Nice! It looks like we need to hold back two Noggle Ransacker discards, to use one during the Finest Hour combat phases, and one during the World at War phases.
Hmmm, if Judge of Currents is the only other way for the opponent to gain life, then we can replace the Merfolk stage with a Spirit/Minotaur stage, and have Hurloon Shaman as the life gain creature, using shenanigans with Primeval Titan. If that works, we have the opportunity to use opponent life gain as the final layer by adding a card that can add arbitrarily many additional combat phases. Unfortunately, nearly every such card also untaps all creatures, which goes infinite since we can have arbitrarily many combat phases so long as we don't deal damage to the opponent. (Only Breath of Fire requires dealing combat damage, and that is a forbidden Enchant Creature aura.) But Godo, Bandit Warlord only untaps Samurai, which should be no problem.
With that, we can give the opponent life as many times as we can force him to discard. We can do that with either Noggle Ransacker, or Pain Magnification; so, we can do that as long as the opponent has either a card in hand or two cards in the library. So we can make the opponent discard up to 59 times; however, the 59th discard won't do any good, since there will be no cards left in his library, so if we try to make him resolve a Spiritual Focus he can choose to deck himself. So I believe 58 discards is the most that we can do.
We can use Godo, Bandit Warlord to replace both Finest Hour and World at War, so we have an extra card to do whatever we want with. Consecrated Sphinx seems like a good call, allowing us to get going with just a couple of Noggle Ransackers, and the final damage we deal should be around F_{w^3 + w14 +8}(N) with N close to 58.
The extra layer would be nice, but unfortunately the opponent can also make use of Radiant Fountain to gain life: We can donate a Mimic Vat that has it imprinted, they create a token and the etb triggers for them.
I think Gerrard's Verdict would allow us to get the mega stage without having life gain that the opponent can use, but I have no idea how to do the connecting stage without such a thing.
Cast Black Lotus, Channel, Perpetual Timepiece, exile the Timepiece to shuffle Black Lotus back in the library, cycle the Rebuild to draw Black Lotus, play Black Lotus, cast Genesis Wave for X=12 (3 life remaining). Reveal:
We get a bunch of Dual Nature triggers and ETB triggers. Resolve the Primeval Titan ETB trigger to put Radiant Foutain and Glimmerpost onto the battiefield tapped, gaining 3 life (6 life remaining). Do not resolve the rest of the triggers yet.
Cast Worldpurge. Bring back Opalescence, Dual Nature, Copy Enchantment, Swarm Intelligence, Noggle Ransacker, and Mirror of Fate back to our hand, along with Allay. Shuffle the other permanents into the library. Resolve the Vedalken Orrery and Omniscience Dual Nature trigges, creating tokens. Resolve the Primeval Titan trigger and get a token; resolve the ETB trigger to put both lifegain lands into play, gaining 3 life (9 life remaining). Resolve the Mirror of Fate Dual Nature trigger, and get a token. Play Mirror of Fate, and sacrifice both Mirror of Fates. The first Mirror of Fate simply puts the whole library into exile. The second one brings back Perpetual Timepiece and say a Flash Defiance into the library, along with five other useful cards, probably including Herbal Poultice. Resolve the Noggle Ransacker ETB trigger, and draw the two cards, discarding Flash of Defiance. Resolve the rest of the triggers, except the remaining Noggle Ransacker trigger. Have the Copy Enchantment token copy Dual Nature. Replay Opalescence, Dual Nature (6 Dual Natures in total), and Copy Enchantment copying Dual Nature (14 Dual Natures in total). Play Swarm Intelligence, getting 16 copies in total. Play Noggle Ransacker, getting 14 Dual Nature triggers, and the equivalent of 16 draw triggers in total. Play Perpetual Timepiece, getting 16 copies in total. Exile a Perpetual Timepiece token to shuffle Black Lotus, Genesis Wave, Mirror of Fate, Flash of Defiance, and Rebuild into the library. Resolve two Noggle Ransacker ETB triggers, drawing and keeping Black Lotus and Genesis Wave, and discarding Flash of Defiance and Rebuild. Cast Black Lotus; it goes to the graveyard, and 16 Black Lotus tokens are triggered. Cast Allay with buy back (4 life remaining), getting 17 copies in total. The original gets a Cowardice trigger and a Psychic Battle trigger; put the Cowardice trigger on top of the stack of abilities, and the Psychic Battle on bottom, below all the Swarm Intelligence triggers. Resolve the Cowardice trigger and bounce Copy Enchantment; this destroys all the Dual Nature tokens. Replay the CE and copy Psychic Battle, getting a Psychic Battle token as well. The first Swarm Intelligence copy resolves, and gets 3 Psychic Battle triggers; we bounce CE four times, getting 2, 4, and 8 Dual Natures, and then 10 Psychic Battles. The second one gives us 11 bounces, getting us 8192 Dual Natures and 8194 Psychic Battles. The third gives us more than 2^8207 > 2^^4 Dual Natures and Psychic Battles, and so the 16th will give us more than 2^^17 Dual Natures and Swarm Intelligences. At the end, bounce Cowardice. Finally, have the final Psychic Battle trigger redirect the original target of Allay to March of the Machines token, which gets destroyed.
We now get 16 Black Lotuses, enough for 48 mana. We can now cast Genesis Wave with X=10 and get more than 2^^17 Swarm Intelligence copies. We will play Mirror of Fate, Cowardice, and March of the Machines, then we can cast Allay to get more enchantments and bounce March of the Machines so that we can use all of the Mirror of Fate copies that we will get. That will give us access to the rest of the deck, and then we can use an Herbal Poutice on a Minion of Tevesh Szat, which can then bounce Perpetual Timeiece to give us all the milling and reshuffling that we will need. So I think we can get the full combo from here. This should generate more than F_{w^3 + w14 + 1} (2^^17) Dual Natures after then third Noggle Ransacker, then the next 47 will take us to more than F_{w^3 + w14 + 2}(48). The final two Noggle Ransackers are used for opponent life gain for Finest Hour and World at War, and we wind up with more than F_{w^3 + w14 + 7} (F_{w^3 + w14 + 7} (F_{w^3 + w14 + 2} (48))) in the end.
But, this does about the same damage as the previous version. Even if we could get started without Noggle Ransacker, I don't know of anything better to use for the card slot.
EDIT: Hmm, I just noticed a very interesting card: Starlit Sanctum. It can tap to gain life equal to the toughness of a CLeric. A Cleric that has 3 toughness is Farrelite Priest. So this seems like it has the potential for card savings.
Unfortunately, our current 60 card deck doesn't use Farrelite Priest, in order to get access to blue mana. So, if we switch to Starlit Sanctum, we either have to use the new card slot to gain access to blue, or we can put in something like Goblin Welder, which means we would need to replace Goblin Bushwhacker with perhaps Herbal Poultice, and we lose the layer that we gain with the extra card. Reality Spasm + Precursor Golem also loses a layer, unless we can find a way to eliminate Genesis Wave. Unfortunately, if we try to hardcast Omniscience, we have only two cards left, not enough to get going. So, I don't see an improvement here.
The deck with sideboard does use Farrelite Priest, so perhaps we can gain a card slot. Unfortunately, Starlit Sanctum requires that we bring lands in untapped, so our shtick with destroying a land as the only way to get that type of mana no longer works. So I don't see how Starlit Sanctum can help in this deck either.
EDIT: Well, we haven't improved the final damage, but we've reached the point where we now have four available card slots to get that 13th layer, I think:
Just one card away from fitting in 60 card slots, and we managed to save Goblin Bushwhacher for a couple of layers at the end. Unfortunately, this deck also uses destroying a land to get a Mimic Vat copy, so we can't use Starlit Sanctum to save a card here either. Just about the only way to have Starlit Sanctum compatible with the land + Mimic Vat would be to use Dryad Arbor, which would require switching to red mana for the megastage.
We save the card by replacing Island + Natural Affinity with Celestial Colonnade. The Colonnade activates itself and as a creature can go under Mimic Vat. Then the hasty version can animate itself again and as it is white we can untap it with Battle Cry multiple times to generate lots of blue. We have to use the hasty version because we can only untap the Colonnade after it is a creature and effected by summoning sickness.
The problem I see here is that we need a blue mana to animate the colonnade in the first place. And while we can generate a lot more than two blue from two activations with multiple battle cries I don't think we can keep any of that blue stockpiled while going through the combo with Worldpurge. I see nothing we could put on the stack to replenish blue when we get to this stage transition again.
quick EDIT: If we use Sea Scryer as the merfolk stage creature we can use tokens of that to produce the initial blue after Worldpurge. And as we have Aquatic Incursion for the transition anyway that should actually work.
So 13 stages in 60 cards might be real.
EDIT 2: Godtoucher is a cleric and using Starlit Sanctum to sacrifice it allows us to get those powerful hasty tokens way too cheap, going infinite. So we need more improvements to get 13 stages.
Those are the only problems I've found so far. Looking good
EDIT: Actually I'm being stupid again. After we animate a hasty Celestial Colonnade there is no reason for us to use Worldpurge again. We can just keep going infinite when our Battle Crys effectively produce blue mana. Ooops.
Winds up taking up the same number of card slots, except I don't think we can get started with just Genesis Wave, so we need three cards for the start.
I'm quoting this post so it's easier to find/know it exists for any potential mad man interested in joining the project. It's not up to date or complete, but it should give you an idea of what you're getting into if you want to join the madness.
@CTNC: The other blue manlands don't work because they never enter the battlefield untapped. So we won't ever be able to get any mana out of them.
@Deedlit11: That 60 card version almost works. But I found one problem with it. If I remember correctly how stage transitions work we get exactly 1 Krark-Clan Stoker for every 2 Flamestick Courier activations. So I think we get exactly enough red mana to drive that stage, but can never use any of it to start the black stage.
Now it might still work if we find some tricky way to resolve everything involved. Maybe Worldpurge can help, bouncing the stoker; although that removes all red mana, so... it's tricky.
Goblin Welder would definitely produce enough red to make the stages work. Of course it also fetches Herbal Poultice, so we'd lose the only layer we have in the end. We could still get one batch of hasty Karplusan Yeti tokens if we use Hazoret's Favor instead of the poultice. Pre-combat we can produce many batches of red mana from the Genesis Wave copies and go through the 10 stages above that.
EDIT: We could replace Titania, Protector of Argoth with Walking Atlas. Then lands would require Genesis Wave to get out of the graveyard/library/exile for an option other than 0 cost artifacts there. But I found no card that actually gets a layer there.
@CTNC: It's been a long time. SadisticMystic started working on the challenge in early 2013, and I joined around that time as well. So it's been about five years. I discovered the stage combo in mid 2015 I think, so it's been almost 3 years of the deck at Ackermann level. Iijil joined in later that year.
We haven't been working on it continuously of course, every few months I would come back to it and think of something new, and we would start talking about it again.
@Iijil: Yeah, it looks hard to make Krark-Clan Stoker work. The problem is that we need a lot of red mana at the same time, not just producing one at a time. After the first Flamestick Courier activation, we can imprint Krark-Clan Stoker on a Mimic Vat, bring the Krark-Clan Stoker back to the battlefield, and then tap the Mimic Vat to activate the token creation. We can then use Worldpurge to bounce the Krark-Clan Stoker, eliminating the need for the second Flamestick Courier activation. But then the ability to create the token is on top of all the Flamestick Courier abilities, and we have to resolve it, leaving either a Krark-Clan Stoker token or two red mana that will be eliminated after the next Worldpurge.
