To get mana from Stomping Ground we need to untap it with Mobilize. That can only be done after putting a new transition on the stack. So in the world without Worldfire and repeated Dark Rituals we don't get black mana after resolving a Worldpurge. Since we need black to get useful Bloodbond March triggers with Deathgrip we can not refresh our normal stages properly. We can only use the transitions to refresh Bloodbond March layers.
Such a creature wouldn't get copies from the delayed Sea Gate Stormcaller triggers, so it would not be able to replace Dark Ritual. The layers would never get any bigger unless we go through another transition.
I was going to suggest replacing Anger with Barbarian Class, but it seems like the sorcery speed is a problem since we will keep losing the enchantment.
Yes, we still need the mountain, but Marchesa's Smuggler in particular is still really useful. To make it work we must not allow the opponent to activate is, so Mox Ruby has to be taken out. We need Mana Crypt for the start again. In addition we now need red mana to give Master Transmuter haste, so Dark Ritual is not enough to restore progress after a Worldpurge. So we also need to add a Battle Hymn for that.
(I think it is still impossible to use the same instant card to catch up on progress after Worldpurge and BB-Computations, so this can't replace the Brightstone Ritual.)
So by using Marchesa's Smuggler instead of Anger we lose a card slot. But now all our hasty creatures can't be blocked! That means we can't use combat damage to trigger Arcbond. That opens up layers from additional combats.
Hmmm... analyzing the sequence, it looks like the Blighted Steppe / Arbiter of the Ideal start is pretty darn good, getting an extra two layers over the usual one layer per card. After that, it is all one layer per card. Of course, we have the ineffiencies with the two support cards. Harmonic Prodigy supports two cards, Arbiter of the Ideal and Brallin, Skyshark Rider, and as we noted the start with Arbiter of the Ideal is quite good. Kaboom! seems ripe for replacement, even if we lose the ability to mine opponent's life.
Looking for further improvements, in addition to the inefficiency of needing Harmonic Prodigy as a support card, I believe Reality Twist is only used to provide mana for [c}Avacyn Guardian Angel[/c] and Blighted Steppe. So, if we can integrate white mana into the layer sequence, we can drop Reality Twist. But again, the Blighted Steppe start is really nice.
Then, there is the possibility of getting more than one layer per card, as we see with Blighted Steppe, and we previously saw with Black Lotus aided by Dual Nature and Doubling Season. Creating Clue tokens seems to be a nice possibility for a double layer. Search the Premises should get us two layers; unfortunately, it hooks directly from combat to our drawing, so even if we add World at War, we only get 9 layers.
I was thinking maybe we could replace Mana Crypt and Reality Twist with Mox Pearl. I guess the problem is donating it to the opponent and allowing them to activate Avacyn, Guardian Angel. It seems like it should be possible to replace Avacyn and Amulet of Safekeeping with another pair of cards - perhaps one card to keep the opponent's life total up, and one to preserve our own life total. It's the first card that seems to be the problem. A creature with lifelink can give the opponent a lot of life, but it won't be able to save the opponent from Kaervek's Spite after a Worldfire. Whereas, something like Solider of the Pantheon can gain the opponent life, but it won't gain them enough for the computation.
Another possibility is simply a replacement for Avacyn, but I haven't found one yet.
A lifelinker would have no problem keeping the opponent alive. The Kaervek's Spite always resolves after our BB computations, because those get triggered from the sacrifice cost when we put the spell on the stack.
Adding World at War we would get BB_{w^2+11}(BB_{w^2+10}(X)) damage. X would be rather small because it's the number of Moraug, Fury of Akoum triggers we get in the first main phase. That means we only get that one big draw from the first Prosperity to try and get that as high as possible, while also making sure that we can continue to draw the deck once we go to the combats.
Oh, excellent! We got the entire sequence we were aiming for.
