Rust Tick token. I haven't gone into a deep analysis but it looks infinite.
I have to think more about whether Metallurgeon can go infinite.
Assuming we can make it all work, I wonder about the possibility of removing Verdant Succession and Natural Order to free up green creatures - without Possessed Centaur I don't know how to do 6 stages in less than 10 cards, so we would need to make the change without adding any more cards. Something to think about.
Also, with Scattershot Archer instead of target fliers/Humans, that would free up Humans anc fliers to be used as transition creatures, or possibly in mana stages... not sure what we can make of that.
Oof, lots of problems then. Nice improvement with Tribal Unity.
Though, I'm wondering now if being able to target Muzzio, Visionary Architect does in fact go infinite. My earlier reasoning was that we have to give up creating a hasted Muzzio token in order to get one later by targeting the nontoken. But, that can still help, provided you give up a token in the higher hyperstage to create one in the lower hyperstage. So I'm thinking we can go infinite there.
Of course, Metallurgeon has the same problem with being able to be targeted. But, when we destroy Wirewood Herald, we also destroy all Metallurgeons - can that save us?
Very interesting idea! At first glance, I'm not seeing anywhere where we need to switch from Anaba Ancestor to Rust Tick without going through a Rebuild, so I don't see yet how it can resolve the Anaba Ancestor issue. Still, Chalice of the Void has some interesting potential to possibly stop infinites, so it's something to keep in mind.
Edit: Okay, let me try and analyze the Anaba Ancestor situation again. First thing I just noticed, after Rebuild resolves, we can get one Mirrorworks artifact, and therefore two each of Mimic Vat, Mirror of Fate, and Perpetual Timepiece before we ever encounter another Psychic Battle trigger for Rust Tick again. So, we won't be able to do what we originally wanted, which was to build a ministage of Anaba Ancestors, while casting Rebuilds from the top, because we will run out of necessary artifacts. To make it work, we need to sprinkle in Rust Tick Psychic Battle triggers amidst all the Anaba Ancestor triggers.
Perhaps the way we want to do things is like so - set up the stack as:
PB triggers for RT
BM triggers for RT
...
PB triggers for RT
BM triggers for RT
Hyperstage transition stuff
PB triggers for AA
BM triggers for AA
PB triggers for RT
BM triggers for RT
...
PB triggers for RT
BM triggers for RT
Hyperstage transition stuff
PB triggers for AA
BM triggers for AA
PB triggers for RT
BM triggers for RT
PB triggers for AA
BM triggers for AA
PB triggers for RT
BM triggers for RT
...
PB triggers for RT
BM triggers for RT
Hyperstage transition stuff
...
...
So, after we resolve out the highest stage, we resolve the hyperstage transition, casting Rebuild and bringing Engineered Explosives back to out hand along with all our other artifacts. We put a Vedalken Orrery trigger at the bottom of the hyperstage transition, so we get a token coming into play. We have enough artifacts to do our usual thing with the Anaba Ancestor stage; use a Psychic Battle trigger to destroy Anaba Ancestor, imprint it on a Mimic Vat, use Mirror of Fate to bring it back to the library, and Perpetual Timepeice to put it back in the graveyard. We still have Bloodbond March triggers, but we are out of Mirror of Fates, so we are forced to resolve down to the Psychic Battle triggers for Rust Tick to create some needed artifacts, and also a hasted Rust Tick token. After we get the required amount, we can tap our newly created Anaba Ancestor token to get a batch of Psychic Battle triggers, use one to bounce Anaba Ancestor, and create a batch of Bloodbond March triggers. Next, we play and sacrifice Engineered Explosives to destroy Anaba Ancestor and gain the token back. Tap the token to get a bunch of Psychic Battle triggers, and after we have prepared for the hyperstage transition, use the top Psychic Battle trigger to bounce Changeling Hero, and we can get started with the hyperstage transtion.
So the top of our stack looks like this:
PB triggers for RT
BM triggers for RT
...
PB triggers for RT
BM triggers for RT
Hyperstage transition stuff
PB triggers for AA
BM triggers for AA
PB triggers for AA
(smaller stack of) PB triggers for RT
BM triggers for RT
...
...
After we resolve again, the top three batches generate one token, but now Anaba Ancestor goes back to our hand. So, after getting the necessary artifacts and the hasted Rust Tick token, we can play the Anaba Ancestor nontoken, getting a bunch of BM triggers, tap the hasted token to get a bunch of PB triggers, then bounce the nontoken and get another bunch of BM triggers. Sacrifice Explosives to kill of Anaba Ancestor, getting another token, resolve out the BM triggers to get down to the PB layer below. Now enter the hyperstage transition, but this time with an Anaba Ancestor hasted token on the battlefield. I think at this point there is nothing stopping us from creating another stage with an Anaba Ancestor set of layers on top, so we can create another stage on top of that. So this looks infinite.
Okay, how about with Chalice of the Void? With this setup, after the hyperstage transition we can replay Chalice of the Void for 2. This allows us to get Bloodbond March triggers for Anaba Ancestor, but not for Rust Tick. But, we didn't need to replay Rust Tick for Bloodbond March triggers, provided we had a healthy stack of Psychic Battle triggers at the top of the Rust Tick part of the stack. After a couple of transitions we can create another two stages above, and don't need to resolve down to this stage again. So this is looking infinite.
So, this looks like bad news.