It would be nice if we could cast a Reality Spasm augmented by Precursor Golem, but Genesis Wave can't retrieve it, and there isn't enough room in the opening hand.
EDIT: Looking at the start, the current deck is a little different since we don't have Sejiri Refuge and Kabira Crossroads, which the previous deck uses to gain 3 life at the cost of 1. Now we have Starlit Sanctum for our lifegain, which would cost us 3 life to gain 3, which doesn't help. But the previous deck needed all of our life for the Genesis Wave, Allay with buyback, and flashback of Acorn Harvest. So, we either need to cut three cards (one of which will be Primeval Titan), or not cast the initial Allay with buyback. I don't see what two cards I can cut efficiently - I thought perhaps Su-Chi and Horobi, Death's Wail might be cut, but then we would need March of the Machines to get enough copies of artifacts.
So, instead we will eschew the initial Allay. We can replace Primeval Titan with another permanent, but nothing particularly pops out, so I will instead just use the life to cast another early Allay. So we start the same way, casting Genesis Wave for X=12 with all the same cards except Primeval Titan. Have the Copy Enchantment token copy Swarm Intelligence again. Flashback the Acorn Harvest, casting Deconstruct. The casting triggers [c]Horobi,
Death's Wail[/c], Cowardice, two Psychic Battles, and three Swarm Intelligences, which we resolve in that order. We get three triggerings of Horobi and Cowardice before the first Swarm Intelligence trigger, which we use to, in order, destroy the Su-Chi token, bounce the original Su-Chi and replay it to get two more token copies, then destroy a token Su-Chi. This gives us 8 more colorless mana, allowing us to cast Allay with buyback three times.
The first casting of Allay gets all the same triggers; this time we order the triggers as follows: Cowardice, Psychic Battle, 3 Swarm Intelligences, Psychic Battle. We get two initial bounces, each time bouncing Copy Enchantment. The first replay of CE gets us 4 Dual Natures, the second gets us 7 Psychic Battles. The first Swarm Intelligence copy will then get us 8 bounces, which we use to increase the number of Dual Natures to 512 and the number of Psychic Battles to 514. The second gets us 515 bounces, which gets us to 2^523 Dual Natures and 2^523 + 2 Psychic Battles. The third gets us to more than 2^2^523 Dual Natures, Swarm Intelligences, and Psychic Battles. At the end of the last group of triggers we have a Copy Enchantment token copy Opalescence, then we bounce the Opalescence. Then we have the Psychic Battle trigger for the original Allay change the target to the Cowardice token, destroying it and allowing Allay to return to our hand.
We get two more Allays, each one taking X Swarm Intelligences to more than 2^^X Swarm Intelligences and Psychic Battles, so by the end we have more than 2^^(2^^(2^2^523)) Psychic Battles. Then the Swarm Intelligence triggers for Deconstruct get resolved, and each one takes X Psychic Battles to more than 2^^^X Psychic Battles, so we wind up with more than 2^^^(2^^^(2^^^(2^^(2^^(2^2^(523)))))) Swarm Intelligences in the end.
Then we cycle Rebuild to redraw Genesis Wave, and recast it to get all those Swarm Intelligence copies. After putting all the permanents we need into play and milling the necessary instants/sorceries, I guess we just use the rest of the Genesis Waves to put Black Lotus into play, which gets a whole bunch of Dual Nature copies, and we can implement the full combo up to the tenth additional stage each time, so we wind up with more than F_{w^3 + w10 + 1}(2^^^(2^^^(2^^^(2^^(2^^(2^2^(523))))))) Dual Natures by the end. Then we make that many copies of Hazoret's Favor and Karplusan Yeti, and go into combat, where we can make that many hasted copies of Karplusan Yeti, and implement the full combo to get more than F_{w^3 + w13} (F_{w^3 + w10 + 1}(2^^^(2^^^(2^^^(2^^(2^^(2^2^(523)))))))) hasted Metallurgeons, which we promptly attack with.
EDIT: I thought about possible improvements to the stage sequence; one idea is to move the blue creatures to later on. Wilderness Hypnotist seems to be a good transition creature, as it is both a Merfolk and a Wizard. Unfortunately, it is somewhat hard to get a lot of blue stages at that point, as Paragon of Gathering Mists and Possessed Aven are often mooted by then. Here are some unsuccessful attempts, in case it gives you any ideas:
Not bad, but it is only 11 stages starting from Everglove Courier, so we would need two more stages before, and that is hard without Godtoucher. Also, both Goblins and Zombies are used later on.
12 stages in 19 cards is pretty good, if only we can add another stage in three cards or less. I haven't found a way yet though; red mana and blue mana are both used later on, as is the obvious choice for black mana, Zombies.
Tried to eliminate some earlier stages to get more blue stages, but wound up losing one; again we need two more stages, with only one obvious one to add (Zombies).
Ugh, I found the infinite in the current deck: Devout Chaplain
It is a white creature and targets artifacts. We just need a hasty token and two other copies on the battlefield and we can repeat the hyperstage transition without need for hasty Metallurgeons. Battle Cry untaps the Devout Chaplains and those target artifacts to give us the mana/other resources we require. Rebuild bounces Mox Emerald for the green mana we need, but leaves Devout Chaplain alone.
I did not find another way to make the tapped creature stage work.
That's a pity. I don't see another way to tap untapped Humans safely - Gallows at Willow Hill is obviously not safe, and I see no other cards. One other way we can get a stage using tapped creatures is to use Great Oyster, with Grand Architect to tapped blue creatures. This would just be an alternative way to get a blue stage if Paragon of Gathering Mists and Possessed Aven are both mooted.
Another idea that came to mind: Use Izzet Guildmage along with something like Disembowel or Postmortem Lunge to use red or blue mana to target one CMC creatures. It costs quite a few cards, but it could be worth it. Postmortem Lunge could also be used in the ending layers.
But we can't use Tidal Warrior as a stage creature, because it is a landshaping ability and we can store that nonmana ability on the stack thorugh Worldpurge. Also with the proposed deck we never get untapped lands.
Another problem with the X spells is that the Genesis Wave start we currently use has no way to ever get them onto the stack with X=1. The upside is that they can enable the initial haste in a Noggle Ransacker + Consecrated Sphinx start.
Funnily enough, we manage to save red mana for the end, but there's no room for Goblin Bushwhacker.
EDIT: I thought about switching Disembowel with Postmortem Lunge, in order to save blue so that we can use Broken Ambitions in place of Cephalid Shrine and Perpetual Timepiece, saving a card. But, upon closer inspection I don't think Postmortem Lunge works; we have no way to send the one-CMC creature to the graveyard, and if we did, it would probably go infinite. All the other 1X sorceries also seem to be of the form "return target creature card from the graveyard". So I guess we are stuck with Disembowel.
We do have red mana available, in case there is a useful cheap sorcery we could use earlier on.
There does seem to be some potential still for card savings; for example, if we remove the Merfolk stage, connecting Everglove Courier to Viridian Acolyte, and then reinstitute Starlit Sanctum, we can save four cards. So if we could just add another stage in three cards or less...
EDIT: We can switch to the Enslaved Dwarf sequence for an extra three cards, but that requires red still be available, and for that we need another card in the Elf section. So it winds up the same.
EDIT: Looking at the start, it would probably be best to switch from Merfolk to Goblins so that Goblin Welder can retrieve artifacts from the graveyard. The start can go the same way that Iijil mentioned before, playing Consecrated Sphinx and Noggle Ransacker to draw six cards and discard one, then resolving another Noggle Ransacker with 11 Consecrated Sphinxes on the battlefield, drawing 46 and discarding one card. By my count we have 38 cards to draw (nonartifact creatures + enchantments + Allay) besides Disembowel of which we have already drawn 6. So 32 of the 45 new cards can be those, and the remaining 13 times we can draw Disembowel. (I'm not sure though - maybe the sequence of play requires that we draw something extra, I haven't checked carefully.) I believe this gets us to more than F_{w^3 + w13} (24), not enough for 51 (we would need another four Consecrated Sphinxes at least). Still, that gets us to more than F_{w^3 + w13 + 1}(50) in the end.
Remember back when we were discussing Panharmonicon? We didn't see how it could be useful. Well, it look like it is very useful, as when it is on the battlefield, Spellweaver Helix can imprint many sorceries, and when you trigger it by casting a duplicate of one of the imprinted sorceries, it will copy all the others! So with just two Acorn Harvests, we can imprint Acorn Harvest plus three other sorceries, and casting Acorn Harvest will trigger the copying of the other three.
For the decks that use lifegain lands, we only need to copy two other sorceries. So we can replace an Acorn Harvest with Panharmonicon (throwing Channel in as a spare imprinted sorcery), but the improvement is only minor. But, for the decks with Gerrard's Verdict, we actually save a card. Unfortunately, Gerrard's Verdict isn't compatible with Hurloon Shaman or Goblin Gardener, which many of our decks use. But, we do have one 61-card deck with Judge of Currents, so it nicely becomes a 60-card deck:
Oh, Panharmonicon is a great find! We were running a bit low on fringe cases of the rules to exploit.
Interestingly we now cast multiple sorceries during the resolution of the same Spellweaver Helix ability, so we put all of their Swarm Intelligence triggers onto the stack at the same time. That means we can interweave the copies of different sorceries. For example we can go Worldpurge -> Deep Reconnaissance -> Worldpurge -> Deep Reconnaissance -> ... and move the land between battlefield and library multiple times. Luckily the land gets stuck in the graveyard when we try to include Gerrard's Verdict in the cycle, so we can't actually gain more life with that. So I haven'T found any infinites with the deck yet.
I like that the Panhamonicon also casually gets an extra layer for Goblin Bushwhackers etb ability and improves the start by getting an extra Dual Nature trigger on Copy Enchantment and Swarm Intelligence. Great results all around!
Great! That ability to interweave different sorcery copies is worrying, but hopefully there is nothing problematic.
Looking at the start: Again, we lose out by not having Primeval Titan to fetch lifegain lands. The obvious adjustment is to forego the initial casting of Allay again. On the plus side, we can replace Primeval Titan with Panharmonicon, and we get three of all the enchantments, except for Swarm Intelligence for which we have five. So we cast Deconstruct and get Cowardice, three Psychic Battle, and five Swarm Intelligence triggers, which we resolve in that order. We get four intial targetings of Su-Chi; we will use three of them to destroy Su-Chi tokens, and the remaining one to bounce the original Su-Chi to get more tokens. That gives us 12 colorless mana, allowing us to cast Allay four times with buyback. The first Allay gets us Cowardice, two Psychic Battle, five Swarm Intelligence, and a final Psychic Battle trigger. So we get three initial bouncings before the first Swarm Intelligence trigger. The first bounce gets us 9 Dual Natures, the second 27, and the third gives us the original, 54 token copies, and the 3 previous Psychic Battles for 58 Psychic Battles total. The first Swarm Intelligence copy gets 59 bouncings, of which we use 58 to increase the number of Dual Natures to 3^61 and the last to make 2*3^61 + 2 Psychic Battles. Each further Swarm Intelligence copy takes X to more than 3^X, so we wind up with more than 3^3^3^3^(2*3^61) Dual Natures, Psychic Battles and Swarm Intelligences in the end. After three more Allays we get more than 3^^3^^3^^(3^3^3^3^(2*3^61)) Dual Natures, and after five Swarm Intelligence copies of Deconstruct we get more than 3^^^3^^^3^^^3^^^3^^^(3^^3^^3^^(3^3^3^3^(2*3^61))) Swarm Intelligences. Finally, we recycle Genesis Wave and cast it with all those Swarm Intelligence copies, to get a final damage of more than F_{w^3 + w13 + 3} (3^^^3^^^3^^^3^^^3^^^(3^^3^^3^^(3^3^3^3^(2*3^61)))).