A couple of things I noted: Since Battle Hymn recovers our progress after a Worldpurge, we don't need Dark Ritual to do so. So, we could perhaps replace Dark Ritual with something like Witch Engine, if it worked out better. Also, since we need red mana to give Master Transmuter haste, there isn't an infinite from Doubling Season, so we could put that in if it helped. Unfortunately, it doesn't seem to add a layer anywhere - For Blighted Steppe and the counters of Night Dealings, the layer that we get from Doubling Season doesn't stack with what we already get from Rings of Brighthearth, because we have to activate everything before they get destroyed by Worldpurge et al. Same for any Clue tokens we would generate I believe. Since the deck is full, there's no room for Doubling Season.
Maximizing the start should be interesting. It doesn't look like we have a way to reacquire Prosperity or draw in some other way prior to the combat phases. So, we can get the up to 19 cards we get from Prosperity, and maybe mill a few cards due to Gravebreaker Lamia. We could try to save some life to pay for Acorn Harvest, but at 3 life per cast, that's a pretty steep price at this point. There is also the question of whether we want to try to do a BB computation this early... perhaps it's just not possible with the amount of resources we have access to at this point.
Edit: Hmmm, mana is kind of a pain in the start. We blew our blue mana cards at the beginning, so I don't see how we would get blue mana now. That keeps us from copying Panharmonicon beyond the two Mirrorworks triggers we get when we play it. It also seems to kill the idea of replacing Tolarian Kraken with Gridlock or Glimpse of the Sun God to get some usage out of Arbiter of the Ideal at the beginning.
We also need some mana at the beginning for the Panharmonicon copies - could we replace Vedalken Orrery with Leyline of Anticipation? I would like to use it to have another creature on the battlefield, for an early Battle Hymn. (it still seems like a waste of a Battle Hymn, but I'm having trouble getting early mana.)
Edit: Quick rules question: If I use Eureka to put Radiant Fountain and Stomping Ground onto the battlefield, can I gain the life from Radiant Fountain before having to pay the cost for Stomping Ground?
Edit: Oh, there's a problem. With the current start, we don't have any blue mana after we cast Prosperity for the first time. I don't see how to get any more blue mana, other than by exiling the Mox Sapphire, putting it into the library with Riftsweeper, and either drawing it or fetching it with Arbiter of the Ideal or Night Dealings. But, to do any of those, we need to attack with a creature first. Right now, we need to activate Marchesa's Smuggler, which requires a blue mana. So we're kind of stuck, I think.
One possibility is to use Break through the Line rather than Marchesa's Smuggler, but that unfortunately that can't target Myr Battleshpere. I was contemplating perhaps replacing Safe Passage with something that doesn't completely prevent damage to ourselves, but the only creature I saw that dealt 3+ damage to ourselves was Hasran Ogress, which also has 3+ power.
I think the key play to address the blue mana issue for the start is casting Worldpurge with Eureka on the stack. Getting Omniscience back into play immediately and also resetting Tolarian Academy and Mox Sapphire. I haven't gone through it further, but it seems to me that it should be possible to continue.
If mana at the start turns out to be the bottleneck, then we can play a second Battle Hymn instead of Brightstone Ritual.
For Eureka, Radiant Fountain and Stomping Ground: I don't think you can gain the life before paying for Stomping grounds. The payment on that is part of a replacement effect that happens during Eureka's resolution. Radiant Fountain's lifegain is a trigger and goes on the stack after Eureka finishes resolving.
Play Vedalken Orrery. (1 card used)
Cast Eureka. (2 cards used)
Respond by casting Worldpurge. (3 cards used)
Respond by playing Wormfang Behemoth, exiling our hand.
Resolve Worldpurge, bringing Omniscience, Mox Pearl, Mox Sapphire, Tolarian Academy, Vedalken Orrery, and Wormfang Behemoth back to our hand.
Wormfang Behemoth triggers, and brings 16 other cards back to our hand.