Edit: Hmm, what if we switch to Metallurgeon? Then, if we do things exactly the same, then, after we sacrifice the Explosives, we destroy all our Metallurgeons, and we can't go into the higher stage and gain any benefit from it. What we can do is double dip - we first resolve down to the Metallurgeon stack to get the Psychic Battle triggers necessary for the artifacts to keep going, then we build the Anaba Ancestor stack back up, and sacrifice the Explosives. We then resolve back down again to generate our Metallurgeon tokens. But, each time we resolve down, we lose half a step in our Anaba Ancestor stack, so after double dipping we have lost a token's worth of the stack. So this exactly compensates for the extra token from Engineered Explosives! Do we have the winning ticket here?
Edit: With the hope that the above is correct, I tried to make a deck:
I thought about using Natural Order to gain lots of life, but I ran into problems trying to do so. We can sacrifice one green creature when we cast it, after than we need ways to get Nylea's Disciple from the battlefield to the library. Child of Alara could do it, so we could certainly gain lots of life by repeatedly destroying Child of Alara, moving Nylea's Disciple to the library with Reclaim, and bringing it back with a copy of Natural Order. But, destroying Child of Alara kills of Vedalken Orrery, which eliminates our ability to take advantage of our newly gained life before Worldfire resolves. So I don't know how to make it work.
Another problem in the Moggcatcher deck: While we do gain one Moggcatcher token per destruction of Wirewood Herald, each Moggcatcher allows to use Goblin Dark-Dwellers twice, once when we bring back the original, and another time when we create a Mimic Vat token after we sacrifice the original.
Yeah, Skyshroud Archer is a problem since if we add another Archer, we can get 2 Coastal Drakes per Engineered Explosives by feeding off the same Bloodbond March set of triggers. So, I would like to use Scattershot Archer, along with something to bring back Coastal Drake. Obviously something that would bring back fliers would be nice, but I don't know of any such cards. The only thing I can think of is adding another Coastal Drake and Assembly Hall. This messes up Nylea's Disciple, since we have two of those. But, what do have Goblin Dark-Dwellers entering the battlefield after the Child of Alara trigger, so we could use that opportunity to bring Nylea's Disciple to the library so that it can be brought back by Verdant Succession. We only want to bring one creature back though, since if we can bring back more then we can bring back Scattershot Archer to boost our devotion. So no Bone Harvest; Reclaim seems good.
After all the changes, we end up using five more cards, reducing us to four stages:
So, worse than the older version. The extra five cards can be entirely attributed to replacing Smite the Monstrous with Brace for Impact; that requires adding another instant, which in turn requires adding Copy Enchantment. Also, we lose Centaur Safeguard, which means adding another card to set up Nylea's Discple, and also Natural Order and Spider Spawning. So finding a replacement for Brace for Impact would be great, but I don't have any ideas at the moment.
Yeah, probably 25-30. (We can mill some cards to avoid drawing them.)
Ah, I see the problem with bouncing and destroying Moggcatcher. Nice ideas on how to fix it. I think Scattershot Archer could avoid that problem, if it is coupled with a way to bring Moggcatcher back from the graveyard; then there is no need to bounce it for Bloodbond March triggers, so it is just a matter of balancing created and used Moggcatchers.
Before I saw your post, I made a deck with Changeling Hero. I guess the Skyshroud Archer bit doesn't quite work, but perhaps it is close:
EDIT: I've been wondering whether the "target artifact" combos like Arcum Dagsson or Goblin Trashmaster could be made to work after all. They would certainly go infinite in the old version of the combo, but in this new version we have a lot of new moving parts, and maybe those can't be refreshed as easily as the artifacts. But I'm not sure.
If it still goes infinite, then I think we can still make it work by getting rid of Mirrorworks. Just replace Mirror of Fate and Mirrorworks with Izzet Guildmage and Pull from Eternity, I think. That resolves the problem of requiring more Psychic Battle triggers of our stage artifact, since we will need lots of mana for the stage transition and one copy of Mana Vault and a Keyrune won't be enough. However, we may have the Muzzio problem of being able to bring a copy of whatever we are using to target/sacrifice an artifact below the hyperstage transition, and getting an extra use out of them. Stakfish, do you know an artifact combo that would be safe from this happening?
EDIT: It just occurred to me that getting rid of Mirrorworks can also solve the problem we had with the Soul Foundry deck. That deck also used Muzzio, so we have to switch that out as well, but perhaps we can squeeze out an extra stage or two with that deck.
Skull of Orm looks like a good cut! As for fetching Academy Rector, we can just use Misery Charm, can we not? That will allow the fifth stage back in, getting us to w^4 + w5 + 4.
Concerning the problem FireRogue517 mentioned, there was indeed an error with the early setup, which came about because I was greedy and tried to squeeze in another couple of copies of Dual Nature by having Copy Enchantment copy Dual Nature at strategic points. The additional Dual Nature means one more Dual Nature token is created, but when we bounce the Copy Enchantment (which is copying Dual Nature) card, we trigger the Dual Nature destruction abilities. I believe there was one point where doing this is okay, but there was another point where it was not. That problem could be easily fixed by simply not having Copy Enchantment copy Dual Nature at the wrong time; this will cost us a Dual Nature token, but not a big deal. Of course, the gigastage deck doesn't currently have Dual Nature in it, although perhaps we should keep an eye for its possible inclusion whenever it may become legal, since it may be more efficient.
If not, then it looks like the best we can do is to remove the Merfolk stage and end with World at War, getting to w^4+w4+4. I'm not seeing any cuts, although the need for both Salvaging Station and Goblin Welder is driving me nuts.
Heh, the ultracombo article. When I started writing it, I had every intention of finishing it. But, as the gigastage deck started coalescing, I lost the motivation to complete a description of what would (perhaps) become an outdated deck. Maybe if this deck never quite comes together, I will write up the older version.
As for this version, we haven't started writing up anything for it, as it is still in the development stages. I can summarize it briefly I suppose.