EDIT: I thought briefly about the deck with sideboard - I thought maybe we could replace the Merfolk stage with the Disembowel stage + Minotaur stage to get 15 stages, but Noble Hierarch gets green mana too early, and also Hurloon Shaman can destroy the Island. So I thought about improving 14 stages - and I don't know how to do that either. Ending with Hurloon Shaman messes up our way to get blue mana. Oh well.
I don't know what to do with the extra slot, but we need to rework the start anyway: Noggle Ransacker goes infinite since we can donate Su-Chi and Perpetual Timepiece allowing the opponent to pick up the discarded cards again.
Hmm, that's tough. Perhaps we can replace Perpetual Timepiece with a card that only mills cards? The only problem I see is that we can't get Black Lotus back out of the graveyard. Which is kind of a problem I guess. We can add two Elvish Spirit Guides to allow the first Genesis Wave to be cast, and then we need to get hasted Vine Trellises going in order to cast Genesis Wave again. Maybe we can do it.
EDIT: We'll be better off replacing Noggle Ransacker with Floating-Dream Zubera; if there is any difficulty in getting started, adding Urgent Exorcism should make it easy. Actually, I'm pretty confident that we can get started without Urgent Exorcism, the question is how to maximize the start.
Herbal Poultice goes to the graveyard. Get triggers to create token copies of everything (besides Opalescence). Resolve the Primeval Titan ETB trigger to put the lifelands onto the battlefield (4 life remaining). Then cast Worldpurge.
Bring back Floating-Dream Zubera, Mirror of Fate, Opalescence, Psychic Battle, Dual Nature, and Copy Enchantment to our hand, while keeping Disciple of Tevesh Szat; the rest of the permanents get shuffled into the library. Resolve all the Dual Nature triggers, getting token copies of everything, except for the March of the Machines token. Resolve the ETB trigger of the Primeval Titan token, putting the lifelands into play again and gaining 3 life (7 life remaining). Play Opalescence, Dual Nature (6 copies), Copy Enchantment copy of Dual Nature (14 copies of Dual Nature total), Floating-Dream Zubera (16 copies total), Psychic Battle (16 copies total), Mirror of Fate (2 copies total), and Disciple of Tevesh Szat.
Sacrifice both Mirror of Fates; the first activation exiles the library, the second one brings back Perpetual Timepiece, Allay, Cowardice, Su-Chi, and three other useful cards. Pay 3 colorless mana (4 life) and sacrifice the Herbal Poultice token, destroying the original Disciple of Tevesh Szat. Imprint it on the Mimic Vat token. Pay 3 mana (1 life remaining) and create a token copy of Minion of Tevesh Szat. Resolve the Dual Nature trigger for March of the Machines, and get a token copy.
Tap the Disciple of Tevesh Szat, triggering 16 Psychic Battles, so we get 17 targetings in total. Use two to destroy two Floating-Dream Zubera tokens, and draw three cards. We draw Perpetual Timepiece, Allay, and Su-Chi. Play Su-Chi, getting 15 total copies. Resolve 14 Psychic Battle triggers of Disciple of Tevesh Szat to destroy all 14 token copies of Su-Chi, gaining 56 colorless mana. Play Perpetual Timepiece, getting 15 copies. Exile a token copy (54 mana remaining) to shuffle Black Lotus, Genesis Wave, and Mirror of Fate into the library. Resolve the last Psychic Battle trigger of Disciple of Tevesh Szat to destroy a Floating-Dream Zubera token, drawing three cards.
Draw Black Lotus, Genesis Wave, and Cowardice. We play Cowardice, and cast Allay with buyback 17 times.
The first Allay gets one Swarm Intelligence trigger, and 16 Psychic Battle triggers. We bounce Copy Enchantment 16 times, generating 32768 Dual Natures, and 32772 Psychic Battles. Then the Swarm Intelligence trigger resolves, and we get more than 2^32787 Swarm Intelligence tokens in the end, or more than 2^^^3. The next 16 Allays each take X to more than 2^^X, so we wind up with more than 2^^^19 Dual Nature and Swarm Intelligence tokens in the end.
Play Black Lotus, triggering more than 2^^^19 token copies. Cast Allay with buyback for the last time, generating more Dual Natures and also destroying the March of the Machines token. The more than 2^^^19 Black Loti come onto the battlefield, and we can cast Allay with buyback many times, to generate more than 2^^^2^^^19 Swarm Intelligences, while having plenty of Black Loti remaining. Cast Genesis Wave with X=10, generating more than 2^^^2^^^19 Swarm Intelligence copies, and we can run the full combo now. We have 57 more possible destructions of Floating-Dream Zubera, so we can generate more than F_{w^3 + w14 + 2} (58) Dual Natures before combat starts.
It's kind of disappointing that I couldn't squeeze in Panharmonicon for this start, but I needed every card slot so that I could start casting Allay by the third Zubera. Anyway, we will clearly need three Zubera destructions to get going, so this estimate looks right.
Floating-Dream Zubera seems like a good call. But remember that we can draw Genesis Wave twice for each Zubera trigger. Once itself and once via Rebuild cycling. We can put the cycle ability on the stack as soon as we draw the card, so Rebuild is available in the graveyard and we can go through the full combo before resolving the cycling to grab Genesis Wave again. We'd get more than F_{w^3 + w14 + 2}(115) Dual Natures before combat.
Killing multiple Zuberas before resolving the first trigger allows us to draw extra cards. That seems like it should help a bit for the start.
Ah, good point about doubling up on Genesis Wave. I did think about somehow killing multiple Zuberas before we resolved their triggers, but then you need to respond to each targeting with a new targeting, which can be tricky.
Get triggers to create token copies of everything (besides Opalescence). Resolve the Primeval Titan ETB trigger to put the lifelands onto the battlefield (4 life remaining). Due to Panharmonicon, we get two token copies of everything; have the Copy Enchantment tokens copy Dual Nature, giving us five copies in total. Leave the March of the Machine triggers on the stack.
Cast Herbal Poultice, triggering five Dual Natures four times each, for 20 Dual Nature triggers in total. Before they resolve, cast Allay without buyback. Three Psychic Battles and three Cowardices trigger. Bounce Copy Enchantment three times; that gives us 25 Dual Natures, then 125 Dual Natures, then 504 Psychic Battles. Use the final targeting to bounce March of the Machines. Allow the Herbal Poultice tokens to come onto the battlefield. Sacrifice one token, getting 505 targetings of arbitrary creatures. Bounce Copy Enchantment 503 times, getting 5^505 Dual Natures, then more than 4*5^505 Psychic Battles. Destroy a Su-Chi token, getting four colorles mana. Use the last Psychic Battle to target a Floating-Dream Zubera token, destroying it; do not resolve the ensuing trigger.
Sacrifice a second Herbal Poultice, getting more than 4*5^505 Psychic Battle triggers. We can bounce Copy Enchantment many times to get more than 5^(4*5^505) Dual Natures and Psychic Battles, and can still bounce and destroy Su-Chi many times to get plenty of colorless mana. Use the last Psychic Battle to destroy the last Zubera token.
After another 5 times, we will more than 2^^10 Dual Natures and Psychic Battle tokens, as much colorless mana as we need, and 7 Zubera triggers waiting on the stack.
Sacrifice the two Mirror of Fate tokens; use the first to exile the library, and the second to bring Perpetual Timepiece, Swarm Intelligence, and five other cards into the library. Resolve the topmost Zubera trigger to draw the seven cards cards. Tap a Timepiece token to mill two Acorn Harvests, then exile it to reshuffle Black Lotus, Genesis Wave, Rebuild, Allay, and Herbal Poultice back into the library.
Sacrifice the remaining Herbal Poultices, getting a whole lot more Dual Natures, Psychic Battles and Swarm Intelligences (at least 2^^23, but probably a whole lot more due to our new cards). We now have 13 Zubera triggers, which we can currently resolve to draw 20 cards. By my count we have 23 cards in our hand or on the battlefield. We can resolve a trigger to draw 20 cards, then cast Living Wish to gain 15 more cards, but that still leaves 17 cards in the library/graveyard/exile, which is a bit too many to get the full combo running. Still we can now cast Genesis Wave and get a gajillion Swarm Intelligence copies, then cycle it back with Rebuild, and repeat that another 58 times. So we can get more than F_{w^3 + w14 + 2} (118) this time.
EDIT: Well, I came up with a possible improvement to the ending sequence:
This should get F_{w^3 + w14 + 8} if it works out. (Using Five-Alarm Fire instead of Glorybringer would increase it to F_{w^3 + w14 + 9}, but we would need a card to keep the opponent from dying, and a card to get started.) But even with Glorybringer, getting started seems hard.
Get triggers. Resolve the Primeval Titan trigger to put lifelands onto the battlefield, gaining 3 life (4 life total). Play Pain Magnification, getting triggers. Play Worldpurge. Keep Dual Nature, Copy Enchantment, Finest Hour, Panharmonicon, Repercussion, Justice, and Primeval Titan. Reshuffle all the other permanents into the library.
Resolve the Pain Magnfication token creations. Resolve a Vedalken Orrery and an Omniscience token creation. Resolve the March of the Machine token creations. Resolve the Sky Swallower triggers; the opponent gains control of all the permanents, except for one Sky Swallower token. Resolve the Primeval Titan token creation, and put the lifelands back onto the battlefield (7 life). Resolve the rest of the token creations; have the two Copy Enchantment tokens copy Dual Nature.
Play Dual Nature; get 15 token creation triggers, for 20 Dual Natures total. Play Panharmonicon, getting 83 total. Play Copy Enchantment copying Dual Nature, getting 1785 Dual Natures total. Play Finest Hour, Repercussion, and Justice, getting 149,943 of each.
Attack with a Glorybringer, exerting it to deal 4 damage to the enemy Sky Swallower. All the Finest Hour, Repercussion, and Justice enchantments trigger. Resolve a Justice trigger, dealing 4 damage to ourselves. This triggers two Pain Magnfications. Resolve one to force us to discard Primeval Titan. This triggers two Spiritual Focus, and we gain 4 life and draw two cards. One of those cards will be Spiritual Focus, which we play to get 149,943 copies. The second Pain Magnfication resolves; we discard the remaining card, and we get a bunch of life and card draws. So we should have no trouble from here.
We wind up with 149,944 combat phases before the first postcombat main phase. I'm not sure whether this will allow us to exceed F_{w^3 + w14 + 8} (149,944), but we will definitely exceed F_{w^3 + w14 + 8} (149,943). Then World at War will get us to F_{w^3 + w14 + 8} (F_{w^3 + w14 + 8} (149,943)) final damage.
The Zubera can also help us get started so if we replace Finest Hour it seems we can use Five-Alarm Fire.