Eureka resolves, put into play:
Moraug, Fury of Akoum (4 cards used)
Omniscience
Mox Pearl
Mox Sapphire
Vedalken Orrery
Play Mirrorworks. (5 cards used)
Play Opalescence. (6 cards used)
Play Gravebreaker Lamia, mill Acorn Harvest (7 cards used)
Play Marchesa's Smuggler. (8 cards used)
Play Night Dealings. (9 cards used)
Play Battle Hymn, get 5 red mana. (10 cards used)
Play Panharmonicon, pay for 2 copies. (11 cards used)
Play Dual Nature, get 4 copies. (12 cards used)
Play Harmonic Prodigy, get 20 copies. (13 cards used)
Play Artificial Evolution, turning Moraug into a Wizard or Shaman. (14 cards used)
Play Spellweaver Helix, imprinting Acorn Harvest, Eureka, Prosperity, and 1 or 3 of the other sorceries. (15 cards used)
Play Acorn Harvest, triggering Spellweaver Helix (16 cards used)
Put Tolarian Academy, Vault of Whispers into play. (17 cards used, 47 Moraug triggers)
Tap Mox Sapphire, Mox Pearl, Vault of Whispers for mana. (1 red, 1 blue, 1 white, 1 black mana)
Pay for two copies of Vault of Whispers. (97 Moraug triggers)
Play Riftsweeper, get 20 copies. Shuffle Acorn Harvest, Eureka, Prosperity, and 1 or 3 of the other sorceries into the library. (18 cards)
Have Battle Hymn remaining in hand.
End precombat main phase, get 98 combat phases.
Enter first combat phase.
Cast Battle Hymn for 52 red mana.
Tap Tolarian Academy for 11 blue mana.
Pay a blue and two red to give a Gravewalker Lamia haste. Attack with it. (5 life, opponent 16 life, 50 red, 10 blue)
Put 4 Theft tokens on Night Dealings.
Tap the Vaults for 2 black mana.
Pay 2 red and 2 black, and remove a Theft token to fetch Prosperity. (48 red, 10 blue, 3 Theft tokens left)
Prosperity. (We have 38 or 40 cards left in our library, depending on what Spellweaver Helix imprinted.)
We should continue this, but with access to our entire deck now, and some spare mana to keep us going, we should be able to continue, and attack with more than 97 Myr Battlespheres next combat phase. So this should get us to BB_{w^2+11}(BB_{w^2+10}(97)).
Can we do better?
Edit: An improved start:
Play Vedalken Orrery (1 card used)
Play Opalescence (2 cards used)
Play Dual Nature (3 cards used)
Play Gravebreaker Lamia, get 2 copies, mill Acorn Harvest, Eureka, and Worldpurge. (4 cards used.)
Play Panharmonicon (5 cards used)
Play Spellweaver Helix, imprint Acorn Harvest, Eureka, Worldpurge, and Show and Tell. (6 cards used)
Play Acorn Harvest, triggering Spellweaver Helix (7 cards used)
Play Wormfang Behemoth, exiling our hand. (8 cards used)
Resolve Worldpurge. Return Omniscience, Mox Sapphire, Tolarian Academy, Vedalken Orrery, Opalescence, Dual Nature, and Panharmonicon to our hand. Gravebreaker Lamia, Spellweaver Helix, Wormfang Behemoth, and Mox Pearl get shuffled into the library.
Wormfang Behemoth triggers, returning our other cards back to our hand.
Resolve Eureka, put Omniscience and Vedalken Orrery back into play.
Play Mirrorworks. (9 cards used, 2 artifacts)
Play Opalescence.
Play Panharmonicon, getting two Mirrorworks triggers.
Play Dual Nature, getting two copies.
