Briefly:
Ideally, to grow a stage/hyperstage/megastage on the stack, the deck forces abilities of a layer/stage/hyperstage below them to reduce. Due to this reduce, there is no infinite loop.
However, there may be some way to play: an intended way using Metallurgeon to reuse artifacts and gain mana, and a special way using Retract. Special way doesn't reduce abilities of a layer/stage/hyperstage below the stage/hyperstage/megastage (on stack). Superfacially there is no change on the stack, but we can still get more combo permanents and TYS counting numbers.
If we gain few mana but spend more, this special play won't last long; to get more combo permanents and TYS counting numbers, we can do better with usual (intended) play. If we gain plenty mana but spend few, this special play will go infinite.
Also for the "EDIT". If you've read my writing about how to fetch Child of Alara by its BM trigger, you can conclude that:
That is an important usage in startup. But it might lead to infinity in usual play.
Hyperstage, Megastage and Gigastage all assume that "we need haste Metallurgeons to continue processing. If there is no, we can't go further. The only way to get haste Metallurgeon is using some PB/BM triggers in "trigger groups" at below. It forces us to do so, so no infinite". However, due to the startup process, this might be not true.
Take Child of Alara-based megastage as example.
We prepare the come-back of Vedalken Orrery and Omniscience, then flashback Acorn Harvest in cost of 3 life. Cast Smite the Monstrous, get TYS triggers, which get (many, even with only 1 TYS + 1 PB on battlefield) PB triggers, which bounce Goblin Dark-Dwellers so we can reuse Retract/Hurkyl's Recall/Rebuild. After some growth, destroy Child of Alara and gain 3 life from Centaur Safeguard. After Vedalken Orrery and Omniscience pop out, we can again spend 3 life for the same thing.
Hyperstage seems safe: for example, in my deck, in a dual cycle, we need to
Spend 2 for token Mimic Vat, 2 times (we need 4 of them in dual cycle, so 2 tokens)
35 mana in total, against only 14 mana we gain each dual cycle. So we will be short of mana using this.
But for megastage, there are many MANY PB triggers bouncing Goblin Dark-Dwellers, we might have plenty of mana to go infinite.
Note: DO NOT read the following. I forgot that Child of Alara is Legendary.
Maybe not. Child of Alara is not so easy to fetch back.
Generally, the stack looks like this. Here shows a slice of megastage.
...... ......
group of PB - Metallurgeon
group of BM - Metallurgeon
group of TYS - Retract
pop out Vedalken Orrery
group of PB - Metallurgeon
group of BM - Metallurgeon
group of PB - Metallurgeon
...
group of PB - Metallurgeon
group of BM - Metallurgeon
group of PB - Smite the Monstrous <-- A
group of TYS - Smite the Monstrous
some preparation abilities<-- B
group of PB - Metallurgeon
group of BM - Metallurgeon
group of PB - Metallurgeon
...
group of PB - Metallurgeon
group of BM - Metallurgeon
group of TYS - Retract
Verdant Succession - Scattershot Archer <-- C
pop out Vedalken Orrery
group of PB - Metallurgeon
group of BM - Metallurgeon
group of PB - Metallurgeon
...
group of PB - Metallurgeon
group of BM - Metallurgeon
group of TYS - Retract
pop out Vedalken Orrery
group of PB - Metallurgeon
group of BM - Metallurgeon
group of PB - Metallurgeon
...
...
group of PB - Metallurgeon
group of BM - Metallurgeon
group of TYS - Retract
pop out Vedalken Orrery
group of PB - Metallurgeon
group of BM - Metallurgeon
group of PB - Metallurgeon
...
group of PB - Metallurgeon
group of BM - Metallurgeon
group of TYS - Retract
pop out Vedalken Orrery
group of PB - Metallurgeon
group of BM - Metallurgeon
group of PB - Metallurgeon
...
group of PB - Metallurgeon
group of BM - Metallurgeon
group of PB - Smite the Monstrous <-- D
group of TYS - Smite the Monstrous
some preparation abilities<-- E
group of PB - Metallurgeon
group of BM - Metallurgeon
group of PB - Metallurgeon
...
group of BM - Metallurgeon
group of PB - Metallurgeon
group of BM - Metallurgeon
group of TYS - Retract
Verdant Succession - Scattershot Archer
pop out Vedalken Orrery
group of PB - Metallurgeon
group of BM - Metallurgeon
group of PB - Metallurgeon
...... ......
If the abilities between A and B gradually resolve, down to several PB - Smite the Monstrous triggers, we would use them to bounce the creatures we need to keep, and put a Centaur Safeguard into library. Final PB - Smite the Monstrous kill Child of Alara. We gain 3 life, and the Centaur Safeguard in library go back to battlefield without any further responses.
Scattershot Archer is fetch by group C.
To fetch Child of Alara, we might have hold it in hand at some time before, then play for its BM triggers inside the complicated "group B" triggers. But, how do we "hold it in hand"? Certainly it should be some PB - Smite the Monstrous trigger, but there are group A and group D.