For the start, have Winter Blast as one of the extra cards in hand and do the typical stuff to get a good Genesis Wave going. Make sure to grab Horobi, Death's Wail and the Zubera along with some token copies. We can kill multiple Zuberas when we target them with Winter Blast. I'll not work through any numbers here, but I'm sure we can get going.
EDIT: Centaur Archer already deals damage to some of our creatures, so the less than 3 part of the damage layer sequence goes infinite.
Oh whoops. I guess then that the best we can do right now is F_{w^3 + w14 + 7}. The best use for the extra card I can think of is Consecrated Sphinx, which can trigger off of donated Floating-Dream Zuberas to draw our own cards. That would get us to around F_{w^3 + w14 + 3}(N) with N about 50 prior to combat. Still, I imagine there is a more powerful ending sequence out there.
If we find a way to save red mana until the end, that would add two layers right there.
I thought about possibly getting a layer using Thrummingbird or Gilder Bairn, possibly aided by Winding Constrictor. But, Worldpurge seems to mess up everything, as it will get rid of all Five-Alarm Fires that have or would get counters. The only way out I can think of would be to use phasing out, but I don't know how to do that in a way that can't be done too cheaply.
EDIT: Well, we can use Teferi's Veil and Time and Tide to phase creatures out and back in again. With lots of Teferi's Veil enchantments, we can stack the triggers so that all but one Five-Alarm Fire is phased in at a time, and use all the counters on the one Five-Alarm Fire. But, this occurs at the end of combat, so I don't think either Thrummingbird or Winding Constrictor alone can increase the number of counters between usages. I think Gilder Bairn combined with Winding Constrictor can, but that is four cards required to gain one layer, and we have only two card slots to give up.
In the presence of donation and with both players able to refill their libraries Consecrated Sphinx goes infinite, since opposing Sphinxes can keep triggering each other.
The best 75th card I can think of is a second copy of Rebuild or any other cycling card that we can't pick up without drawing it. But yeah, there is probably some better layer sequence left to find.
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Hmmm, if Judge of Currents is the only other way for the opponent to gain life, then we can replace the Merfolk stage with a Spirit/Minotaur stage, and have Hurloon Shaman as the life gain creature, using shenanigans with Primeval Titan. If that works, we have the opportunity to use opponent life gain as the final layer by adding a card that can add arbitrarily many additional combat phases. Unfortunately, nearly every such card also untaps all creatures, which goes infinite since we can have arbitrarily many combat phases so long as we don't deal damage to the opponent. (Only Breath of Fire requires dealing combat damage, and that is a forbidden Enchant Creature aura.) But Godo, Bandit Warlord only untaps Samurai, which should be no problem.
With that, we can give the opponent life as many times as we can force him to discard. We can do that with either Noggle Ransacker, or Pain Magnification; so, we can do that as long as the opponent has either a card in hand or two cards in the library. So we can make the opponent discard up to 59 times; however, the 59th discard won't do any good, since there will be no cards left in his library, so if we try to make him resolve a Spiritual Focus he can choose to deck himself. So I believe 58 discards is the most that we can do.
We can use Godo, Bandit Warlord to replace both Finest Hour and World at War, so we have an extra card to do whatever we want with. Consecrated Sphinx seems like a good call, allowing us to get going with just a couple of Noggle Ransackers, and the final damage we deal should be around F_{w^3 + w14 +8}(N) with N close to 58.
I think Gerrard's Verdict would allow us to get the mega stage without having life gain that the opponent can use, but I have no idea how to do the connecting stage without such a thing.
Additionally Hurloon Shaman conflicts with the Island stage transition.
2 Grip of Chaos
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 Dual Nature
14 Copy Enchantment
15 Allay
16 Su-Chi
17 Farrelite Priest
18 Metallurgeon
19 Bump in the Night
20 Battle Cry
21 Rebuild
22 Spellweaver Volute
23 Mox Ruby
24 Wormfang Behemoth
25 Vile Redeemer
27 Sky Swallower
28 Swarm Intelligence
29 Worldpurge
30 Flash of Defiance
31 Flash of Defiance
32 Flash of Defiance
33 Spellweaver Helix
34 Primeval Titan
35 Glimmerpost
36 Radiant Fountain
37 Judge of Currents
38 Merfolk Sovereign
39 Aquatic Incursion
40 Volcanic Island
41 Guardian Zendikon
42 Ulvenwald Captive
43 Assault Formation
44 Cinder Glade
45 Goblin Clearcutter
46 Mad Auntie
47 Facevaulter
48 Basal Thrull
49 Thrull Champion
50 Godtoucher
51 Everglove Courier
53 Ghosthelm Courier
54 Possessed Aven
55 Centaur Archer
56 Maze Glider
57 Possessed Centaur
58 Eastern Paladin
59 Frightshroud Courier
60 Dwarven Warriors
61 Possessed Barbarian
62 Minion of Tevesh Szat
63 Herbal Poultice
64 Genesis Wave
65 Spiritual Focus
66 Pain Magnification
67 Justice
68 Repercussion
69 Five-Alarm Fire
70 Finest Hour
71 World at War
72 Noggle Ransacker
73 Black Lotus
74 Channel
75 Living Wish
Working through the start:
Opening hand
Black Lotus
Channel
Perpetual Timepiece
Rebuild
Genesis Wave
Worldpurge
Allay
Cast Black Lotus, Channel, Perpetual Timepiece, exile the Timepiece to shuffle Black Lotus back in the library, cycle the Rebuild to draw Black Lotus, play Black Lotus, cast Genesis Wave for X=12 (3 life remaining). Reveal:
Vedlaken Orrery
Omniscience
Opalescence
Dual Nature
Copy Enchantment
Cowardice
Psychic Battle
Noggle Ransacker
Swarm Intelligence
Mirror of Fate
March of the Machines
Primeval Titan
We get a bunch of Dual Nature triggers and ETB triggers. Resolve the Primeval Titan ETB trigger to put Radiant Foutain and Glimmerpost onto the battiefield tapped, gaining 3 life (6 life remaining). Do not resolve the rest of the triggers yet.
Cast Worldpurge. Bring back Opalescence, Dual Nature, Copy Enchantment, Swarm Intelligence, Noggle Ransacker, and Mirror of Fate back to our hand, along with Allay. Shuffle the other permanents into the library. Resolve the Vedalken Orrery and Omniscience Dual Nature trigges, creating tokens. Resolve the Primeval Titan trigger and get a token; resolve the ETB trigger to put both lifegain lands into play, gaining 3 life (9 life remaining). Resolve the Mirror of Fate Dual Nature trigger, and get a token. Play Mirror of Fate, and sacrifice both Mirror of Fates. The first Mirror of Fate simply puts the whole library into exile. The second one brings back Perpetual Timepiece and say a Flash Defiance into the library, along with five other useful cards, probably including Herbal Poultice. Resolve the Noggle Ransacker ETB trigger, and draw the two cards, discarding Flash of Defiance. Resolve the rest of the triggers, except the remaining Noggle Ransacker trigger. Have the Copy Enchantment token copy Dual Nature. Replay Opalescence, Dual Nature (6 Dual Natures in total), and Copy Enchantment copying Dual Nature (14 Dual Natures in total). Play Swarm Intelligence, getting 16 copies in total. Play Noggle Ransacker, getting 14 Dual Nature triggers, and the equivalent of 16 draw triggers in total. Play Perpetual Timepiece, getting 16 copies in total. Exile a Perpetual Timepiece token to shuffle Black Lotus, Genesis Wave, Mirror of Fate, Flash of Defiance, and Rebuild into the library. Resolve two Noggle Ransacker ETB triggers, drawing and keeping Black Lotus and Genesis Wave, and discarding Flash of Defiance and Rebuild. Cast Black Lotus; it goes to the graveyard, and 16 Black Lotus tokens are triggered. Cast Allay with buy back (4 life remaining), getting 17 copies in total. The original gets a Cowardice trigger and a Psychic Battle trigger; put the Cowardice trigger on top of the stack of abilities, and the Psychic Battle on bottom, below all the Swarm Intelligence triggers. Resolve the Cowardice trigger and bounce Copy Enchantment; this destroys all the Dual Nature tokens. Replay the CE and copy Psychic Battle, getting a Psychic Battle token as well. The first Swarm Intelligence copy resolves, and gets 3 Psychic Battle triggers; we bounce CE four times, getting 2, 4, and 8 Dual Natures, and then 10 Psychic Battles. The second one gives us 11 bounces, getting us 8192 Dual Natures and 8194 Psychic Battles. The third gives us more than 2^8207 > 2^^4 Dual Natures and Psychic Battles, and so the 16th will give us more than 2^^17 Dual Natures and Swarm Intelligences. At the end, bounce Cowardice. Finally, have the final Psychic Battle trigger redirect the original target of Allay to March of the Machines token, which gets destroyed.
We now get 16 Black Lotuses, enough for 48 mana. We can now cast Genesis Wave with X=10 and get more than 2^^17 Swarm Intelligence copies. We will play Mirror of Fate, Cowardice, and March of the Machines, then we can cast Allay to get more enchantments and bounce March of the Machines so that we can use all of the Mirror of Fate copies that we will get. That will give us access to the rest of the deck, and then we can use an Herbal Poutice on a Minion of Tevesh Szat, which can then bounce Perpetual Timeiece to give us all the milling and reshuffling that we will need. So I think we can get the full combo from here. This should generate more than F_{w^3 + w14 + 1} (2^^17) Dual Natures after then third Noggle Ransacker, then the next 47 will take us to more than F_{w^3 + w14 + 2}(48). The final two Noggle Ransackers are used for opponent life gain for Finest Hour and World at War, and we wind up with more than F_{w^3 + w14 + 7} (F_{w^3 + w14 + 7} (F_{w^3 + w14 + 2} (48))) in the end.
EDIT: It would be nice if we could replace Spiritual Focus with Waste Not (donated to the opponent) and Consecrated Sphinx. Or, if we could replace Spiritual Focus with Telekinetic Bonds / Keldon Megaliths / Repercussion / Justice / Angelheart Vial, getting two layers for two extra cards. Unfortunately, both Waste Not and Telekinetic Bonds run afoul of Rebuild, and we need Rebuild for our start.
EDIT: An alternate ending is to go
Herbal Poultice
Genesis Wave
Angelheart Vial
Justice
Repercussion
Keldon Megaliths
Ahn-Crop Champion
Finest Hour
World at War
Noggle Ransacker
But, this does about the same damage as the previous version. Even if we could get started without Noggle Ransacker, I don't know of anything better to use for the card slot.
EDIT: Hmm, I just noticed a very interesting card: Starlit Sanctum. It can tap to gain life equal to the toughness of a CLeric. A Cleric that has 3 toughness is Farrelite Priest. So this seems like it has the potential for card savings.
Unfortunately, our current 60 card deck doesn't use Farrelite Priest, in order to get access to blue mana. So, if we switch to Starlit Sanctum, we either have to use the new card slot to gain access to blue, or we can put in something like Goblin Welder, which means we would need to replace Goblin Bushwhacker with perhaps Herbal Poultice, and we lose the layer that we gain with the extra card. Reality Spasm + Precursor Golem also loses a layer, unless we can find a way to eliminate Genesis Wave. Unfortunately, if we try to hardcast Omniscience, we have only two cards left, not enough to get going. So, I don't see an improvement here.