Play Moraug, getting copies that die. (10 cards used, 5 creatures)
Play Marchesa's Smuggler, getting 6 copies. (11 cards used, 12 creatures)
Play Night Dealings, getting 6 copies. (12 cards used, 19 creatures)
Play Master Transmuter, getting 6 copies. Ignore the Mirrorworks triggers. (13 cards used, 26 creatures)
Play Battle Hymn, get 26 red mana. (14 cards used, 26 red mana)
Pay for the two Panharmonicon triggers. (22 red mana, 5 artifacts)
Play Harmonic Prodigy, get 12 copies. (15 cards used)
Play Artificial Evolution, turn Moraug into a Wizard or Shaman. (16 cards used)
Resolve Show and Tell, put Tolarian Academy into play. (16 cards used, 14 Moraug triggers)
Play Mox Sapphire, pay for 4 copies, tap for mana. (16 cards used, 5 blue mana, 14 red mana, 10 artifacts)
Activate Marchesa's Smuggler to give a Master Transmuter haste (4 blue mana, 12 red mana)
Activate Master Transmuter, bounce Mox Sapphire, put Vault of Whispers into play. (17 cards used, 3 blue mana, 12 red mana, 31 Moraug triggers, 10 artifacts)
Pay for 4 copies of Vault of Whispers. Tap the Vaults for mana. (1 blue mana, 6 red mana, 5 black mana, 99 Moraug triggers, 14 artifacts)
Play Mox Sapphire, pay for 4 copies, tap 3 for mana. (1 blue mana, 6 red mana, 19 artifacts)
Tap Tolarian Academy for 19 blue mana. (20 blue mana, 6 red mana, 99 Moraug triggers)
Activate Marchesa's Smuggler and Master Trasmuter to bounce and replay Vault of Whispers, pay for 4 copies and tap them. (13 blue mana, 5 red mana, 1 black mana, 184 Moraug triggers)
Activate Marchesa's Smuggler and Master Trasmuter to bounce and replay Vault of Whispers, pay for 4 copies and tap them. (7 blue mana, 4 red mana, 1 black mana, 269 Moraug triggers)
Activate Marchesa's Smuggler and Master Trasmuter to bounce and replay Vault of Whispers, pay for 4 copies. (0 mana, 354 Moraug triggers)
We have Battle Hymn and Riftsweeper in our hand.
End precombat main phase, get 355 combat phases.
Cast Battle Hymn, get 39 red mana.
Tap two Mox Sapphire for 2 blue mana.
Give a Night Dealings haste and attack. (37 red mana, 1 blue mana) (I'm not sure which creature to attack with, Moraug gets us more Theft tokens, but we might want to save our opponent's life.)
Each Night Dealings gets 5 Theft tokens.
Tap 5 Vault of Whispers for mana. (37 red mana 1 blue mana, 5 black mana)
Use Night Dealings to fetch Spellweaver Helix. (35 red mana, 1 blue mana, 3 black mana)
Play Spellweaver Helix, exile Prosperity and Acorn Harvest.
Play Riftsweeper, get 12 copies, shuffle all our exiled cards into our library.
Use Night Dealings to fetch Prosperity. (33 red mana, 1 blue mana, 1 black mana)
Cast Prosperity for up to 34.
I'm hoping we can get going with this Prosperity cast, we get most but not all of the deck. The biggest issue seems to be we don't get red mana anymore without Worldfire, but we should be able to incorporate Worldfire now?
Edit: Improved the start more. Got pretty greedy; I got 1795 combat phases, but we have to see whether we can continue with a Prosperity for up to 9.
Play Vedalken Orrery (1 card used)
Play Opalescence (2 cards used)
Play Dual Nature (3 cards used)
Play Gravebreaker Lamia, get 2 copies, mill Acorn Harvest, Eureka, and Worldpurge. (4 cards used.)
Play Panharmonicon (5 cards used)
Play Spellweaver Helix, imprint Acorn Harvest, Eureka, Worldpurge, and Show and Tell. (6 cards used)
Play Acorn Harvest, triggering Spellweaver Helix (7 cards used)
Play Wormfang Behemoth, exiling our hand. (8 cards used)
Resolve Worldpurge. Return Omniscience, Mox Sapphire, Tolarian Academy, Vedalken Orrery, Opalescence, Dual Nature, and Panharmonicon to our hand. Gravebreaker Lamia, Spellweaver Helix, Wormfang Behemoth, and Mox Pearl get shuffled into the library.
Wormfang Behemoth triggers, returning our other cards back to our hand.
Resolve Eureka, put Omniscience and Vedalken Orrery back into play.
Play Mirrorworks. (9 cards used, 2 artifacts)
Play Opalescence.