The setup is a little different from the previous version. Like before, the basic mechanic is to generate more and more Psychic Battle and Bloodbond March enchantments, and the number of these enchantments are basically our "current number" throughout the combo. However, in this version we removed Dual Nature, since it causes certain problems (currently the problem is with Child of Alara I think). So to get lots of copies of enchantments, we destroy them (using Psychatog in the above deck), and then imprint them on a Mimic Vat to generate a token copy. Then we use Skull of Orm to bring the enchantment back so we can sacrifice it again. This is less efficient then Dual Nature, but that won't affect the final estimate.
The primary stage is similar to the previous version - we have an artifact creature (either Metallurgeon or Rust Tick) that functions as our stage resource, and the stage is built up with alternating Psychic Battle and Bloodbond March groups of triggers.
The hyperstage is the biggest difference in the new version. In the previous version, we had Spellweaver Volute in the hyperstage andSpellweaver Helix in the megastage - in this version, those two cards are bumped up to the megastage and gigastage respectively, and the hyperstage is what's new here. The new spell triggerer is Goblin Dark-Dwellers, which can cast an instant or sorcery of CMC 3 or less when it enters the battlefield. With Panharmonicon, it can cast multiple spells. So we use Battle Cry, or Goryo's Vengeance couple with Muzzio, Visionary Architect, to get lots of Metallurgeons or Rust Ticks; we use Rebuild to regain our hyperstage resource, but at the cost of losing all our stage creatures.
The hyperstage mechanism is actually pretty complicated, as we couldn't get anything simple to work out. So, Rebuild has to replenish our hyperstage resource (which will turn out to be Moggcatcher tokens). It does this by bringing Engineered Explosives back to our hand, so that it can be cast again with a counter, and sacrificed. (Note that if we just bring Engineered Explosives back from the graveyard to the battlefield, it won't get a counter and we can't use it properly - this is quite handy.) Sacrificing Explosives will destroy Scattershot Archer, which can then be imprinted on a Mimic Vat to create a hasted copy. (Engineered Explosives can be brought back from the graveyard using Muzzio or Salvaging Station, while Scattershot Archer can be brought back using Verdant Succession.) The Scattershot Archer can then be activated to destroy Moggcatcher and Strongarm Thug, with the aid of Dearly Departed, Abzan Falconer, and Gratuitous Violence. The Moggcatcher can be imprinted to create a Moggcatcher token, and our hyperstage resource is renewed; the Strongarm Thug can be imprinted to create a token copy, which along with Panharmonicon can bring back both the Moggcatcher and Strongarm Thug to our hand. The Moggcatcher can then be tapped to bring Goblin Dark-Dwellers from the graveyard, which triggers the casting of our cheap instants, including Rebuild to bring Engineered Explosives back to our hand again.
The megastage, like the hyperstage of our previous version, uses Spellweaver Volute as our spell triggerer, and it triggers on the casting of an sorcery. So we use Acorn Harvest as our sorcery (which has CMC greater than 3, so no conflict with Goblin Dark-Dweller), which we can flashback for mana (which we can get cheaply) and 3 life. So life becomes are megastage resource. The instant that renews our hyperstage resource, and the instant that renews our megstage resource but eliminates all of our hyperstage resource, are combined into one: Smite the Monstrous. When we cast Acorn Harvest, we get many copies of Smite the Monstrous via Thousand-Year Storm. Most of the copies can be used to bounce Goblin Dark-Dwellers, which can then be replayed to cast our cheap instants and build up the hyperstage. (Note: we can't rebuild the hyperstage all at once, rather it gradually gets built as it resolves, with the lower Smite the Monstrous triggers standing as placeholders for hyperstage layers until the eventually get resolved and replaced by Battle Cry/Rebuild.) A few more Smite the Monstrous can be used to bounce large creatures that we need to return to our hand. The last Smite the Monstrous is used to destroy Child of Alara, which destroys all nonland permanents, and therefore all of our hyperstage resources (Moggcatcher tokens), but also destroys Centaur Safeguard, which allows us to gain 3 life, renewing our megastage resource. Note that we can't use multiple copies of Smite the Monstrous to destroy Child of Alara and therefore Centaur Safeguard multiple times, because - hmm, I'm forgetting the exact way that works. Stakfish, could you go over that again?
The gigastage uses Spellweaver Helix to cast sorceries, which can only be triggered by a sorcery we have more than one of, so no flashbacking Acorn Harvest to trigger it. So only Spider Spawning can trigger it, which requires a black mana to cast it via flashback. The we get a Frightshroud Courier stage that produces black mana, and a few stages after that; the last deck gets us to around F_{w^4 + w5 + 4}, assuming it works properly.
As for the challenges the deck presents, there have been many. Having four different stage types in the main combo leads to a lot of possible conflict with one level potentially affecting another in undesirable ways. And the newest hyperstage is partcularly complicated; the more complicated, the greater the chance of a flaw or a hidden infinite. Probably the greatest lingering problem is the potential infinite that can come from the megastage and gigastage transitions potentially renewing lower level resources improperly. For example, the way the megastage transition is supposed to work is that we spend three life, go to a higher hyperstage, and gain three life back; but to do so we need to use up a minimal amount of resources from below the megastage transition so as not to go infinite. (Basically, we need to use a few Metallurgeon/Rust Tick triggers to set up the megastage transition). Unfortunately, passing to the higher hyperstage allows us to bring Engineered Explosives and Goblin Dark-Dwellers back to our hand, and keep them in our hand when we pass back down to the lower hyperstage. This allows us to add a couple Moggcatcher tokens, which more then compensates for a couple of lost Metallurgeons, so that goes infinite. So we need to find a way for the megastage transition to use up those extra uses of Engineered Explosives that we gain, and that has been plaguing us for a while. We may have solved it with the necessity to resolve Verdant Succession to gain certain green creatures back, but I'm not totally sure there isn't a hidden infinite somewhere.