The deck with sideboard does use Farrelite Priest, so perhaps we can gain a card slot. Unfortunately, Starlit Sanctum requires that we bring lands in untapped, so our shtick with destroying a land as the only way to get that type of mana no longer works. So I don't see how Starlit Sanctum can help in this deck either.
EDIT: Well, we haven't improved the final damage, but we've reached the point where we now have four available card slots to get that 13th layer, I think:
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 Dual Nature
14 Copy Enchantment
15 Allay
16 Su-Chi
17 Farrelite Priest
18 Metallurgeon
19 Chatter of the Squirrel
20 Battle Cry
21 Rebuild
22 Spellweaver Volute
23 Mox Emerald
25 Vile Redeemer
26 Deconstruct
27 Swarm Intelligence
28 Worldpurge
29 Acorn Harvest
30 Acorn Harvest
31 Acorn Harvest
32 Spellweaver Helix
33 Quarry Beetle
34 Starlit Sanctum
35 Judge of Currents
36 Merfolk Sovereign
37 Aquatic Incursion
38 Goblin Welder
39 Mad Auntie
40 Godtoucher
41 Everglove Courier
43 Ghosthelm Courier
44 Possessed Aven
45 Centaur Archer
46 Maze Glider
47 Possessed Centaur
48 Eastern Paladin
49 Frightshroud Courier
50 Dwarven Warriors
51 Possessed Barbarian
52 Minion of Tevesh Szat
53 Herbal Poultice
54 Genesis Wave
55 Channel
56 Black Lotus
As always, the key thing would be finding a way for Goblins to produce blue mana, or find a use for the red mana that Goblins do efficiently produce.
I believe are current best 13-stage deck is:
2 Grip of Chaos
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 Dual Nature
14 Copy Enchantment
15 Allay
16 Su-Chi
17 Farrelite Priest
18 Metallurgeon
19 Deep Reconnaissance
20 Battle Cry
21 Rebuild
22 Spellweaver Volute
23 Mox Emerald
25 Vile Redeemer
26 Deconstruct
27 Swarm Intelligence
28 Worldpurge
29 Acorn Harvest
30 Acorn Harvest
31 Acorn Harvest
32 Acorn Harvest
33 Spellweaver Helix
34 Gerrard's Verdict
35 Island
36 Judge of Currents
37 Merfolk Sovereign
38 Aquatic Incursion
39 Natural Affinity
40 Goblin Gardener
41 Mad Auntie
42 Facevaulter
43 Basal Thrull
44 Thrull Champion
46 Everglove Courier
47 Nectar Faerie
48 Ghosthelm Courier
49 Possessed Aven
50 Centaur Archer
51 Maze Glider
52 Possessed Centaur
53 Eastern Paladin
54 Frightshroud Courier
55 Dwarven Warriors
56 Possessed Barbarian
57 Minion of Tevesh Szat
58 Goblin Bushwhacker
59 Genesis Wave
60 Channel
61 Black Lotus
Just one card away from fitting in 60 card slots, and we managed to save Goblin Bushwhacher for a couple of layers at the end. Unfortunately, this deck also uses destroying a land to get a Mimic Vat copy, so we can't use Starlit Sanctum to save a card here either. Just about the only way to have Starlit Sanctum compatible with the land + Mimic Vat would be to use Dryad Arbor, which would require switching to red mana for the megastage.
An idea that seems close to working:
We take the 61 card version you posted and replace Acorn Harvest + Gerrard's Verdict with Titania, Protector of Argoth + Starlit Sanctum to make the megastage work.
We save the card by replacing Island + Natural Affinity with Celestial Colonnade. The Colonnade activates itself and as a creature can go under Mimic Vat. Then the hasty version can animate itself again and as it is white we can untap it with Battle Cry multiple times to generate lots of blue. We have to use the hasty version because we can only untap the Colonnade after it is a creature and effected by summoning sickness.
The problem I see here is that we need a blue mana to animate the colonnade in the first place. And while we can generate a lot more than two blue from two activations with multiple battle cries I don't think we can keep any of that blue stockpiled while going through the combo with Worldpurge. I see nothing we could put on the stack to replenish blue when we get to this stage transition again.
quick EDIT: If we use Sea Scryer as the merfolk stage creature we can use tokens of that to produce the initial blue after Worldpurge. And as we have Aquatic Incursion for the transition anyway that should actually work.
So 13 stages in 60 cards might be real.
EDIT 2: Godtoucher is a cleric and using Starlit Sanctum to sacrifice it allows us to get those powerful hasty tokens way too cheap, going infinite. So we need more improvements to get 13 stages.
Fortunately, there is an alternate sequence that doesn't use Godtoucher, and it appears to work in this case:
2 Grip of Chaos
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 Dual Nature
14 Copy Enchantment
15 Allay
16 Su-Chi
17 Farrelite Priest
18 Metallurgeon
19 Deep Reconnaissance
20 Battle Cry
21 Rebuild
22 Spellweaver Volute
23 Mox Emerald
25 Vile Redeemer
26 Deconstruct
27 Swarm Intelligence
28 Worldpurge
29 Acorn Harvest
30 Acorn Harvest
31 Acorn Harvest
32 Spellweaver Helix
33 Primeval Titan
34 Starlit Sanctum
35 Judge of Currents
36 Sea Scryer
37 Aquatic Incursion
38 Celestial Colonnade
39 Goblin Gardener
40 Mad Auntie
41 Dralnu's Crusade
42 Llanowar Dead
43 Boneknitter
45 Nectar Faerie
46 Ghosthelm Courier
47 Possessed Aven
48 Centaur Archer
49 Maze Glider
50 Paragon of Eternal Wilds
51 Devout Chaplain
52 Royal Assassin
53 Paragon of Open Graves
54 Lightbringer
55 Dwarven Warriors
56 Karplusan Yeti
57 Goblin Bushwhacker
58 Genesis Wave
59 Channel
60 Black Lotus
I have a good feeling about this.
Two nitpicks:
- We need Titania, Protector of Argoth instead of Primeval Titan for the untapped land.
- Boneknitter is a cleric that gets tougher via Paragon of Open Graves, so we could get too much life in the mega stage. Use Drunau Corpse Trawler instead.
Those are the only problems I've found so far. Looking good
EDIT: Actually I'm being stupid again. After we animate a hasty Celestial Colonnade there is no reason for us to use Worldpurge again. We can just keep going infinite when our Battle Crys effectively produce blue mana. Ooops.
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 Dual Nature
14 Copy Enchantment
15 Allay
16 Su-Chi
17 Farrelite Priest
18 Metallurgeon
19 Bump in the Night
20 Battle Cry
21 Rebuild
22 Spellweaver Volute
23 Mox Ruby
25 Vile Redeemer
26 Rude Awakening
27 Swarm Intelligence
28 Worldpurge
29 Flash of Defiance
30 Flash of Defiance
31 Flash of Defiance
32 Spellweaver Helix
33 Primeval Titan
34 Wind-Scarred Crag
35 Kabira Crossroads
36 Guardian Zendikon
37 Ulvenwald Captive
38 Assault Formation
39 Dryad Arbor
40 Goblin Clearcutter
41 Mad Auntie
42 Facevaulter
43 Basal Thrull
44 Thrull Champion
46 Everglove Courier
47 Nectar Faerie
48 Ghosthelm Courier
49 Possessed Aven
50 Centaur Archer
51 Maze Glider
52 Possessed Centaur
53 Eastern Paladin
54 Frightshroud Courier
55 Dwarven Warriors
56 Possessed Barbarian
57 Minion of Tevesh Szat
58 Reality Spasm
59 Consecrated Sphinx
60 Noggle Ransacker
61 Channel
62 Black Lotus
Winds up taking up the same number of card slots, except I don't think we can get started with just Genesis Wave, so we need three cards for the start.
EDIT: Another 61-card version:
2 Grip of Chaos
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 Dual Nature
14 Copy Enchantment
15 Allay
16 Su-Chi
17 Farrelite Priest
18 Metallurgeon
19 Deep Reconnaissance
20 Battle Cry
21 Rebuild
22 Spellweaver Volute
23 Mox Emerald
25 Vile Redeemer
26 Deconstruct
27 Swarm Intelligence
28 Worldpurge
29 Acorn Harvest
30 Acorn Harvest
31 Acorn Harvest
32 Spellweaver Helix
33 Titania, Protector of Argoth
34 Starlit Sanctum
35 Judge of Currents
36 Sea Scryer
37 Aquatic Incursion
38 Urborg Elf
39 Everglove Courier
40 Nectar Faerie
41 Ghosthelm Courier
42 Possessed Aven
43 Centaur Archer
44 Maze Glider
46 Liberated Dwarf
47 Krark-Clan Stoker
48 Mad Auntie
49 Dralnu's Crusade
50 Frightshrould Courier
51 Embalmer's Tools
52 Devout Chaplain
53 Royal Assassin
54 Paragon of Open Graves
55 Lightbringer
56 Dwarven Warriors
57 Karplusan Yeti
58 Herbal Poultice
59 Genesis Wave
60 Channel
61 Black Lotus
EDIT: I hope this works:
2 Grip of Chaos
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 Dual Nature
14 Copy Enchantment
15 Allay
16 Su-Chi
17 Farrelite Priest
18 Metallurgeon
19 Deep Reconnaissance
20 Battle Cry
21 Rebuild
22 Spellweaver Volute
23 Mox Emerald
25 Vile Redeemer
26 Deconstruct
27 Swarm Intelligence
28 Worldpurge
29 Acorn Harvest
30 Acorn Harvest
31 Acorn Harvest
32 Spellweaver Helix
33 Titania, Protector of Argoth
34 Starlit Sanctum
35 Judge of Currents
36 Sea Scryer
37 Aquatic Incursion
38 Urborg Elf
39 Everglove Courier
40 Nectar Faerie
41 Ghosthelm Courier
42 Possessed Aven
43 Centaur Archer
44 Maze Glider
46 Eastern Paladin
57 Frightshroud Courier
48 Embalmer's Tools
49 Devout Chaplain
50 Royal Assassin
51 Paragon of Open Graves
52 Enslaved Dwarf
53 Krark-Clan Stoker
54 Flamestick Courier
55 Dwarven Warriors
56 Karplusan Yeti
57 Herbal Poultice
58 Genesis Wave
59 Channel
60 Black Lotus
I'm quoting this post so it's easier to find/know it exists for any potential mad man interested in joining the project. It's not up to date or complete, but it should give you an idea of what you're getting into if you want to join the madness. I just noticed the date of the last deck and I just have to ask, how long have you guys been working on this deck?
The
Necromancer (or Noob)
Cat.
Don't ask, I don't know why ether...
@Deedlit11: That 60 card version almost works. But I found one problem with it. If I remember correctly how stage transitions work we get exactly 1 Krark-Clan Stoker for every 2 Flamestick Courier activations. So I think we get exactly enough red mana to drive that stage, but can never use any of it to start the black stage.
Now it might still work if we find some tricky way to resolve everything involved. Maybe Worldpurge can help, bouncing the stoker; although that removes all red mana, so... it's tricky.
Goblin Welder would definitely produce enough red to make the stages work. Of course it also fetches Herbal Poultice, so we'd lose the only layer we have in the end. We could still get one batch of hasty Karplusan Yeti tokens if we use Hazoret's Favor instead of the poultice. Pre-combat we can produce many batches of red mana from the Genesis Wave copies and go through the 10 stages above that.