Play Moraug, Fury of Akoum. (10 cards used, 2 creatures)
Play Marchesa's Smuggler. (11 cards used, 3 creatures)
Play Night Dealings. (12 cards used, 4 creatures)
Play Battle Hymn, getting 4 red mana. (13 cards used, 4 red mana, 4 creatures)
Play Panharmonicon, and pay for two Mirrorworks triggers. (13 cards used, 0 red mana, 4 creatures, 5 artifacts)
Play Dual Nature, getting four copies. (13 creatures used, 0 mana, 9 creatures, 5 artifacts)
Play Master Transmuter, getting 20 copies. Ignore the Mirrorworks triggers. (14 cards used, 30 creatures, 26 artifacts)
Play Harmonic Prodigy, get 20 copies. (15 cards used, 51 creatures, 26 artifacts)
Play Artificial Evolution, turn Moraug into a Wizard or Shaman. (16 cards used, 51 creatures, 26 artifacts)
Play Wood Elves, get 20 copies, fetch Stomping Ground from the library and put it in play. (17 cards, 72 creatures, 26 artifacts, 22 Moraug triggers)
Resolve Show and Tell, put Tolarian Academy into play. (17 cards used, 72 creatures, 26 artifacts, 44 Moraug triggers)
Play Battle Hymn, getting 72 red mana. (18 cards used, 72 red mana, 26 artifacts, 44 Moraug triggers)
Play Mox Sapphire, pay for 4 copies, tap for mana. (18 cards used, 5 blue mana, 64 red mana, 31 artifacts, 44 Moraug triggers)
Activate Marchesa's Smuggler to give a Master Transmuter haste (4 blue mana, 62 red mana)
Activate Master Transmuter, bounce Mox Sapphire, put Vault of Whispers into play. (18 cards used, 3 blue mana, 62 red mana, 31 artifacts, 69 Moraug triggers, 20 Master Transmuters)
Pay for 4 copies of Vault of Whispers. Tap the Vaults for mana. (3 blue mana, 58 red mana, 1 black mana, 35 artifacts, 169 Moraug triggers)
Play Mox Sapphire, pay for 4 copies, tap for mana. (8 blue mana, 50 red mana, 1 black mana, 40 artifacts, 169 Moraug triggers)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. (6 blue mana, 45 red mana, 1 black mana, 44 artifacts, 294 Moraug triggers, 19 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. (4 blue mana, 40 red mana, 1 black mana, 48 artifacts, 419 Moraug triggers, 18 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. (2 blue mana, 35 red mana, 1 black mana, 52 artifacts, 544 Moraug triggers, 17 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Mox Sapphire, pay for 4 copies, tap 4 of them. (4 blue mana, 25 red mana, 1 black mana, 56 artifacts, 544 Moraug triggers, 16 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. (2 blue mana, 20 red mana, 1 black mana, 60 artifacts, 669 Moraug triggers, 15 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. (0 blue mana, 15 red mana, 1 black mana, 64 artifacts, 794 Moraug triggers, 14 Master Transmuters)
Tap Tolarian Academy for 64 blue mana.
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. (58 blue mana, 14 red mana, 1 black mana, 919 Moraug triggers, 13 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. (52 blue mana, 13 red mana, 1 black mana, 1044 Moraug triggers, 12 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. (46 blue mana, 12 red mana, 1 black mana, 1169 Moraug triggers, 11 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. Do not tap the Vault copies (37 blue mana, 11 red mana, 1294 Moraug triggers, 10 Master Transmuters, 4 untapped Vaults)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. Do not tap the Vault copies (28 blue mana, 9 red mana, 1419 Moraug triggers, 9 Master Transmuters, 8 untapped Vaults)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. Do not tap the Vault copies. (19 blue mana, 7 red mana, 1544 Moraug triggers, 8 Master Transmuters, 12 untapped Vaults)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. Do not tap the Vault copies. (10 blue mana, 5 red mana, 1669 Moraug triggers, 7 Master Transmuters, 16 untapped Vaults)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. Do not tap any Vaults. (2 blue mana, 1 red mana, 1794 Moraug triggers, 6 Master Transmuters, 21 untapped Vaults)
Spend the remaining mana to give Moraug, Fury of Akoum haste.
End the precombat main phase, we get 1795 combat phases.
Begin the first combat phase.
Attack with Moraug, the Night Dealings gets 7 Thief counters.
Tap 12 untapped Vaults.
Use Night Dealings to fetch Spellweaver Helix. Play it to imprint Prosperity and Acorn Harvest.
Use Night Dealings to fetch Riftsweeper. Play it and shuffle our exiled cards into our library.