Another problem is that Iijil has left, and he was the best one at finding problems and infinities in our prospective decks.
Stakfish, feel free to point out any further details that are worth mentioning.
Yeah, I also would prefer to use Psychic Battle over Grip of Chaos, so that the probabilities remain "reasonable". I had a discussion with Iijil over this, and he was of the opinion that we should just present the deck that had the maximum possible damage. I guess that makes sense. I think, if our deck winds up favoring Grip of Chaos, we would write up the article about that deck, but include an addendum on how things change if we want to replace Grip of Chaos with Psychic Battle.
So long as Grip of Chaos is not in the deck, there is really nothing that requires chance other than card drawing, and with Mirror of Fate we can arrange the library however we want to. So the probability of getting the combo off only includes the cards we draw up until we start using Mirror of Fate, so really it can be no worse (and in fact will be much better than) 1 in 60!, which I would consider firmly in "imaginable numbers".
About your question: Yes, any possible infinite damage combo is prohibited; I'm not sure what you mean by "optimal luck" never reaching that state, could you clarify?
I played around certain times with combos that would be finite if the opponent always acted in a way to keep the maximum damage down, rather than cooperate to go infinite; but Iijil and Stakfish seem to like the rules as they are.
Yes, the fast-growing hierarchy is consistent with the definition of ordinals. Now, F_w (64) is not greater than F_m (64) for all finite ordinals m, and cannot possibly be, since F_m (64) can be arbitrarily large. But, F_w (n), as a function of n, is faster growing than F_m (n) for any fixed m; we have F_w (n) = F_n (n) < F_m (n) for n < m, but once n passes m we have F_w (n) = F_n (n) > F_m (n). So past a certain point F_w (n) will always be greater. More generally, if we have two ordinals a < b < epsilon_0, then F_b will be a faster growing function than F_a. So the ordinals match up orderwise with their corresponding functions.
This might strike one as an academic point, since F_w (n) = F_n (n) doesn't seem like a major leap forward from the finite ordinals. But really it is. To see the big difference, look at what happens with F_{w+1} (n). For example, take F_{w+1} (4). This is equal to F_w (F_w (F_w (F_w (4)))). First we have F_w (4) = F_4 (4) ~ an exponential stack of 10's of height an exponential stack of 10's of height an exponential stack of 10's of height about 10^10^10^21. Big, but not that big given F_m on finite ordinals. But then we go to F_w (F_w (4)) = F_{F_4 (4)) (F_4 (4)) - now, that big number we just described goes into both the variable and the subscript of F, so now we are at an extremely high level in the finite hierarchy. Then we plug the extremely big result of that into the next F_w, so the extremely big result goes into both the variable and the subscript again. Then we plug that value into F_w one final time. Clearly, this is much bigger than an F_m (n) that we can easily describe without this iteration process. That's the power of diagonalization at limit ordinals.
If I recall correctly, the problem with Rust Tick was the same as with Metallurgeon; targeting the Human (in this case Muzzio, Visionary Architect) with Skyshroud Archer. So I think there isn't an obvious problem with Muzzio and Scattershot Archer.
If that is okay, we can maybe save three cards and get something like:
2 Psychic Battle
3 Cowardice
4 Horobi, Death’s Wail
5 Bloodbond March
6 Cephalid Shrine
7 Mimic Vat
8 Omniscience
9 Vedalken Orrery
10 Mirror of Fate
11 March of the Machines
12 Perpetual Timepiece
13 Phantatog
14 Skull of Orm
15 Mirrorworks
16 Mana Vault
17 Simic Keyrune
18 Rust Tick
19 Muzzio, Visionary Architect
20 Goryo's Vengeance
21 Rebuild
22 Goblin Dark-Dwellers
23 Moggcatcher
24 Strongarm Thug
25 Panharmonicon
26 Engineered Explosives
27 Scattershot Archer
28 Gratuitous Violence
29 Thousand-Year Storm
30 Dearly Departed
31 Abzan Falconer
32 Wrap in Vigor
34 Acorn Harvest
35 Smite the Monstrous
36 Child of Alara
37 Centaur Safeguard
38 Centaur Safeguard
39 Verdant Succession
40 Spellweaver Helix
41 Worldfire
42 Spider Spawning
43 Spider Spawning
44 Molderhulk
45 Natural Order
46 Bayou
47 Mox Emerald
48 Eureka
49 Polluted Dead
50 Frightshroud Courier
51 Simian Spirit Guide
52 Goblin Kites
54 Streambed Aquitects
55 Old Man of the Sea
56 Xathrid Gorgon
57 Tribal Unity
58 Military Intelligence
59 World at War
60 Reforge the Soul
So it looks like we save two cards, using the extra card slot to get a partial layer. Do you see any problem with the above?
I wonder if it might be possible to replace Verdant Succession; that might allow an Everglove Courier layer prior to the Frightshroud Courier layer.
As I said earlier in a discussion on the potential limits, I don't really know how to construct an omega^omega structure, at least not using the stack. I did however just think of a way to create an omega^omega structure using creatures on the battlefield, with +0/+X counters for various X.
So, we will make use of Thousand-Year Storm to keep increasing the number of times an instant or sorcery gets copied. So we will have an instant/sorcery that says something like:
"As an additional cost to cast this spell, remove a +0/+X counter from target creature you control, where X is at least 2."
"Put a +0/+(X-1) counter on that creature."
and an instant sorcery that says something like:
"As an additional cost to cast this spell, remove a +0/+1 counter from target creature you control."