EDIT: We could replace Titania, Protector of Argoth with Walking Atlas. Then lands would require Genesis Wave to get out of the graveyard/library/exile for an option other than 0 cost artifacts there. But I found no card that actually gets a layer there.
We haven't been working on it continuously of course, every few months I would come back to it and think of something new, and we would start talking about it again.
@Iijil: Yeah, it looks hard to make Krark-Clan Stoker work. The problem is that we need a lot of red mana at the same time, not just producing one at a time. After the first Flamestick Courier activation, we can imprint Krark-Clan Stoker on a Mimic Vat, bring the Krark-Clan Stoker back to the battlefield, and then tap the Mimic Vat to activate the token creation. We can then use Worldpurge to bounce the Krark-Clan Stoker, eliminating the need for the second Flamestick Courier activation. But then the ability to create the token is on top of all the Flamestick Courier abilities, and we have to resolve it, leaving either a Krark-Clan Stoker token or two red mana that will be eliminated after the next Worldpurge.
It would be nice if we could cast a Reality Spasm augmented by Precursor Golem, but Genesis Wave can't retrieve it, and there isn't enough room in the opening hand.
EDIT: Looking at the start, the current deck is a little different since we don't have Sejiri Refuge and Kabira Crossroads, which the previous deck uses to gain 3 life at the cost of 1. Now we have Starlit Sanctum for our lifegain, which would cost us 3 life to gain 3, which doesn't help. But the previous deck needed all of our life for the Genesis Wave, Allay with buyback, and flashback of Acorn Harvest. So, we either need to cut three cards (one of which will be Primeval Titan), or not cast the initial Allay with buyback. I don't see what two cards I can cut efficiently - I thought perhaps Su-Chi and Horobi, Death's Wail might be cut, but then we would need March of the Machines to get enough copies of artifacts.
So, instead we will eschew the initial Allay. We can replace Primeval Titan with another permanent, but nothing particularly pops out, so I will instead just use the life to cast another early Allay. So we start the same way, casting Genesis Wave for X=12 with all the same cards except Primeval Titan. Have the Copy Enchantment token copy Swarm Intelligence again. Flashback the Acorn Harvest, casting Deconstruct. The casting triggers [c]Horobi,
Death's Wail[/c], Cowardice, two Psychic Battles, and three Swarm Intelligences, which we resolve in that order. We get three triggerings of Horobi and Cowardice before the first Swarm Intelligence trigger, which we use to, in order, destroy the Su-Chi token, bounce the original Su-Chi and replay it to get two more token copies, then destroy a token Su-Chi. This gives us 8 more colorless mana, allowing us to cast Allay with buyback three times.
The first casting of Allay gets all the same triggers; this time we order the triggers as follows: Cowardice, Psychic Battle, 3 Swarm Intelligences, Psychic Battle. We get two initial bounces, each time bouncing Copy Enchantment. The first replay of CE gets us 4 Dual Natures, the second gets us 7 Psychic Battles. The first Swarm Intelligence copy will then get us 8 bounces, which we use to increase the number of Dual Natures to 512 and the number of Psychic Battles to 514. The second gets us 515 bounces, which gets us to 2^523 Dual Natures and 2^523 + 2 Psychic Battles. The third gets us to more than 2^2^523 Dual Natures, Swarm Intelligences, and Psychic Battles. At the end of the last group of triggers we have a Copy Enchantment token copy Opalescence, then we bounce the Opalescence. Then we have the Psychic Battle trigger for the original Allay change the target to the Cowardice token, destroying it and allowing Allay to return to our hand.
We get two more Allays, each one taking X Swarm Intelligences to more than 2^^X Swarm Intelligences and Psychic Battles, so by the end we have more than 2^^(2^^(2^2^523)) Psychic Battles. Then the Swarm Intelligence triggers for Deconstruct get resolved, and each one takes X Psychic Battles to more than 2^^^X Psychic Battles, so we wind up with more than 2^^^(2^^^(2^^^(2^^(2^^(2^2^(523)))))) Swarm Intelligences in the end.
Then we cycle Rebuild to redraw Genesis Wave, and recast it to get all those Swarm Intelligence copies. After putting all the permanents we need into play and milling the necessary instants/sorceries, I guess we just use the rest of the Genesis Waves to put Black Lotus into play, which gets a whole bunch of Dual Nature copies, and we can implement the full combo up to the tenth additional stage each time, so we wind up with more than F_{w^3 + w10 + 1}(2^^^(2^^^(2^^^(2^^(2^^(2^2^(523))))))) Dual Natures by the end. Then we make that many copies of Hazoret's Favor and Karplusan Yeti, and go into combat, where we can make that many hasted copies of Karplusan Yeti, and implement the full combo to get more than F_{w^3 + w13} (F_{w^3 + w10 + 1}(2^^^(2^^^(2^^^(2^^(2^^(2^2^(523)))))))) hasted Metallurgeons, which we promptly attack with.
EDIT: I thought about possible improvements to the stage sequence; one idea is to move the blue creatures to later on. Wilderness Hypnotist seems to be a good transition creature, as it is both a Merfolk and a Wizard. Unfortunately, it is somewhat hard to get a lot of blue stages at that point, as Paragon of Gathering Mists and Possessed Aven are often mooted by then. Here are some unsuccessful attempts, in case it gives you any ideas:
2 Nectar Faerie
3 Centaur Archer
4 Maze Glider
5 Paragon of Eternal Wilds
7 Goblin Welder
8 Flamestick Courier
9 Paragon of Fierce Defiance
10 Wilderness Hypnotist
11 Streambed Aquitects
13 Devout Chaplain
14 Royal Assassin
15 Paragon of Open Graves
16 Blinding Drone
Not bad, but it is only 11 stages starting from Everglove Courier, so we would need two more stages before, and that is hard without Godtoucher. Also, both Goblins and Zombies are used later on.
2 Nectar Faerie
3 Centaur Archer
4 Maze Glider
5 Paragon of Eternal Wilds
6 Eastern Paladin
7 Frightshroud Courier
9 Enslaved Dwarf
10 Krark-Clan Stoker
11 Krark-Clan Stoker
12 Flamestick Courier
13 Paragon of Fierce Defiance
15 Sea Scryer
16 Aquatic Incursion
17 Ghosthelm Courier
18 Old Man of the Sea
19 Endbringer
12 stages in 19 cards is pretty good, if only we can add another stage in three cards or less. I haven't found a way yet though; red mana and blue mana are both used later on, as is the obvious choice for black mana, Zombies.
2 Paragon of Eternal Wilds
3 Liberated Dwarf
4 Krark-Clan Stoker
5 Krark-Clan Stoker
6 Flamestick Courier
8 Wilderness Hypnotist
9 Sea Scryer
10 Aquatic Incursion
11 Ghosthelm Courier
13 Royal Assassin
14 Illusionary Mount
15 Old Man of the Sea
16 Possessed Aven
Tried to eliminate some earlier stages to get more blue stages, but wound up losing one; again we need two more stages, with only one obvious one to add (Zombies).
2 Llanowar Dead
3 Drunau Corpse Trawler
4 Everglove Courier
5 Nectar Faerie
6 Centaur Archer
7 Maze Glider
9 Liberated Dwarf
10 Krark-Clan Stoker
11 Krark-Clan Stoker
12 Flamestick Courier
13 Paragon of Fierce Defiance
14 Wilderness Hypnotist
15 Sea Scryer
16 Aquatic Incursion
18 Devout Chaplain
19 Royal Assassin
20 Paragon of Open Graves
21 Lightbringer
22 Old Man of the Sea
23 Endbringer
This one finally gets us to 13 stages, but requires one more card than the current sequence - the need for two Krark-Clan Stokers hurt.
2 Llanowar Dead
3 Boneknitter
4 Basal Thrull
5 Thrull Champion
6 Godtoucer
7 Everglove Courier
9 Liberated Dwarf
10 Krark-Clan Stoker
11 Krark-Clan Stoker
12 Flamestick Courier
13 Possessed Barbarian
14 Wilderness Hypnotist
15 Sea Scryer
16 Aquatic Incursion
18 Devout Chaplian
19 Royal Assassin
20 Phantasmal Mount
21 Old Man of the Sea
22 Possessed Aven
23 Minion of Tevesh Szat
Another 23 card sequence, but this time with Godtoucher.
It is a white creature and targets artifacts. We just need a hasty token and two other copies on the battlefield and we can repeat the hyperstage transition without need for hasty Metallurgeons. Battle Cry untaps the Devout Chaplains and those target artifacts to give us the mana/other resources we require. Rebuild bounces Mox Emerald for the green mana we need, but leaves Devout Chaplain alone.
I did not find another way to make the tapped creature stage work.
Another idea that came to mind: Use Izzet Guildmage along with something like Disembowel or Postmortem Lunge to use red or blue mana to target one CMC creatures. It costs quite a few cards, but it could be worth it. Postmortem Lunge could also be used in the ending layers.
Prospective deck:
2 Grip of Chaos
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 Dual Nature
14 Copy Enchantment
15 Allay
16 Su-Chi
17 Farrelite Priest
18 Metallurgeon
19 Deep Reconnaissance
20 Battle Cry
21 Rebuild
22 Spellweaver Volute
23 Mox Emerald
25 Vile Redeemer
26 Deconstruct
27 Swarm Intelligence
28 Worldpurge
29 Acorn Harvest
30 Acorn Harvest
31 Acorn Harvest
32 Spellweaver Helix
33 Primeval Titan
34 Glimmerpost
35 Radiant Fountain
36 Goblin Gardener
37 Mad Auntie
38 Facevaulter
39 Elves of Deep Shadow
40 Izzet Guildmage
41 Disembowel
42 Tidal Warrior
43 Merfolk Sovereign
45 Everglove Courier
46 Nectar Faerie
47 Ghosthelm Courier
48 Possessed Aven
49 Centaur Archer
50 Maze Glider
51 Possessed Centaur
52 Eastern Paladin
53 Frightshroud Courier
54 Dwarven Warriors
55 Possessed Barbarian
56 Minion of Tevesh Szat
57 Goblin Bushwhacker
58 Genesis Wave
59 Channel
60 Black Lotus
But we can't use Tidal Warrior as a stage creature, because it is a landshaping ability and we can store that nonmana ability on the stack thorugh Worldpurge. Also with the proposed deck we never get untapped lands.
The only fix I see needs an extra card with Noble Hierarch and Sea Scryer.
Another problem with the X spells is that the Genesis Wave start we currently use has no way to ever get them onto the stack with X=1. The upside is that they can enable the initial haste in a Noggle Ransacker + Consecrated Sphinx start.
2 Grip of Chaos
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 Dual Nature
14 Copy Enchantment
15 Allay
16 Su-Chi
17 Candelabra of Tawnos
18 Metallurgeon
19 Deep Reconnaissance
20 Battle Cry
21 Rebuild
22 Spellweaver Volute
23 Mox Emerald
25 Vile Redeemer
26 Deconstruct
27 Swarm Intelligence
28 Worldpurge
29 Acorn Harvest
30 Acorn Harvest
31 Acorn Harvest
32 Spellweaver Helix
33 Primeval Titan
34 Scoured Barrens
35 Kabira Crossroads
36 Hurloon Shaman
37 Anaba Ancestor
38 Promised Kannushi
39 Izzet Guildmage
40 Disembowel
41 Noble Hierarch
42 Sea Scryer
43 Merfolk Sovereign
45 Everglove Courier
46 Nectar Faerie
47 Ghosthelm Courier
48 Possessed Aven
49 Centaur Archer
50 Maze Glider
51 Possessed Centaur
52 Eastern Paladin
53 Frightshroud Courier
54 Dwarven Warriors
55 Possessed Barbarian
56 Minion of Tevesh Szat
57 Consecrated Sphinx
58 Noggle Ransacker
59 Channel
60 Black Lotus
Funnily enough, we manage to save red mana for the end, but there's no room for Goblin Bushwhacker.