If we use group D to bounce Child of Alara, that is very expensive. We lost all the googological content of layer, stage and hyperstage between D and B, making Child of Alara megastage a stage (alternative groups of TYS - Smite the Monstrous, PB - Smite the Monstrous and possibly BM - Child of Alara).
If we use group A to bounce Child of Alara, we should have a token Child of Alara when stack resolve down from A to B. This is quite tricky, separated into two phases.
Short phase. Start with Child of Alara card in hand. Stack is a little below "group B". Play Child of Alara for BM triggers (lower position in group B). We prepare a specific token Mimic Vat, and should keep it on battlefield without Retract. When we prepared enough (higher position in group B), activate the token Mimic Vat, without resolving.
Flashback Acorn Harvest, build group A on stack. In short phase, PB - Smite the Monstrous bounce Goblin Dark-Dwellers, which use Battle Cry (no Retract!), getting TYS - Battle Cry triggers, which can further build one Metallurgeon stage. Since we cannot Retract, this is the furthest we can do.
When group A resolve down to final PB - Smite the Monstrous, we hold Goblin Dark-Dwellers in hand. Final PB - Smite the Monstrous kill Child of Alara, imprinting on that specific token Mimic Vat, but don't let the Child of Alara trigger resolve.
In response, we play Goblin Dark-Dwellers, Retract the token Mimic Vat along with other artifacts.
Notice: for last known information of that token Mimic Vat, it remembered the Child of Alara card.
Stack resolve. Down to the activated ability of that Mimic Vat, token Child of Alara is out.
Get Vedalken Orrery and Omniscience back. Put Child of Alara into graveyard.
Then BM - Child of Alara fetch it.
Now there is Child of Alara card and token on battlefield.
Long phase. Start with Child of Alara card on battlefield, along with its token copy. Normally push abilities on stack. At group A, use one PB - Smite the Monstrous to bounce Child of Alara. Normally play. There can be many stages above this. When stack resolve down to final PB - Smite the Monstrous above B, kill the token Child of Alara.
Actually, we can also prepare token Child of Alara when we successively resolve down many hyperstages. Each time we need Short phase to get such a token.
Back to the startup playing. What if we continuely play short phase without haste Metallurgeon? Well, we can only get one Retract for each short phase play, rewarding 7 mana. But we need more mana than this.
1G flashback mana
3 making token Child of Alara
2 for a Mirror of Fate token
3 to prepare Vedalken Orrery + Omniscience
... (already 10 mana, but I don't know more details of that)
Okay. That looks safe.
Still unsafe. We can alternatively play short phase (which gets very few growth) and long phase (which allows a lot growth), both using the startup playing, without Metallurgeon.
EDIT:
Another problem about megastage. When we end up a long phase, use several PB - Smite the Monstrous triggers, we play Goblin Dark-Dwellers to Retract, then PB trigger bounce Goblin Dark-Dwellers, finally destroy Child of Alara. Down to the preparation abilities, we have both Engineered Explosives and Goblin Dark-Dwellers in hand. There is one stage between group B and group C (fetching Scattershot Archer), but we can build two groups from Engineered Explosives and Goblin Dark-Dwellers. Net gain one stage. So this will go infinite.
It is not a hyperstage specific problem. As long as each stage requires one play of Engineered Explosives or one ETB of Goblin Dark-Dwellers, there is the problem.
Use 2 untapped haste Scattershot Archers to get one death of Moggcatcher, which means 2 controllable ETB of Goblin Dark-Dwellers, provided Clickslither to freely kill Goblin Dark-Dwellers, and Strongarm Thug to easily fetch itself and Moggcatcher.
We need one Explosives to get one haste Scattershot Archer, which means 2 haste Moggcatchers, then another Explosives to make a haste Goblin Lookout. Also "2 Scattershot Archer + 1 Moggcatcher" looks similarly.
In this deck, we see an untapped haste Moggcatcher as hyperstage resource, but if Goblin Dark-Dwellers card is on battlefield, we add half resource, because we can still get one controllable ETB trigger.
Use 0.5 hyperstage resources to cast Hurkyl's Recall. Get Chalice and Explosives back to hand. Resolve down and pop Vedalken Orrery.
top
group of TYS triggers of False Memories
group of PB triggers of Metallurgeon
maybe other abilities
Now Hurkyl's Recall is in exile. Resolve a TYS copy of False Memories, so it goes graveyard.
Use the Explosives to get one untapped haste Skyshroud Archer.
Next, replay Vedalken Orrery.
top
Mirrorworks trigger of Vedalken Orrery
group of TYS triggers of False Memories
group of PB triggers of Metallurgeon
maybe other abilities
Again use 0.5 hyperstage resource to get Explosives back to hand. And resolve to mill Hurkyl's Recall. And then replay Vedalken Orrery.
top
Mirrorworks trigger of Vedalken Orrery
group of TYS triggers of False Memories
group of PB triggers of Metallurgeon
maybe other abilities
It is notable that we cannot get two untapped haste Skyshroud Archers, which will be gone on Explosives. So the best result we can save is: Moggcatcher card and Explosives in hand, plus one untapped haste Skyshroud Archer on battlefield - this is the scenario we are now.