"Create a token copy of that creature. For each counter on that creature, put a counter of the same type on the token copy."
And then, we create a deck that has the ability to cast those above two instants/sorceries as many times as we want, as long as we have creatures with +0/+X counters on them. Also, we need to be able to put a +0/+X counter on a creature for some relatively large X, but only a finite number of times.
This gets us to omega^omega in the fast-growing hierarchy. When you have a X creatures with one +0/+1 counter each (and no other counters on them), and the Thousand-Year Storm counter is at Y, we can cast the second spell X times, taking the counter from Y to Y+X. If we have one creature with two +0/+1 counters on it, then casting the second spell gets us about Y creatures with one +0/+1 counter each, so we can cast Y more spells and take the TYS counter from Y to about 2Y. So a creature with three +0/+1 counters will take Y to f_2(Y), a creature with four counters will take Y to f_3(Y) and so on. Next, for a creature with a single +0/+2 counter we cast the first spell, creating a creature with Y +0/+1 counters, so we get about f_Y(Y), or f_omega(Y). Then a creature with one +0/+2 counter and one +0/+1 counter can be targeted by the second spell to create Y creatures with one +0/+2 counter each, so we get f_{omega+1}(Y). Continuing in the fashion, a creature with two +0/+2 counters will take Y to f_{omega*2}(Y), a creature with one +0/+3 counter will take Y to f_{omega^2}(Y), a creature with one +0/+4 counter will take Y to f_{omega^3}(Y), and so on. So the whole structure is at the omega^omega level, and if we can recurse over that structure (say by having an ability that creatures a +0/+X counter, where X is say the number of creatures), we can get f_{omega^omega + alpha}(Y) for some smaller alpha.
Then, we could use +X/+0 counters to get up to omega^{omega*2}, or general +X/+Y counters to get to omega^{omega^2}, but it gets more and more complicated and contrived.
Looking at the above spells, the first doesn't generally do anything positive, while the second seems pretty strong. I guess it wouldn't be too hard to balance the spells, say by giving the first spell some positive effect (maybe generating mana or something), while the second can be nerfed by giving it a high mana cost or some drawback. The real problem is that Wizards has gone away from having lots of different +X/+Y counters, and everything is +1/+1 now. So we wouldn't get spells that dealt with general +0/+X counters. Still, the above spells seem like they could fit in a reasonable card game, if not our current state of MtG, rather than being totally contrived cards that are only designed to create a massive function.
As for encoding something at the level of epsilon_0, I have no idea how we would do that. Beklemishev's worms seems like the most likely possibility, since it doesn't rely on a tree structure or complicated arithmetic functions. But I don't know how we would implement the reduction procedure: if we use the stack to represent integer sequences, then the reduction procedure means resolving the stack until we find an ability representing a smaller number than the top ability of the stack; then we need to recreate the part of the stack we just resolved, except with the top ability decremented; then we copy that part of the stack X times where X keeps increasing. I don't really see how we can recreate the stack that we just resolved, unless it gets copied onto the battlefield or something. Or we could represent the integer sequence on the battlefield. But, since the battlefield is unordered, we need something to represent the order, like the toughness of a creature or something like that. But then the reduction procedure seems equally ridiculous. So this remains a pipe dream, for now.
It would be nice if we could now get rid of Mimic Vat, but unfortunately I don't see how we are going to create token copies of our enchantments. I had an idea that we could go back to using Splinter Twin and Crown of the Ages, but for now, let's just keep Mimic Vat in the deck.
So perhaps we can start with something like:
2 Psychic Battle
3 Cowardice
4 Brudiclad, Telchor Engineer
5 Bloodbond March
6 Cephalid Shrine
7 Soul Foundry
8 Omniscience
9 Vedalken Orrery
10 Mirror of Fate
11 Karn, Silver Golem
12 Perpetual Timepiece
13 Mimic Vat
14 Ray of Revelation
15 Skull of Orm
16 Mirrorworks
17 Mana Vault
18 Obelisk of Bant
19 Rust Tick
20 Muzzio, Visionary Architect
21 Goryo's Vengeance
22 Rebuild
23 Goblin Dark-Dwellers
24 Boggart Mob
25 Godtoucher
26 Wirewood Herald
27 Engineered Explosives
29 Acorn Harvest
30 Smite the Monstrous
31 Thousand-Year Storm
32 Child of Alara
33 Tireless Mercenaries
34 Celestial Gatekeeper
35 Celestial Gatekeeper
36 Spellweaver Helix
37 Worldfire
38 Spider Spawning
39 Spider Spawning
40 Molderhulk
41 Divine Congregation
42 Bayou
43 Eureka
44 Mox Emerald
45 Fault Riders
46 Grassland Crusader
47 Hazdhur the Abbot
48 Mirror Gallery
50 Streambed Aquitects
51 Benthicore
52 Devout Chaplain
53 Royal Assassin
54 Simian Spirit Guide
55 Goblin Kites
56 Old Man of the Sea
57 Xathrid Gorgon
58 Tribal Unity
59 Consecrated Sphinx
60 Words of Wisdom
8 stages would be great, but I imagine there's a problem or two in there.
Edit: Okay, so going with Tajuru Archer handles the problem of creating two Moggcatchers with one run through the combo. But, it still doesn't handle the problem of creating an unwanted Metallurgeon token. I believe you can do the same thing as what I described before: Create a stage for Metallurgeon, then each time you sacrifice Engineered Explosives to destroy Beastcaller Savant, you also destroy the original Metallurgeon, and can create a token copy of it, allowing you to extend the Metallurgeon stage. So I don't know how to handle this.