EDIT: I thought about switching Disembowel with Postmortem Lunge, in order to save blue so that we can use Broken Ambitions in place of Cephalid Shrine and Perpetual Timepiece, saving a card. But, upon closer inspection I don't think Postmortem Lunge works; we have no way to send the one-CMC creature to the graveyard, and if we did, it would probably go infinite. All the other 1X sorceries also seem to be of the form "return target creature card from the graveyard". So I guess we are stuck with Disembowel.
We do have red mana available, in case there is a useful cheap sorcery we could use earlier on.
There does seem to be some potential still for card savings; for example, if we remove the Merfolk stage, connecting Everglove Courier to Viridian Acolyte, and then reinstitute Starlit Sanctum, we can save four cards. So if we could just add another stage in three cards or less...
EDIT: We can switch to the Enslaved Dwarf sequence for an extra three cards, but that requires red still be available, and for that we need another card in the Elf section. So it winds up the same.
Alternate deck:
2 Grip of Chaos
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 Dual Nature
14 Copy Enchantment
15 Allay
16 Su-Chi
17 Farrelite Priest
18 Metallurgeon
19 Deep Reconnaissance
20 Battle Cry
21 Rebuild
22 Spellweaver Volute
23 Mox Emerald
25 Vile Redeemer
26 Deconstruct
27 Swarm Intelligence
28 Worldpurge
29 Acorn Harvest
30 Acorn Harvest
31 Acorn Harvest
32 Spellweaver Helix
33 Titania, Protector of Argoth
34 Starlit Sanctum
35 Hurloon Shaman
36 Anaba Ancestor
37 Promised Kannushi
38 Izzet Guildmage
39 Disembowel
40 Noble Hierarch
41 Urborg Elf
42 Everglove Courier
43 Nectar Faerie
45 Possessed Aven
46 Centaur Archer
47 Maze Glider
48 Possessed Centaur
49 Eastern Paladin
50 Frightshroud Courier
51 Paragon of Open Graves
52 Enslaved Dwarf
53 Goblin Welder
54 Flamestick Courier
55 Dwarven Warriors
56 Karplusan Yeti
57 Consecrated Sphinx
58 Noggle Ransacker
59 Channel
60 Black Lotus
EDIT: Looking at the start, it would probably be best to switch from Merfolk to Goblins so that Goblin Welder can retrieve artifacts from the graveyard. The start can go the same way that Iijil mentioned before, playing Consecrated Sphinx and Noggle Ransacker to draw six cards and discard one, then resolving another Noggle Ransacker with 11 Consecrated Sphinxes on the battlefield, drawing 46 and discarding one card. By my count we have 38 cards to draw (nonartifact creatures + enchantments + Allay) besides Disembowel of which we have already drawn 6. So 32 of the 45 new cards can be those, and the remaining 13 times we can draw Disembowel. (I'm not sure though - maybe the sequence of play requires that we draw something extra, I haven't checked carefully.) I believe this gets us to more than F_{w^3 + w13} (24), not enough for 51 (we would need another four Consecrated Sphinxes at least). Still, that gets us to more than F_{w^3 + w13 + 1}(50) in the end.
Still, the merfolk + Godtoucher version looks good
For the decks that use lifegain lands, we only need to copy two other sorceries. So we can replace an Acorn Harvest with Panharmonicon (throwing Channel in as a spare imprinted sorcery), but the improvement is only minor. But, for the decks with Gerrard's Verdict, we actually save a card. Unfortunately, Gerrard's Verdict isn't compatible with Hurloon Shaman or Goblin Gardener, which many of our decks use. But, we do have one 61-card deck with Judge of Currents, so it nicely becomes a 60-card deck:
2 Grip of Chaos
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 Dual Nature
14 Copy Enchantment
15 Allay
16 Su-Chi
17 Farrelite Priest
18 Metallurgeon
19 Deep Reconnaissance
20 Battle Cry
21 Rebuild
22 Spellweaver Volute
23 Mox Emerald
25 Vile Redeemer
26 Deconstruct
27 Swarm Intelligence
28 Worldpurge
29 Acorn Harvest
30 Acorn Harvest
31 Spellweaver Helix
32 Panharmonicon
33 Gerrard's Verdict
34 Island
35 Judge of Currents
36 Merfolk Sovereign
37 Aquatic Incursion
38 Natural Affinity
39 Goblin Gardener
40 Mad Auntie
41 Facevaulter
42 Basal Thrull
43 Thrull Champion
45 Everglove Courier
46 Nectar Faerie
47 Ghosthelm Courier
48 Possessed Aven
49 Centaur Archer
50 Maze Glider
51 Possessed Centaur
52 Eastern Paladin
53 Frightshroud Courier
54 Dwarven Warriors
55 Possessed Barbarian
56 Minion of Tevesh Szat
57 Goblin Bushwhacker
58 Genesis Wave
59 Channel
60 Black Lotus
This beats out the previous deck by a couple of layers.
Interestingly we now cast multiple sorceries during the resolution of the same Spellweaver Helix ability, so we put all of their Swarm Intelligence triggers onto the stack at the same time. That means we can interweave the copies of different sorceries. For example we can go Worldpurge -> Deep Reconnaissance -> Worldpurge -> Deep Reconnaissance -> ... and move the land between battlefield and library multiple times. Luckily the land gets stuck in the graveyard when we try to include Gerrard's Verdict in the cycle, so we can't actually gain more life with that. So I haven'T found any infinites with the deck yet.
I like that the Panhamonicon also casually gets an extra layer for Goblin Bushwhackers etb ability and improves the start by getting an extra Dual Nature trigger on Copy Enchantment and Swarm Intelligence. Great results all around!
Looking at the start: Again, we lose out by not having Primeval Titan to fetch lifegain lands. The obvious adjustment is to forego the initial casting of Allay again. On the plus side, we can replace Primeval Titan with Panharmonicon, and we get three of all the enchantments, except for Swarm Intelligence for which we have five. So we cast Deconstruct and get Cowardice, three Psychic Battle, and five Swarm Intelligence triggers, which we resolve in that order. We get four intial targetings of Su-Chi; we will use three of them to destroy Su-Chi tokens, and the remaining one to bounce the original Su-Chi to get more tokens. That gives us 12 colorless mana, allowing us to cast Allay four times with buyback. The first Allay gets us Cowardice, two Psychic Battle, five Swarm Intelligence, and a final Psychic Battle trigger. So we get three initial bouncings before the first Swarm Intelligence trigger. The first bounce gets us 9 Dual Natures, the second 27, and the third gives us the original, 54 token copies, and the 3 previous Psychic Battles for 58 Psychic Battles total. The first Swarm Intelligence copy gets 59 bouncings, of which we use 58 to increase the number of Dual Natures to 3^61 and the last to make 2*3^61 + 2 Psychic Battles. Each further Swarm Intelligence copy takes X to more than 3^X, so we wind up with more than 3^3^3^3^(2*3^61) Dual Natures, Psychic Battles and Swarm Intelligences in the end. After three more Allays we get more than 3^^3^^3^^(3^3^3^3^(2*3^61)) Dual Natures, and after five Swarm Intelligence copies of Deconstruct we get more than 3^^^3^^^3^^^3^^^3^^^(3^^3^^3^^(3^3^3^3^(2*3^61))) Swarm Intelligences. Finally, we recycle Genesis Wave and cast it with all those Swarm Intelligence copies, to get a final damage of more than F_{w^3 + w13 + 3} (3^^^3^^^3^^^3^^^3^^^(3^^3^^3^^(3^3^3^3^(2*3^61)))).
EDIT: I thought briefly about the deck with sideboard - I thought maybe we could replace the Merfolk stage with the Disembowel stage + Minotaur stage to get 15 stages, but Noble Hierarch gets green mana too early, and also Hurloon Shaman can destroy the Island. So I thought about improving 14 stages - and I don't know how to do that either. Ending with Hurloon Shaman messes up our way to get blue mana. Oh well.
I don't know what to do with the extra slot, but we need to rework the start anyway: Noggle Ransacker goes infinite since we can donate Su-Chi and Perpetual Timepiece allowing the opponent to pick up the discarded cards again.
EDIT: We'll be better off replacing Noggle Ransacker with Floating-Dream Zubera; if there is any difficulty in getting started, adding Urgent Exorcism should make it easy. Actually, I'm pretty confident that we can get started without Urgent Exorcism, the question is how to maximize the start.
EDIT: So, this is what I got.
Opening hand:
Black Lotus
Channel
Perpetual Timepiece
Rebuild
Genesis Wave
Worldpurge
Disciple of Tevesh Szat
Do the normal start, cast Genesis Wave with X=14 (1 life remaining):
Floating-Dream Zubera
Mirror of Fate
Opalescence
Psychic Battle
Dual Nature
Copy Enchantment
Omniscience
Horobi, Death's Wail
March of the Machines
Vedalken Orrery
Mimic Vat
Herbal Poultice
Swarm Intelligence
Primeval Titan
Herbal Poultice goes to the graveyard. Get triggers to create token copies of everything (besides Opalescence). Resolve the Primeval Titan ETB trigger to put the lifelands onto the battlefield (4 life remaining). Then cast Worldpurge.
Bring back Floating-Dream Zubera, Mirror of Fate, Opalescence, Psychic Battle, Dual Nature, and Copy Enchantment to our hand, while keeping Disciple of Tevesh Szat; the rest of the permanents get shuffled into the library. Resolve all the Dual Nature triggers, getting token copies of everything, except for the March of the Machines token. Resolve the ETB trigger of the Primeval Titan token, putting the lifelands into play again and gaining 3 life (7 life remaining). Play Opalescence, Dual Nature (6 copies), Copy Enchantment copy of Dual Nature (14 copies of Dual Nature total), Floating-Dream Zubera (16 copies total), Psychic Battle (16 copies total), Mirror of Fate (2 copies total), and Disciple of Tevesh Szat.
Sacrifice both Mirror of Fates; the first activation exiles the library, the second one brings back Perpetual Timepiece, Allay, Cowardice, Su-Chi, and three other useful cards. Pay 3 colorless mana (4 life) and sacrifice the Herbal Poultice token, destroying the original Disciple of Tevesh Szat. Imprint it on the Mimic Vat token. Pay 3 mana (1 life remaining) and create a token copy of Minion of Tevesh Szat. Resolve the Dual Nature trigger for March of the Machines, and get a token copy.
Tap the Disciple of Tevesh Szat, triggering 16 Psychic Battles, so we get 17 targetings in total. Use two to destroy two Floating-Dream Zubera tokens, and draw three cards. We draw Perpetual Timepiece, Allay, and Su-Chi. Play Su-Chi, getting 15 total copies. Resolve 14 Psychic Battle triggers of Disciple of Tevesh Szat to destroy all 14 token copies of Su-Chi, gaining 56 colorless mana. Play Perpetual Timepiece, getting 15 copies. Exile a token copy (54 mana remaining) to shuffle Black Lotus, Genesis Wave, and Mirror of Fate into the library. Resolve the last Psychic Battle trigger of Disciple of Tevesh Szat to destroy a Floating-Dream Zubera token, drawing three cards.