Also we have 0 hyperstage resources now.
Play Chalice on 4, then play Moggcatcher for BM triggers. Use the untapped haste Skyshroud Archer for PB triggers. Play Moggcatcher for BM triggers.
top
group of BM triggers of Moggcatcher
group of PB triggers of Skyshroud Archer
group of BM triggers of Moggcatcher
Mirrorworks trigger of Vedalken Orrery
group of TYS triggers of False Memories
group of PB triggers of Metallurgeon
maybe other abilities
Use Explosive to get untapped haste Skyshroud Archer. Use it to get another PB group.
top
group of PB triggers of Skyshroud Archer
group of BM triggers of Moggcatcher
group of PB triggers of Skyshroud Archer
group of BM triggers of Moggcatcher
Mirrorworks trigger of Vedalken Orrery
group of TYS triggers of False Memories
group of PB triggers of Metallurgeon
maybe other abilities
Each PB-BM double group make one hyperstage resource. So we have 2 hyperstage resources as the topmost 4th group resolves.
top
Mirrorworks trigger of Vedalken Orrery
group of TYS triggers of False Memories
group of PB triggers of Metallurgeon
maybe other abilities
Use 0.5 hyperstage resource for Hurkyl's Recall. Resolve down: pop Vedalken Orrery and then mill Hurkyl's Recall.
top
group of TYS triggers of False Memories
group of PB triggers of Metallurgeon
maybe other abilities
Play Chalice on 2. Use Explosive for untapped haste Skyshroud Archer, then bounce Moggcatcher card to hand.
Compared with the paused point: now we have 1.5 hyperstage resources, 0.5 more than the paused point; now we have 3 fewer TYS copies of False Memories.
If we loop this until the group of TYS triggers of False Memories exhaust, we will have MANY hyperstage resources.
That means: each time we want BM triggers of Moggcatcher (in order to get the hyperstage resource - untapped haste Moggcatcher token), we need to set Chalice on 4.
EDIT:
Also, there is Goblin Lookout. I don't know whether it is useful (instead of Clickslither).
Untapped haste Goblin Lookout token can be obtained from its death by Engineered Explosives. Then it can be fetched by Moggcatcher. So, one cycle of Goblin Dark-Dwellers means
get untapped haste Goblin Lookout + get untapped haste Moggcatcher
which means
use Engineered Explosives on 2 + (get untapped haste Moggcatcher)*2
which means (assume one untapped haste Skyshroud Archer can get one untapped haste Moggcatcher, but I don't know the process exactly)
use Engineered Explosives on 2 + (get untapped haste Skyshroud Archer)*2
which means
use Engineered Explosives on 2 + (use Engineered Explosives on 1)*2
which means
(effective Hurkyl's Recall + Vedalken Orrery refill)*3
which means
3 controllable ETB of Goblin Dark-Dwellers
sounds bad.
EDIT 2:
Matsu-Tribe Sniper has mana value 2, the same as Goblin Lookout. One use of Engineered Explosives can destroy and get both haste tokens.
As usual, use top group of PB and one of BM trigger to get one untapped haste Metallurgeon token (i.e. core stage resource). Do this twice. Activate to push PB triggers, so the tokens become tapped. Bounce and replay Vedalken Orrery.
top
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
maybe other abilities
As usual, use hyperstage resource:
top
group of PB triggers of Skyshroud Archer
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
maybe other abilities
Bounce Boggart Mob, get ETB trigger of Goblin Dark-Dwellers. Cast Battle Cry, then cast-counter False Memories.
top
group of TYS triggers of False Memories
group of PB triggers of Skyshroud Archer
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
maybe other abilities
Mill all three instants. Replay Boggart Mob, champion Goblin Dark-Dwellers.
Use the two new stage resource:
top
group of PB triggers of Metallurgeon
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
group of TYS triggers of False Memories
group of PB triggers of Skyshroud Archer
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
maybe other abilities
We still have one hyperstage resource, so we can do the above again
top
group of PB triggers of Metallurgeon
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
group of TYS triggers of False Memories
group of PB triggers of Skyshroud Archer
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
group of TYS triggers of False Memories
group of PB triggers of Skyshroud Archer
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
maybe other abilities
Do some usual growth, until
top
PB triggers of Skyshroud Archer
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
group of TYS triggers of False Memories
group of PB triggers of Skyshroud Archer
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
maybe other abilities
Bounce Boggart Mob, get ETB trigger of Goblin Dark-Dwellers. Cast Hurkyl's Recall. Now all artifacts are in hand. Wait for a Vedalken Orrery.
top
group of PB triggers of Metallurgeon
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
group of TYS triggers of False Memories
group of PB triggers of Skyshroud Archer
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
maybe other abilities
Even without Chalice of the Void, we can gain the one hyperstage resource back.