Can we go back to Scattershot Archer? Maybe something like:
2 Psychic Battle
3 Cowardice
4 Horobi, Death's Wail
5 Bloodbond March
6 Cephalid Shrine
7 Mimic Vat
8 Omniscience
9 Vedalken Orrery
10 Mirror of Fate
11 Karn, Silver Golem
12 Perpetual Timepiece
13 Allay
14 Skull of Orm
15 Mirrorworks
16 Mana Vault
17 Simic Keyrune
18 Rust Tick
19 Muzzio, Visionary Architect
20 Goryo's Vengeance
21 Rebuild
22 Goblin Dark-Dwellers
23 Moggcatcher
24 Moggcatcher
25 Assembly Hall
26 Goblin Turncoat
27 Panharmonicon
28 Engineered Explosives
29 Scattershot Archer
30 Scattershot Archer
31 Gratuitous Violence
32 Dearly Departed
33 Abzan Falconer
35 Acorn Harvest
36 Smite the Monstrous
37 Child of Alara
38 Centaur Safeguard
39 Centaur Safeguard
40 Spellweaver Helix
41 Worldfire
42 Spider Spawning
43 Spider Spawning
44 Titania, Protector of Argoth
45 Archangel's Light
46 Bayou
47 Eureka
48 Mox Emerald
49 Llanowar Dead
50 Everglove Courier
51 Eastern Paladin
52 Frightshroud Courier
53 Simian Spirit Guide
54 Goblin Kites
56 Xathrid Gorgon
57 Reality Spasm
58 Thousand-Year Storm
59 Consecrated Sphinx
60 Words of Wisdom
I'm thinking that Metallurgeon still goes infinite. We can use our Metallurgeon tokens to create a stage, with Bloodbond March triggers on the top. We can then crack an Explosives to destroy both Wirewood Herald and Metallurgeon, creating tokens of both. We use the Wirewood Herald trigger to return it to our hand, and then resolve a Bloodbond March trigger to return Metallurgeon to the battlefield. Use the Metallurgeon token to extend the stage by a couple layers. Cast the Herald to bounce Moggcatcher, sacrifice Goblin Dark-Dwellers, creating a token copy, make the hyperstage transition, get Explosives back with Rebuild, and sacrifice it again to destroy Herald and Metallurgeon again. Create a couple more layers of the Metallurgeon stage, play Moggcatcher for Bloodbond March triggers and destroy it with the Herald, and create a Moggcatcher token. Tap the token to bring back Dark-Dwellers, and get Explosives back, going back to where we started, but with four more layers in the Metallurgeon stage.
We do need a hasted token of Rust Tick to do anything artifact-wise, so we do need to dip into Psychic Battle triggers wherever those are on the stack. The potential problem is that we can use a PB trigger to destory the nontoken Rust Tick, create a Rust Tick token, tap the hasted Muzzio to retrieve the nontoken Rust Tick, target it with the next PB trigger, and create another Rust Tick token. I haven't gone into a deep analysis but it looks infinite.
I have to think more about whether Metallurgeon can go infinite.
Assuming we can make it all work, I wonder about the possibility of removing Verdant Succession and Natural Order to free up green creatures - without Possessed Centaur I don't know how to do 6 stages in less than 10 cards, so we would need to make the change without adding any more cards. Something to think about.
Also, with Scattershot Archer instead of target fliers/Humans, that would free up Humans anc fliers to be used as transition creatures, or possibly in mana stages... not sure what we can make of that.
Though, I'm wondering now if being able to target Muzzio, Visionary Architect does in fact go infinite. My earlier reasoning was that we have to give up creating a hasted Muzzio token in order to get one later by targeting the nontoken. But, that can still help, provided you give up a token in the higher hyperstage to create one in the lower hyperstage. So I'm thinking we can go infinite there.
Of course, Metallurgeon has the same problem with being able to be targeted. But, when we destroy Wirewood Herald, we also destroy all Metallurgeons - can that save us?
Edit: Okay, let me try and analyze the Anaba Ancestor situation again. First thing I just noticed, after Rebuild resolves, we can get one Mirrorworks artifact, and therefore two each of Mimic Vat, Mirror of Fate, and Perpetual Timepiece before we ever encounter another Psychic Battle trigger for Rust Tick again. So, we won't be able to do what we originally wanted, which was to build a ministage of Anaba Ancestors, while casting Rebuilds from the top, because we will run out of necessary artifacts. To make it work, we need to sprinkle in Rust Tick Psychic Battle triggers amidst all the Anaba Ancestor triggers.
So first, I will analyze the combo without Chalice of the Void.
Perhaps the way we want to do things is like so - set up the stack as:
PB triggers for RT
BM triggers for RT
...
PB triggers for RT
BM triggers for RT
Hyperstage transition stuff
PB triggers for AA
BM triggers for AA
PB triggers for RT
BM triggers for RT
...
PB triggers for RT
BM triggers for RT
Hyperstage transition stuff
PB triggers for AA
BM triggers for AA
PB triggers for RT
BM triggers for RT
PB triggers for AA
BM triggers for AA
PB triggers for RT
BM triggers for RT
...
PB triggers for RT
BM triggers for RT
Hyperstage transition stuff
...
...