Use Night Dealings to fetch Prosperity.
Tap Mox Sapphire.
Prosperity for up to 9.
Edit: Even greedier, gets 2045 combat phases, but can only Prosperity for 6.
Play Vedalken Orrery (1 card used)
Play Opalescence (2 cards used)
Play Dual Nature (3 cards used)
Play Gravebreaker Lamia, get 2 copies, mill Acorn Harvest, Eureka, and Worldpurge. (4 cards used.)
Play Panharmonicon (5 cards used)
Play Spellweaver Helix, imprint Acorn Harvest, Eureka, Worldpurge, and Show and Tell. (6 cards used)
Play Acorn Harvest, triggering Spellweaver Helix (7 cards used)
Play Wormfang Behemoth, exiling our hand. (8 cards used)
Resolve Worldpurge. Return Omniscience, Mox Sapphire, Tolarian Academy, Vedalken Orrery, Opalescence, Dual Nature, and Panharmonicon to our hand. Gravebreaker Lamia, Spellweaver Helix, Wormfang Behemoth, and Mox Pearl get shuffled into the library.
Wormfang Behemoth triggers, returning our other cards back to our hand.
Resolve Eureka, put Omniscience and Vedalken Orrery back into play.
Play Mirrorworks. (9 cards used, 2 artifacts)
Play Opalescence.
Play Moraug, Fury of Akoum. (10 cards used, 2 creatures)
Play Marchesa's Smuggler. (11 cards used, 3 creatures)
Play Night Dealings. (12 cards used, 4 creatures)
Play Battle Hymn, getting 4 red mana. (13 cards used, 4 red mana, 4 creatures)
Play Panharmonicon, and pay for two Mirrorworks triggers. (13 cards used, 0 red mana, 4 creatures, 5 artifacts)
Play Dual Nature, getting four copies. (13 creatures used, 0 mana, 9 creatures, 5 artifacts)
Play Master Transmuter, getting 20 copies. Ignore the Mirrorworks triggers. (14 cards used, 30 creatures, 26 artifacts)
Play Harmonic Prodigy, get 20 copies. (15 cards used, 51 creatures, 26 artifacts)
Play Artificial Evolution, turn Moraug into a Wizard or Shaman. (16 cards used, 51 creatures, 26 artifacts)
Play Wood Elves, get 20 copies, fetch Stomping Ground from the library and put it in play. (17 cards, 72 creatures, 26 artifacts, 22 Moraug triggers)
Resolve Show and Tell, put Tolarian Academy into play. (17 cards used, 72 creatures, 26 artifacts, 44 Moraug triggers)
Play Battle Hymn, getting 72 red mana. (18 cards used, 72 red mana, 26 artifacts, 44 Moraug triggers)
Play Mox Sapphire, pay for 4 copies, tap for mana. (18 cards used, 5 blue mana, 64 red mana, 31 artifacts, 44 Moraug triggers)
Activate Marchesa's Smuggler to give a Master Transmuter haste (4 blue mana, 62 red mana)
Activate Master Transmuter, bounce Panharmonicon, put Vault of Whispers into play. (18 cards used, 3 blue mana, 62 red mana, 31 artifacts, 69 Moraug triggers, 20 Master Transmuters)
Pay for 4 copies of Vault of Whispers. Tap the Vaults for mana. (3 blue mana, 58 red mana, 1 black mana, 35 artifacts, 169 Moraug triggers)
Play Panharmonicon, pay for 4 copies. (3 blue mana, 50 red mana, 1 black mana, 40 artifacts, 169 Moraug triggers)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Mox Sapphire, pay for 8 copies, tap 8 Moxen. (9 blue mana, 32 red mana, 1 black mana, 48 artifacts, 169 Moraug triggers, 19 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. Tap Vaults for mana. (7 blue mana, 23 red mana, 1 black mana, 56 artifacts, 394 Moraug triggers, 18 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (5 blue mana, 14 red mana, 1 black mana, 64 artifacts, 619 Moraug triggers, 17 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (0 blue mana, 8 red mana, 1 black mana, 72 artifacts, 844 Moraug triggers, 16 Master Transmuters)
Tap Tolarian Academy for 72 blue mana.(72 blue mana, 8 red mana, 1 black mana, 72 artifacts, 844 Moraug triggers, 16 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (62 blue mana, 7 red mana, 1 black mana, 80 artifacts, 1069 Moraug triggers, 15 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (52 blue mana, 6 red mana, 1 black mana, 88 artifacts, 1294 Moraug triggers, 14 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (42 blue mana, 5 red mana, 1 black mana, 96 artifacts, 1519 Moraug triggers, 13 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. Do not tap Vault copies. (24 blue mana, 4 red mana, 1 black mana, 104 artifacts, 1744 Moraug triggers, 12 Master Transmuters, 8 untapped Vaults)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (6 blue mana, 3 red mana, 1 black mana, 112 artifacts, 1969 Moraug triggers, 11 Master Transmuters, 16 untapped Vaults)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 2 copies, tap 1 for mana (1 blue mana, 1 red mana, 1 black mana, 114 artifacts, 2044 Moraug triggers, 10 Master Transmuters, 18 untapped Vaults)
Spend the remaining mana to give Moraug, Fury of Akoum haste.