And then, resolve down to get one stage resource.
top
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
group of TYS triggers of False Memories
group of PB triggers of Skyshroud Archer
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
maybe other abilities
Resolve down, mill Hurkyl's Recall.
top
group of TYS triggers of False Memories
group of PB triggers of Skyshroud Archer
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
maybe other abilities
Next, use stage resource, bounce and replay Vedalken Orrery.
top
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of TYS triggers of False Memories
group of PB triggers of Skyshroud Archer
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
maybe other abilities
Use hyperstage resource. Bounce Boggart Mob, get ETB trigger of Goblin Dark-Dwellers. Cast Battle Cry. So we still have one stage resource.
top
group of PB triggers of Skyshroud Archer
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of TYS triggers of False Memories
group of PB triggers of Skyshroud Archer
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
maybe other abilities
Use the stage resource, bounce and replay Vedalken Orrery.
top
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of PB triggers of Skyshroud Archer
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of TYS triggers of False Memories
group of PB triggers of Skyshroud Archer
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
maybe other abilities
Now we play Chalice with X=4. Then play Boggart Mob for its BM trigger.
top
group of BM triggers of Boggart Mob
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of PB triggers of Skyshroud Archer
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of TYS triggers of False Memories
group of PB triggers of Skyshroud Archer
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
maybe other abilities
Flicker Goblin Dark-Dwellers, casting Hurkyl's Recall. Resolve down and pop a Vedalken Orrery.
top
group of PB triggers of Metallurgeon
group of PB triggers of Skyshroud Archer
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of TYS triggers of False Memories
group of PB triggers of Skyshroud Archer
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
maybe other abilities
Now we can get 1 hyperstage resource. Play Chalice with X=2. Continue down to a PB trigger of Skyshroud Archer. Use False Memories to mill all instants. Then cast Hurkyl's Recall. Resolve down and pop a Vedalken Orrery.
top
group of PB triggers of Metallurgeon
group of TYS triggers of False Memories
group of PB triggers of Skyshroud Archer
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
maybe other abilities
Now we can get 2 hyperstage resources. Continue down to a TYS trigger of False Memories. Mill Hurkyl's Recall.
top
group of PB triggers of Skyshroud Archer
Mirrorworks trigger of Vedalken Orrery
group of PB triggers of Metallurgeon
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
maybe other abilities
Use PB trigger of Skyshroud Archer to cast Hurkyl's Recall. Resolve down and pop a Vedalken Orrery.
top
group of PB triggers of Metallurgeon
group of BM triggers of Metallurgeon
group of PB triggers of Metallurgeon
maybe other abilities
Now we can get 3 hyperstage resources. We are back, with a little loss of the topmost 2nd group of triggers, but we have 3 hyperstage resources now, instead of 2. So this can go infinity, with more and more hyperstage transitions.
If you want to get Bloodbond March triggers for Boggart Mob, you need X=4 for Chalice of the Void, which stops gaining Metallurgeon-BM triggers and you cannot self-mill False Memories.
However, when you flashback Acorn Harvest, you need Chalice on 4 to counter it, in order to stack many megastages.
As an opposite, when the activated ability of Mimic Vat resolves, it checks last known information of the Mimic Vat, which had not remembered any creature yet, so no token will be created. Cards exiled after the Mimic Vat leave the battlefield will not affect what is created when the activated ability resolves.
EDIT:
More severely, this is a cheap way to get untapped haste tokens of later stages, e.g. Xathrid Gorgon, Old Man of the Sea, etc.
Actually, we use one BM trigger at the topmost layer of that key creature, then we can push one group of PB triggers and one group of BM triggers. So this leads to infinity.
Suppose we have a specific Mimic Vat token (called V). Activate it, so we push it on the stack:
top
activated ability of Mimic Vat V
maybe other abilities
Then we do normal hyperstage thing, and finally destroy Child of Alara. The stack now looks like
top
death trigger of Child of Alara
activated ability of Mimic Vat V
maybe other abilities
Resolve the death trigger, destroy all nonland permanents. This will include Mimic Vat V and many creatures.
Now the question comes: will these deaths trigger the trigger ability of Mimic Vat V? If yes, if we exile some creature (like, C), will V remember the exiled card C? (will a C token be created when the "activated ability of Mimic Vat V" resolves?)
If the latter is not used, we still need X=3 to cast-counter Rebuild. Hurkyl's Recall is at X=2, which may be used in the case we need Moggcatcher-BM triggers.
As a result, when you turn Goblin Dark-Dwellers on you have its ETB trigger. When you turn it off, you can still have its ETB trigger. So you can make 2 Engineered Explosives usages and thus 2 key resources (in this case the key resource is untapped haste Moggcatcher), which leads to infinite.
Then, how to let Goblin Dark-Dwellers leave the battlefield? Both "killing" and "champion" go infinite.
However, there might be a problem. When first Spellweaver Helix trigger resolve, we cast a copy of Worldfire. Does it count as "whenever a player casts a card"?
Ideally, to grow a stage/hyperstage/megastage on the stack, the deck forces abilities of a layer/stage/hyperstage below them to reduce. Due to this reduce, there is no infinite loop.