Draw Black Lotus, Genesis Wave, and Cowardice. We play Cowardice, and cast Allay with buyback 17 times.
The first Allay gets one Swarm Intelligence trigger, and 16 Psychic Battle triggers. We bounce Copy Enchantment 16 times, generating 32768 Dual Natures, and 32772 Psychic Battles. Then the Swarm Intelligence trigger resolves, and we get more than 2^32787 Swarm Intelligence tokens in the end, or more than 2^^^3. The next 16 Allays each take X to more than 2^^X, so we wind up with more than 2^^^19 Dual Nature and Swarm Intelligence tokens in the end.
Play Black Lotus, triggering more than 2^^^19 token copies. Cast Allay with buyback for the last time, generating more Dual Natures and also destroying the March of the Machines token. The more than 2^^^19 Black Loti come onto the battlefield, and we can cast Allay with buyback many times, to generate more than 2^^^2^^^19 Swarm Intelligences, while having plenty of Black Loti remaining. Cast Genesis Wave with X=10, generating more than 2^^^2^^^19 Swarm Intelligence copies, and we can run the full combo now. We have 57 more possible destructions of Floating-Dream Zubera, so we can generate more than F_{w^3 + w14 + 2} (58) Dual Natures before combat starts.
It's kind of disappointing that I couldn't squeeze in Panharmonicon for this start, but I needed every card slot so that I could start casting Allay by the third Zubera. Anyway, we will clearly need three Zubera destructions to get going, so this estimate looks right.
Killing multiple Zuberas before resolving the first trigger allows us to draw extra cards. That seems like it should help a bit for the start.
EDIT: Trying again.
Opening hand:
Black Lotus
Channel
Perpetual Timepiece
Rebuild
Genesis Wave
Allay
Herbal Poultice
Do the normal start, cast Genesis Wave with X=14 (1 life remaining):
Floating-Dream Zubera
Mirror of Fate
Opalescence
Psychic Battle
Dual Nature
Copy Enchantment
Cowardice
Omniscience
Horobi, Death's Wail
March of the Machines
Vedalken Orrery
Su-Chi
Panharmonicon
Primeval Titan
Get triggers to create token copies of everything (besides Opalescence). Resolve the Primeval Titan ETB trigger to put the lifelands onto the battlefield (4 life remaining). Due to Panharmonicon, we get two token copies of everything; have the Copy Enchantment tokens copy Dual Nature, giving us five copies in total. Leave the March of the Machine triggers on the stack.
Cast Herbal Poultice, triggering five Dual Natures four times each, for 20 Dual Nature triggers in total. Before they resolve, cast Allay without buyback. Three Psychic Battles and three Cowardices trigger. Bounce Copy Enchantment three times; that gives us 25 Dual Natures, then 125 Dual Natures, then 504 Psychic Battles. Use the final targeting to bounce March of the Machines. Allow the Herbal Poultice tokens to come onto the battlefield. Sacrifice one token, getting 505 targetings of arbitrary creatures. Bounce Copy Enchantment 503 times, getting 5^505 Dual Natures, then more than 4*5^505 Psychic Battles. Destroy a Su-Chi token, getting four colorles mana. Use the last Psychic Battle to target a Floating-Dream Zubera token, destroying it; do not resolve the ensuing trigger.
Sacrifice a second Herbal Poultice, getting more than 4*5^505 Psychic Battle triggers. We can bounce Copy Enchantment many times to get more than 5^(4*5^505) Dual Natures and Psychic Battles, and can still bounce and destroy Su-Chi many times to get plenty of colorless mana. Use the last Psychic Battle to destroy the last Zubera token.
After another 5 times, we will more than 2^^10 Dual Natures and Psychic Battle tokens, as much colorless mana as we need, and 7 Zubera triggers waiting on the stack.
Sacrifice the two Mirror of Fate tokens; use the first to exile the library, and the second to bring Perpetual Timepiece, Swarm Intelligence, and five other cards into the library. Resolve the topmost Zubera trigger to draw the seven cards cards. Tap a Timepiece token to mill two Acorn Harvests, then exile it to reshuffle Black Lotus, Genesis Wave, Rebuild, Allay, and Herbal Poultice back into the library.
Sacrifice the remaining Herbal Poultices, getting a whole lot more Dual Natures, Psychic Battles and Swarm Intelligences (at least 2^^23, but probably a whole lot more due to our new cards). We now have 13 Zubera triggers, which we can currently resolve to draw 20 cards. By my count we have 23 cards in our hand or on the battlefield. We can resolve a trigger to draw 20 cards, then cast Living Wish to gain 15 more cards, but that still leaves 17 cards in the library/graveyard/exile, which is a bit too many to get the full combo running. Still we can now cast Genesis Wave and get a gajillion Swarm Intelligence copies, then cycle it back with Rebuild, and repeat that another 58 times. So we can get more than F_{w^3 + w14 + 2} (118) this time.
EDIT: Well, I came up with a possible improvement to the ending sequence:
2 Grip of Chaos
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 Dual Nature
14 Copy Enchantment
15 Allay
16 Su-Chi
17 Farrelite Priest
18 Metallurgeon
19 Bump in the Night
20 Battle Cry
21 Rebuild
22 Spellweaver Volute
23 Mox Ruby
24 Wormfang Behemoth
25 Vile Redeemer
27 Sky Swallower
28 Swarm Intelligence
29 Worldpurge
30 Flash of Defiance
31 Flash of Defiance
32 Panharmonicon
33 Spellweaver Helix
34 Primeval Titan
35 Glimmerpost
36 Radiant Fountain
37 Judge of Currents
38 Merfolk Sovereign
39 Aquatic Incursion
40 Volcanic Island
41 Guardian Zendikon
42 Vine Trellis
43 Assault Formation
44 Goblin Digging Team
45 Mad Auntie
46 Facevaulter
47 Basal Thrull
48 Thrull Champion
49 Godtoucher
50 Everglove Courier
52 Ghosthelm Courier
53 Possessed Aven
54 Centaur Archer
55 Maze Glider
56 Possessed Centaur
57 Eastern Paladin
58 Frightshroud Courier
59 Dwarven Warriors
60 Possessed Barbarian
61 Minion of Tevesh Szat
62 Korozda Gorgon
63 Blood Hound
64 Justice
65 Repercussion
66 Winter Blast
67 Spiritual Focus
68 Pain Magnfication
69 Glorybringer
70 Finest Hour
71 World at War
72 Genesis Wave
73 Black Lotus
74 Channel
75 Living Wish
This should get F_{w^3 + w14 + 8} if it works out. (Using Five-Alarm Fire instead of Glorybringer would increase it to F_{w^3 + w14 + 9}, but we would need a card to keep the opponent from dying, and a card to get started.) But even with Glorybringer, getting started seems hard.
EDIT: It looks like we can in fact get started.
Opening hand:
Black Lotus
Channel
Perpetual Timepiece
Rebuild
Genesis Wave
Worldpurge
Pain Magnification
Do the normal start, cast Genesis Wave with X=14 (1 life remaining):
1 Vedalken Orrery
2 Omniscience
3 Glorybringer
4 Justice
5 Sky Swallower
6 Spiritual Focus
7 Primeval Titan
8 Finest Hour
9 Opalescence
10 Dual Nature
11 Panharmonicon
12 Copy Enchantment
13 March of the Machines
14 Repercussion
Get triggers. Resolve the Primeval Titan trigger to put lifelands onto the battlefield, gaining 3 life (4 life total). Play Pain Magnification, getting triggers. Play Worldpurge. Keep Dual Nature, Copy Enchantment, Finest Hour, Panharmonicon, Repercussion, Justice, and Primeval Titan. Reshuffle all the other permanents into the library.
Resolve the Pain Magnfication token creations. Resolve a Vedalken Orrery and an Omniscience token creation. Resolve the March of the Machine token creations. Resolve the Sky Swallower triggers; the opponent gains control of all the permanents, except for one Sky Swallower token. Resolve the Primeval Titan token creation, and put the lifelands back onto the battlefield (7 life). Resolve the rest of the token creations; have the two Copy Enchantment tokens copy Dual Nature.
Play Dual Nature; get 15 token creation triggers, for 20 Dual Natures total. Play Panharmonicon, getting 83 total. Play Copy Enchantment copying Dual Nature, getting 1785 Dual Natures total. Play Finest Hour, Repercussion, and Justice, getting 149,943 of each.
Attack with a Glorybringer, exerting it to deal 4 damage to the enemy Sky Swallower. All the Finest Hour, Repercussion, and Justice enchantments trigger. Resolve a Justice trigger, dealing 4 damage to ourselves. This triggers two Pain Magnfications. Resolve one to force us to discard Primeval Titan. This triggers two Spiritual Focus, and we gain 4 life and draw two cards. One of those cards will be Spiritual Focus, which we play to get 149,943 copies. The second Pain Magnfication resolves; we discard the remaining card, and we get a bunch of life and card draws. So we should have no trouble from here.
We wind up with 149,944 combat phases before the first postcombat main phase. I'm not sure whether this will allow us to exceed F_{w^3 + w14 + 8} (149,944), but we will definitely exceed F_{w^3 + w14 + 8} (149,943). Then World at War will get us to F_{w^3 + w14 + 8} (F_{w^3 + w14 + 8} (149,943)) final damage.
The Zubera can also help us get started so if we replace Finest Hour it seems we can use Five-Alarm Fire.
For the start, have Winter Blast as one of the extra cards in hand and do the typical stuff to get a good Genesis Wave going. Make sure to grab Horobi, Death's Wail and the Zubera along with some token copies. We can kill multiple Zuberas when we target them with Winter Blast. I'll not work through any numbers here, but I'm sure we can get going.
EDIT: Centaur Archer already deals damage to some of our creatures, so the less than 3 part of the damage layer sequence goes infinite.
If we find a way to save red mana until the end, that would add two layers right there.
EDIT: I think previously we had a layer with Dragon Tempest, Mirror Mockery, and Sarkhan Vol. But, I guess it runs into the same problem that Glorybringer has, with Worldpurge getting rid of all the targets.
I thought about possibly getting a layer using Thrummingbird or Gilder Bairn, possibly aided by Winding Constrictor. But, Worldpurge seems to mess up everything, as it will get rid of all Five-Alarm Fires that have or would get counters. The only way out I can think of would be to use phasing out, but I don't know how to do that in a way that can't be done too cheaply.
EDIT: Well, we can use Teferi's Veil and Time and Tide to phase creatures out and back in again. With lots of Teferi's Veil enchantments, we can stack the triggers so that all but one Five-Alarm Fire is phased in at a time, and use all the counters on the one Five-Alarm Fire. But, this occurs at the end of combat, so I don't think either Thrummingbird or Winding Constrictor alone can increase the number of counters between usages. I think Gilder Bairn combined with Winding Constrictor can, but that is four cards required to gain one layer, and we have only two card slots to give up.
The best 75th card I can think of is a second copy of Rebuild or any other cycling card that we can't pick up without drawing it. But yeah, there is probably some better layer sequence left to find.