So, after we resolve out the highest stage, we resolve the hyperstage transition, casting Rebuild and bringing Engineered Explosives back to out hand along with all our other artifacts. We put a Vedalken Orrery trigger at the bottom of the hyperstage transition, so we get a token coming into play. We have enough artifacts to do our usual thing with the Anaba Ancestor stage; use a Psychic Battle trigger to destroy Anaba Ancestor, imprint it on a Mimic Vat, use Mirror of Fate to bring it back to the library, and Perpetual Timepeice to put it back in the graveyard. We still have Bloodbond March triggers, but we are out of Mirror of Fates, so we are forced to resolve down to the Psychic Battle triggers for Rust Tick to create some needed artifacts, and also a hasted Rust Tick token. After we get the required amount, we can tap our newly created Anaba Ancestor token to get a batch of Psychic Battle triggers, use one to bounce Anaba Ancestor, and create a batch of Bloodbond March triggers. Next, we play and sacrifice Engineered Explosives to destroy Anaba Ancestor and gain the token back. Tap the token to get a bunch of Psychic Battle triggers, and after we have prepared for the hyperstage transition, use the top Psychic Battle trigger to bounce Changeling Hero, and we can get started with the hyperstage transtion.
So the top of our stack looks like this:
PB triggers for RT
BM triggers for RT
...
PB triggers for RT
BM triggers for RT
Hyperstage transition stuff
PB triggers for AA
BM triggers for AA
PB triggers for AA
(smaller stack of) PB triggers for RT
BM triggers for RT
...
...
After we resolve again, the top three batches generate one token, but now Anaba Ancestor goes back to our hand. So, after getting the necessary artifacts and the hasted Rust Tick token, we can play the Anaba Ancestor nontoken, getting a bunch of BM triggers, tap the hasted token to get a bunch of PB triggers, then bounce the nontoken and get another bunch of BM triggers. Sacrifice Explosives to kill of Anaba Ancestor, getting another token, resolve out the BM triggers to get down to the PB layer below. Now enter the hyperstage transition, but this time with an Anaba Ancestor hasted token on the battlefield. I think at this point there is nothing stopping us from creating another stage with an Anaba Ancestor set of layers on top, so we can create another stage on top of that. So this looks infinite.
Okay, how about with Chalice of the Void? With this setup, after the hyperstage transition we can replay Chalice of the Void for 2. This allows us to get Bloodbond March triggers for Anaba Ancestor, but not for Rust Tick. But, we didn't need to replay Rust Tick for Bloodbond March triggers, provided we had a healthy stack of Psychic Battle triggers at the top of the Rust Tick part of the stack. After a couple of transitions we can create another two stages above, and don't need to resolve down to this stage again. So this is looking infinite.
So, this looks like bad news.
Edit: Hmm, what if we switch to Metallurgeon? Then, if we do things exactly the same, then, after we sacrifice the Explosives, we destroy all our Metallurgeons, and we can't go into the higher stage and gain any benefit from it. What we can do is double dip - we first resolve down to the Metallurgeon stack to get the Psychic Battle triggers necessary for the artifacts to keep going, then we build the Anaba Ancestor stack back up, and sacrifice the Explosives. We then resolve back down again to generate our Metallurgeon tokens. But, each time we resolve down, we lose half a step in our Anaba Ancestor stack, so after double dipping we have lost a token's worth of the stack. So this exactly compensates for the extra token from Engineered Explosives! Do we have the winning ticket here?
Edit: With the hope that the above is correct, I tried to make a deck:
2 Psychic Battle
3 Cowardice
4 Horobi, Death's Wail
5 Bloodbond March
6 Cephalid Shrine
7 Mimic Vat
8 Omniscience
9 Vedalken Orrery
10 Mirror of Fate
11 Karn, Silver Golem
12 Perpetual Timepiece
13 Ray of Revelation
14 Skull of Orm
15 Mirrorworks
16 Mana Vault
17 Selesnya Keyrune
18 Metallurgeon
19 Battle Cry
20 Rebuild
21 Goblin Dark-Dwellers
22 Changeling Hero
23 Changeling Hero
24 Anaba Ancestor
25 Engineered Explosives
26 Salvaging Station
28 Copy Enchantment
30 Acorn Harvest
31 Into Thin Air
32 Brace for Impact
33 Child of Alara
34 Tireless Missionaries
35 Celestial Gatekeeper
36 Celestial Gatekeeper
37 Spellweaver Helix
38 Worldfire
39 Spider Spawning
40 Spider Spawning
41 Spider Spawning
42 Titania, Protector of Argoth
43 Divine Congregation
44 Bayou
45 Eureka
46 Mox Emerald
48 Thrull Champion
49 Godtoucher
50 Everglove Courier
51 Possessed Centaur
52 Eastern Paladin
53 Frightshroud Courier
54 Dwarven Warriors
55 Possessed Barbarian
56 Minion of Tevesh Szat
57 Reality Spasm
58 Thousand-Year Storm
59 Consecrated Sphinx
60 Words of Wisdom
The Tireless Missionaries / Celestial Gatekeeper interaction seems nice, although perhaps not the most efficient. (It also prevents me from using Possessed Aven down below, so something else could be better for the lifegain.) There are two Changeling Heros to Champion Goblin Dark-Dwellers and Omniscience. Looking at it again though, we don't have a way to get back Horobi, Death's Wail and Titania, Protector of Argoth. I suppose we could add Goryo's Vengeance for them both.