However, there may be some way to play: an intended way using Metallurgeon to reuse artifacts and gain mana, and a special way using Retract. Special way doesn't reduce abilities of a layer/stage/hyperstage below the stage/hyperstage/megastage (on stack). Superfacially there is no change on the stack, but we can still get more combo permanents and TYS counting numbers.
If we gain few mana but spend more, this special play won't last long; to get more combo permanents and TYS counting numbers, we can do better with usual (intended) play. If we gain plenty mana but spend few, this special play will go infinite.
Also for the "EDIT". If you've read my writing about how to fetch Child of Alara by its BM trigger, you can conclude that:
In this deck, startup is quite hard (against Dual Nature-based quick start, e.g. this classic deck). We are very short of mana.
In the startup, Retract/Hurkyl's Recall/Rebuild is not a destructive card, but able to gain mana and comsumable artifacts. Prepare a Mirrorworks trigger of Vedalken Orrery (or Twinning Glass ability in my proposal deck), then return artifacts. After Vedalken Orrery pop out, play Mirrorworks, Panharmonicon, Mana Vault (get 2 tokens), Mox Pearl and Mox Emerald. We gain 5WG, subtracted by 2 for Mirrorworks-Vedalken Orrery (or 1 in my deck), and by 2 for token Mirror of Fate to reuse Retract/Hurkyl's Recall/Rebuild, so there is 3 mana (4 mana in my deck) of net gain. This instant is cast via Goblin Dark-Dwellers, which is reused by Smite the Monstrous, which is reused by paying life via Acorn Harvest. 20 life (6 flashbacks) is enough to build some enchantments and TYS counting number.
That is an important usage in startup. But it might lead to infinity in usual play.
Hyperstage, Megastage and Gigastage all assume that "we need haste Metallurgeons to continue processing. If there is no, we can't go further. The only way to get haste Metallurgeon is using some PB/BM triggers in "trigger groups" at below. It forces us to do so, so no infinite". However, due to the startup process, this might be not true.
Take Child of Alara-based megastage as example.
We prepare the come-back of Vedalken Orrery and Omniscience, then flashback Acorn Harvest in cost of 3 life. Cast Smite the Monstrous, get TYS triggers, which get (many, even with only 1 TYS + 1 PB on battlefield) PB triggers, which bounce Goblin Dark-Dwellers so we can reuse Retract/Hurkyl's Recall/Rebuild. After some growth, destroy Child of Alara and gain 3 life from Centaur Safeguard. After Vedalken Orrery and Omniscience pop out, we can again spend 3 life for the same thing.
Hyperstage seems safe: for example, in my deck, in a dual cycle, we need to
But for megastage, there are many MANY PB triggers bouncing Goblin Dark-Dwellers, we might have plenty of mana to go infinite.
Note: DO NOT read the following. I forgot that Child of Alara is Legendary.
Maybe not. Child of Alara is not so easy to fetch back.
Generally, the stack looks like this. Here shows a slice of megastage.
Scattershot Archer is fetch by group C.
To fetch Child of Alara, we might have hold it in hand at some time before, then play for its BM triggers inside the complicated "group B" triggers. But, how do we "hold it in hand"? Certainly it should be some PB - Smite the Monstrous trigger, but there are group A and group D.
If we use group D to bounce Child of Alara, that is very expensive. We lost all the googological content of layer, stage and hyperstage between D and B, making Child of Alara megastage a stage (alternative groups of TYS - Smite the Monstrous, PB - Smite the Monstrous and possibly BM - Child of Alara).
If we use group A to bounce Child of Alara, we should have a token Child of Alara when stack resolve down from A to B. This is quite tricky, separated into two phases.
Short phase. Start with Child of Alara card in hand. Stack is a little below "group B". Play Child of Alara for BM triggers (lower position in group B). We prepare a specific token Mimic Vat, and should keep it on battlefield without Retract. When we prepared enough (higher position in group B), activate the token Mimic Vat, without resolving.
Flashback Acorn Harvest, build group A on stack. In short phase, PB - Smite the Monstrous bounce Goblin Dark-Dwellers, which use Battle Cry (no Retract!), getting TYS - Battle Cry triggers, which can further build one Metallurgeon stage. Since we cannot Retract, this is the furthest we can do.
When group A resolve down to final PB - Smite the Monstrous, we hold Goblin Dark-Dwellers in hand. Final PB - Smite the Monstrous kill Child of Alara, imprinting on that specific token Mimic Vat, but don't let the Child of Alara trigger resolve.
In response, we play Goblin Dark-Dwellers, Retract the token Mimic Vat along with other artifacts.
Notice: for last known information of that token Mimic Vat, it remembered the Child of Alara card.
Stack resolve. Down to the activated ability of that Mimic Vat, token Child of Alara is out.
Get Vedalken Orrery and Omniscience back. Put Child of Alara into graveyard.
Then BM - Child of Alara fetch it.
Now there is Child of Alara card and token on battlefield.
Long phase. Start with Child of Alara card on battlefield, along with its token copy. Normally push abilities on stack. At group A, use one PB - Smite the Monstrous to bounce Child of Alara. Normally play. There can be many stages above this. When stack resolve down to final PB - Smite the Monstrous above B, kill the token Child of Alara.
Actually, we can also prepare token Child of Alara when we successively resolve down many hyperstages. Each time we need Short phase to get such a token.
Back to the startup playing. What if we continuely play short phase without haste Metallurgeon? Well, we can only get one Retract for each short phase play, rewarding 7 mana. But we need more mana than this.
Okay. That looks safe.Still unsafe. We can alternatively play short phase (which gets very few growth) and long phase (which allows a lot growth), both using the startup playing, without Metallurgeon.
EDIT:
Another problem about megastage. When we end up a long phase, use several PB - Smite the Monstrous triggers, we play Goblin Dark-Dwellers to Retract, then PB trigger bounce Goblin Dark-Dwellers, finally destroy Child of Alara. Down to the preparation abilities, we have both Engineered Explosives and Goblin Dark-Dwellers in hand. There is one stage between group B and group C (fetching Scattershot Archer), but we can build two groups from Engineered Explosives and Goblin Dark-Dwellers. Net gain one stage. So this will go infinite.
It is not a hyperstage specific problem. As long as each stage requires one play of Engineered Explosives or one ETB of Goblin Dark-Dwellers, there is the problem.
Use 2 untapped haste Scattershot Archers to get one death of Moggcatcher, which means 2 controllable ETB of Goblin Dark-Dwellers, provided Clickslither to freely kill Goblin Dark-Dwellers, and Strongarm Thug to easily fetch itself and Moggcatcher.
Looks similar to this deck, but without Gratuitous Violence.
EDIT:
Oh no! We need 3 untapped haste Scattershot Archers to get one death of Moggcatcher, rewarding only 2 usages of Engineered Explosives.
EDIT2:
How about this?
1 Vedalken Orrery
2 Omniscience
3 Opalescence
4 Karn, Silver Golem
5 Cowardice
6 Horobi, Death's Wail
7 Cephalid Shrine
Mana Sources
8 Mana Vault
9 Mox Pearl
10 Mox Emerald
Consumable Artifacts
11 Mirror of Fate
12 Mimic Vat
13 Skull of Orm
14 Perpetual Timepiece
Combo Permanents
15 Mirrorworks
16 Panharmonicon
17 Psychic Battle
18 Bloodbond March
19 Thousand-Year Storm
Core Stage
20 Verdant Succession
21 Phantatog
22 Salvaging Station
23 Metallurgeon
24 Battle Cry
25 Retract
26 Goblin Dark-Dwellers
27 Goblin Lookout
28 Moggcatcher
29 Courageous Outrider
30 Dearly Departed
31 Abzan Falconer
32 Scattershot Archer
33 Gratuitous Violence
34 Engineered Explosives
35 Wrap in Vigor
Megastage
36 Smite the Monstrous
37 Spellweaver Volute
38 Acorn Harvest
39 Child of Alara
40 Centaur Safeguard
41 Woodland Bellower
42 Twinning Glass
Gigastage
43 Divine Congregation
44 Spellweaver Helix
45 Spider Spawning
46 Spider Spawning
47 Worldfire
48 Bayou
49 Titania, Protector of Argoth
50 Wormfang Behemoth
51 Polluted Dead
52 Frightshroud Courier
53 Simian Spirit Guide
54 Goblin Kites
55 Old Man of the Sea
56 Xathrid Gorgon
Final Layers
57 Tribal Unity
58 Consecrated Sphinx
59 Sphinx of Enlightenment
Startup
60 Eureka
No. Still 3 Explosives uses against 2 regain uses.
And this one doesn't work, unless one untapped haste Matsu-Tribe Sniper can make one untapped haste Moggcatcher.
1 Vedalken Orrery
2 Omniscience
3 Opalescence
4 Karn, Silver Golem
5 Cowardice
6 Horobi, Death's Wail
7 Cephalid Shrine
Mana Sources
8 Mana Vault
9 Mox Pearl
10 Mox Emerald
Consumable Artifacts
11 Mirror of Fate
12 Mimic Vat
13 Skull of Orm
14 Perpetual Timepiece
Combo Permanents
15 Mirrorworks
16 Panharmonicon
17 Psychic Battle
18 Bloodbond March
19 Thousand-Year Storm
Core Stage
20 Verdant Succession
21 Phantatog
22 Salvaging Station
23 Metallurgeon
24 Battle Cry
25 Retract
26 Goblin Dark-Dwellers
27 Goblin Lookout
28 Moggcatcher
29 Dearly Departed
30 Abzan Falconer
31 Matsu-Tribe Sniper
32 Engineered Explosives
Megastage
33 Smite the Monstrous
34 Spellweaver Volute
35 Acorn Harvest
36 Child of Alara
37 Centaur Safeguard
38 Woodland Bellower
39 Twinning Glass
Gigastage
40 Divine Congregation
41 Spellweaver Helix
42 Spider Spawning
43 Spider Spawning
44 Worldfire
45 Bayou
46 Titania, Protector of Argoth
47 Wormfang Behemoth
48 Polluted Dead
49 Frightshroud Courier
50 Simian Spirit Guide
51 Goblin Kites
52 Wilderness Hypnotist
53 Streambed Aquitects
54 Old Man of the Sea
55 Xathrid Gorgon
Final Layers
56 Tribal Unity
57 Glorious Sunrise
58 Finest Hour
Startup
59 Sphinx of Enlightenment
60 Eureka
And how about this?