2 Psychic Battle
3 Cowardice
4 Horobi, Death's Wail
5 Bloodbond March
6 Cephalid Shrine
7 Mimic Vat
8 Omniscience
9 Vedalken Orrery
10 Mirror of Fate
11 Karn, Silver Golem
12 Perpetual Timepiece
13 Ray of Revelation
14 Skull of Orm
15 Mirrorworks
16 Mana Vault
17 Selesnya Keyrune
18 Metallurgeon
19 Battle Cry
20 Rebuild
21 Goblin Dark-Dwellers
22 Changeling Hero
23 Changeling Hero
24 Anaba Ancestor
25 Engineered Explosives
26 Salvaging Station
28 Copy Enchantment
29 Acorn Harvest
30 Into Thin Air
31 Brace for Impact
32 Child of Alara
33 Tireless Missionaries
34 Celestial Gatekeeper
35 Celestial Gatekeeper
36 Spellweaver Helix
37 Worldfire
38 Spider Spawning
39 Spider Spawning
40 Spider Spawning
41 Titania, Protector of Argoth
42 Goryo's Vengeance
43 Divine Congregation
44 Bayou
45 Eureka
46 Mox Emerald
48 Thrull Champion
49 Godtoucher
50 Everglove Courier
51 Possessed Centaur
52 Eastern Paladin
53 Frightshroud Courier
54 Dwarven Warriors
55 Possessed Barbarian
56 Minion of Tevesh Szat
57 Reality Spasm
58 Thousand-Year Storm
59 Consecrated Sphinx
60 Words of Wisdom
I thought about using Natural Order to gain lots of life, but I ran into problems trying to do so. We can sacrifice one green creature when we cast it, after than we need ways to get Nylea's Disciple from the battlefield to the library. Child of Alara could do it, so we could certainly gain lots of life by repeatedly destroying Child of Alara, moving Nylea's Disciple to the library with Reclaim, and bringing it back with a copy of Natural Order. But, destroying Child of Alara kills of Vedalken Orrery, which eliminates our ability to take advantage of our newly gained life before Worldfire resolves. So I don't know how to make it work.
Another problem in the Moggcatcher deck: While we do gain one Moggcatcher token per destruction of Wirewood Herald, each Moggcatcher allows to use Goblin Dark-Dwellers twice, once when we bring back the original, and another time when we create a Mimic Vat token after we sacrifice the original.
After all the changes, we end up using five more cards, reducing us to four stages:
2 Psychic Battle
3 Cowardice
4 Horobi, Death's Wail
5 Bloodbond March
6 Cephalid Shrine
7 Mimic Vat
8 Omniscience
9 Vedalken Orrery
10 Mirror of Fate
11 Karn, Silver Golem
12 Perpetual Timepiece
13 Ray of Revelation
14 Skull of Orm
15 Mirrorworks
16 Mana Vault
17 Simic Keyrune
18 Rust Tick
19 Muzzio, Visionary Architect
20 Goryo's Vengeance
21 Rebuild
22 Goblin Dark-Dwellers
23 Changeling Hero
24 Coastal Drake
25 Coastal Drake
26 Assembly Hall
27 Engineered Explosives
28 Scattershot Archer
29 Verdant Succession
31 Copy Enchantment
32 Acorn Harvest
33 Into Thin Air
34 Brace for Impact
35 Child of Alara
36 Nylea's Disciple
37 Reclaim
38 Pharika, God of Affliction
39 Spellweaver Helix
40 Worldfire
41 Spider Spawning
42 Spider Spawning
43 Spider Spawning
44 Spider Spawning
45 Natural Order
46 Titania, Protector of Argoth
47 Divine Congregation
48 Bayou
49 Eureka
50 Mox Emerald
52 Frightshroud Courier
53 Dwarven Warriors
54 Possessed Barbarian
55 Minion of Tevesh Szat
56 Mana Crypt
57 Reality Spasm
58 Thousand-Year Storm
59 Consecrated Sphinx
60 Words of Wisdom
So, worse than the older version. The extra five cards can be entirely attributed to replacing Smite the Monstrous with Brace for Impact; that requires adding another instant, which in turn requires adding Copy Enchantment. Also, we lose Centaur Safeguard, which means adding another card to set up Nylea's Discple, and also Natural Order and Spider Spawning. So finding a replacement for Brace for Impact would be great, but I don't have any ideas at the moment.
Ah, I see the problem with bouncing and destroying Moggcatcher. Nice ideas on how to fix it. I think Scattershot Archer could avoid that problem, if it is coupled with a way to bring Moggcatcher back from the graveyard; then there is no need to bounce it for Bloodbond March triggers, so it is just a matter of balancing created and used Moggcatchers.
Before I saw your post, I made a deck with Changeling Hero. I guess the Skyshroud Archer bit doesn't quite work, but perhaps it is close:
2 Psychic Battle
3 Cowardice
4 Horobi, Death's Wail
5 Bloodbond March
6 Cephalid Shrine
7 Mimic Vat
8 Omniscience
9 Vedalken Orrery
10 Mirror of Fate
11 Karn, Silver Golem
12 Perpetual Timepiece
13 Ray of Revelation
14 Skull of Orm
15 Mirrorworks
16 Mana Vault
17 Simic Keyrune
18 Rust Tick
19 Muzzio, Visionary Architect
20 Goryo's Vengeance
21 Rebuild
22 Goblin Dark-Dwellers
23 Changeling Hero
24 Coastal Drake
25 Engineered Explosives
26 Skyshroud Archer
27 Verdant Succession
29 Acorn Harvest
30 Into Thin Air
31 Brace for Impact
32 Child of Alara
33 Nylea's Disciple
34 Nylea's Disciple
35 Arixmethes, Slumbering Isle
36 Spellweaver Helix
37 Worldfire
38 Spider Spawning
39 Spider Spawning
40 Spider Spawning
41 Titania, Protector of Argoth
42 Archangel's Light
43 Bayou
44 Eureka
45 Mox Emerald
46 Goblin Gardener
47 Mad Auntie
49 Frightshroud Courier
50 Slayer of the Wicked
51 Grassland Crusader
52 Dwarven Warriors
53 Possessed Barbarian
54 Minion of Tevesh Szat
55 Mana Crypt
56 Reality Spasm
57 Thousand-Year Storm
58 Military Intelligence
59 World at War
60 Words of Wisdom
Perhaps seven stages should be possible, but I didn't see a way. We will probably need the spare card slots anyway.