1 Vedalken Orrery
2 Omniscience
3 Opalescence
4 Karn, Silver Golem
5 Cowardice
6 Horobi, Death's Wail
7 Cephalid Shrine
Mana Sources
8 Mana Vault
9 Mox Pearl
10 Mox Emerald
Consumable Artifacts
11 Mirror of Fate
12 Mimic Vat
13 Skull of Orm
14 Perpetual Timepiece
Combo Permanents
15 Mirrorworks
16 Panharmonicon
17 Psychic Battle
18 Bloodbond March
19 Thousand-Year Storm
Core Stage
20 Verdant Succession
21 Phantatog
22 Salvaging Station
23 Metallurgeon
24 Battle Cry
25 Retract
26 Goblin Dark-Dwellers
27 Goblin Lookout
28 Moggcatcher
29 Moggcatcher
30 Courageous Outrider
31 Dearly Departed
32 Abzan Falconer
33 Scattershot Archer
34 Gratuitous Violence
35 Engineered Explosives
36 Wrap in Vigor
Megastage
37 Smite the Monstrous
38 Spellweaver Volute
39 Acorn Harvest
40 Child of Alara
41 Centaur Safeguard
42 Centaur Safeguard
43 Twinning Glass
44 Divine Congregation
45 Spellweaver Helix
46 Spider Spawning
47 Spider Spawning
48 Worldfire
49 Bayou
50 Titania, Protector of Argoth
51 Wormfang Behemoth
Final Stages
52 Polluted Dead
53 Frightshroud Courier
54 Simian Spirit Guide
55 Goblin Kites
56 Old Man of the Sea
57 Xathrid Gorgon
Final Layers
58 Tribal Unity
59 Sphinx of Enlightenment
Startup
60 Eureka
We need one Explosives to get one haste Scattershot Archer, which means 2 haste Moggcatchers, then another Explosives to make a haste Goblin Lookout. Also "2 Scattershot Archer + 1 Moggcatcher" looks similarly.
In this deck, we see an untapped haste Moggcatcher as hyperstage resource, but if Goblin Dark-Dwellers card is on battlefield, we add half resource, because we can still get one controllable ETB trigger.
Start with 1.5 hyperstage resources. Moggcatcher card is in hand. On field, there is Vedalken Orrery with its token, Skyshroud Archer with no untapped haste token, Clickslither, Chalice of the Void at 2 and Engineered Explosives at 0 (used up). Stack is:
Use 0.5 hyperstage resource to get Goblin Dark-Dwellers ETB. Cast-counter False Memories. Use one to mill all instants.
Next, play Vedalken Orrery.
Use the Explosives to get one untapped haste Skyshroud Archer.
Next, replay Vedalken Orrery.
Also we have 0 hyperstage resources now.
Play Chalice on 4, then play Moggcatcher for BM triggers. Use the untapped haste Skyshroud Archer for PB triggers. Play Moggcatcher for BM triggers.
Compared with the paused point: now we have 1.5 hyperstage resources, 0.5 more than the paused point; now we have 3 fewer TYS copies of False Memories.
If we loop this until the group of TYS triggers of False Memories exhaust, we will have MANY hyperstage resources.
Clickslither
Moggcatcher
Dearly Departed
Abzan Falconer
Skyshroud Archer
?
That means: each time we want BM triggers of Moggcatcher (in order to get the hyperstage resource - untapped haste Moggcatcher token), we need to set Chalice on 4.
EDIT:
Also, there is Goblin Lookout. I don't know whether it is useful (instead of Clickslither).
Untapped haste Goblin Lookout token can be obtained from its death by Engineered Explosives. Then it can be fetched by Moggcatcher. So, one cycle of Goblin Dark-Dwellers means
get untapped haste Goblin Lookout + get untapped haste Moggcatcher
which means
use Engineered Explosives on 2 + (get untapped haste Moggcatcher)*2
which means (assume one untapped haste Skyshroud Archer can get one untapped haste Moggcatcher, but I don't know the process exactly)
use Engineered Explosives on 2 + (get untapped haste Skyshroud Archer)*2
which means
use Engineered Explosives on 2 + (use Engineered Explosives on 1)*2
which means
(effective Hurkyl's Recall + Vedalken Orrery refill)*3
which means
3 controllable ETB of Goblin Dark-Dwellers
sounds bad.
EDIT 2:
Matsu-Tribe Sniper has mana value 2, the same as Goblin Lookout. One use of Engineered Explosives can destroy and get both haste tokens.
Now there is the question: Does every untapped haste Matsu-Tribe Sniper (or Skyshroud Archer) token exactly make one untapped haste Moggcatcher token?
Start with 2 untapped haste Skyshroud Archer tokens (i.e. hyperstage resource). Engineered Explosives is used (no charge counter), and Chalice of the Void is on X=2. Boggart Mob champions Goblin Dark-Dwellers. Out of battlefield, False Memories and Battle Cry are in graveyard, but Hurkyl's Recall is in exile (this is also a usual case after a Hurkyl's Recall resolve). Stack looks like
Use the two new stage resource:
And then, resolve down to get one stage resource.
1 Vedalken Orrery
2 Omniscience
3 Opalescence
4 Karn, Silver Golem
5 Cowardice
6 Horobi, Death's Wail
Mana Sources
7 Mana Vault
8 Mox Pearl
9 Mox Emerald
Consumable Artifacts
10 Mirror of Fate
11 Mimic Vat
12 Skull of Orm
Combo Permanents
13 Mirrorworks
14 Psychic Battle
15 Bloodbond March
16 Thousand-Year Storm
Core Stage
17 Chalice of the Void
18 Verdant Succession
19 Phantatog
20 Salvaging Station
21 Metallurgeon
22 Battle Cry
23 Hurkyl's Recall
24 False Memories
25 Goblin Dark-Dwellers
26 Boggart Mob
27 Bramblewood Paragon
28 Abzan Falconer
29 Skyshroud Archer
30 Engineered Explosives
Megastage
31 Smite the Monstrous
32 Spellweaver Volute
33 Acorn Harvest
34 Child of Alara
35 Centaur Healer
36 Woodland Bellower
37 Twinning Glass
Gigastage
38 Divine Congregation
39 Spellweaver Helix
40 Spider Spawning
41 Spider Spawning
42 Spider Spawning
43 Worldfire
44 Llanowar Wastes
45 Titania, Protector of Argoth
46 Wormfang Behemoth
47 Polluted Dead
48 Frightshroud Courier
49 Simian Spirit Guide
50 Goblin Kites
51 Wilderness Hypnotist
52 Streambed Aquitects
53 Old Man of the Sea
54 Xathrid Gorgon
Final Layers
55 Tribal Unity
56 Sylvan Echoes
57 Sentry Oak
58 World at War
Startup
59 Eureka
60 Words of Wisdom
Usually Chalice of the Void is locked at X=2.
If you want to get Bloodbond March triggers for Boggart Mob, you need X=4 for Chalice of the Void, which stops gaining Metallurgeon-BM triggers and you cannot self-mill False Memories.
However, when you flashback Acorn Harvest, you need Chalice on 4 to counter it, in order to stack many megastages.
I don't know whether and how to make this work.
3 life from the Centaur Safeguard card, 3 life from a Centaur Safeguard token.
EDIT:
More severely, this is a cheap way to get untapped haste tokens of later stages, e.g. Xathrid Gorgon, Old Man of the Sea, etc.
Actually, we use one BM trigger at the topmost layer of that key creature, then we can push one group of PB triggers and one group of BM triggers. So this leads to infinity.
An explicit example is when Child of Alara destroy creatures and along with Mimic Vat.
Suppose we have a specific Mimic Vat token (called V). Activate it, so we push it on the stack:
Now the question comes: will these deaths trigger the trigger ability of Mimic Vat V? If yes, if we exile some creature (like, C), will V remember the exiled card C? (will a C token be created when the "activated ability of Mimic Vat V" resolves?)
If the latter is not used, we still need X=3 to cast-counter Rebuild. Hurkyl's Recall is at X=2, which may be used in the case we need Moggcatcher-BM triggers.
It makes Goblin Dark-Dwellers die, which can be imprinted on Mimic Vat and get a token enter-the-battlefield.
As a result, when you turn Goblin Dark-Dwellers on you have its ETB trigger. When you turn it off, you can still have its ETB trigger. So you can make 2 Engineered Explosives usages and thus 2 key resources (in this case the key resource is untapped haste Moggcatcher), which leads to infinite.
Then, how to let Goblin Dark-Dwellers leave the battlefield? Both "killing" and "champion" go infinite.
Notice that Thousand-Year Storm is absent in the deck.
The only number keeper is Brain Freeze because of Storm. But how to regain your number with massive storm copies but few of other resources?
How high can it (non-arithmetic) be, in terms of growth rate?
Flashback Spider Spawning, which triggers the Spellweaver Helix imprinting another Spider Spawning and a Worldfire. We manage to take Thousand-Year Storm off, then the trigger resolve to cast a Worldfire copy.
This triggers another Spellweaver Helix imprinting another Worldfire and the life gain card (Multani's Decree). We put Thousand-Year Storm on, then the trigger resolve to cast the Multani's Decree, getting its TYS trigger.
However, there might be a problem. When first Spellweaver Helix trigger resolve, we cast a copy of Worldfire. Does it count as "whenever a player casts a card"?