End the precombat main phase, we get 2045 combat phases.
Begin the first combat phase.
Attack with Moraug, the Night Dealings gets 7 Thief counters.
Tap 12 untapped Vaults.
Use Night Dealings to fetch Spellweaver Helix. Play it to imprint Prosperity and Acorn Harvest.
Use Night Dealings to fetch Riftsweeper. Play it and shuffle our exiled cards into our library.
Use Night Dealings to fetch Prosperity.
Tap Mox Sapphire.
Prosperity for up to 6.
Edit: Another improvement, 2448 combat phases, Prosperity for up to 5.
Play Vedalken Orrery (1 card used)
Play Opalescence (2 cards used)
Play Dual Nature (3 cards used)
Play Gravebreaker Lamia, get 2 copies, mill Acorn Harvest, Eureka, and Worldpurge. (4 cards used.)
Play Panharmonicon (5 cards used)
Play Spellweaver Helix, imprint Acorn Harvest, Eureka, Worldpurge, and Show and Tell. (6 cards used)
Play Acorn Harvest, triggering Spellweaver Helix (7 cards used)
Play Wormfang Behemoth, exiling our hand. (8 cards used)
Resolve Worldpurge. Return Omniscience, Mox Sapphire, Tolarian Academy, Vedalken Orrery, Opalescence, Dual Nature, and Panharmonicon to our hand. Gravebreaker Lamia, Spellweaver Helix, Wormfang Behemoth, and Mox Pearl get shuffled into the library.
Wormfang Behemoth triggers, returning our other cards back to our hand.
Resolve Eureka, put Omniscience and Vedalken Orrery back into play.
Play Mirrorworks. (9 cards used, 2 artifacts)
Play Opalescence.
Play Moraug, Fury of Akoum. (10 cards used, 2 creatures)
Play Marchesa's Smuggler. (11 cards used, 3 creatures)
Play Night Dealings. (12 cards used, 4 creatures)
Play Battle Hymn, getting 4 red mana. (13 cards used, 4 red mana, 4 creatures)
Play Panharmonicon, and pay for two Mirrorworks triggers. (13 cards used, 0 red mana, 4 creatures, 5 artifacts)
Play Dual Nature, getting four copies. (13 creatures used, 0 mana, 9 creatures, 5 artifacts)
Play Master Transmuter, getting 20 copies. Ignore the Mirrorworks triggers. (14 cards used, 30 creatures, 26 artifacts)
Play Harmonic Prodigy, get 20 copies. (15 cards used, 51 creatures, 26 artifacts)
Play Artificial Evolution, turn Moraug into a Wizard or Shaman. (16 cards used, 51 creatures, 26 artifacts)
Play Myr Battlesphere, get 20 copies. (17 cards, 72 creatures, 47 artifacts, 22 Moraug triggers)
Resolve Show and Tell, put Tolarian Academy into play. (17 cards used, 72 creatures, 47 artifacts, 22 Moraug triggers)
Play Battle Hymn, getting 72 red mana. (18 cards used, 72 red mana, 47 artifacts, 22 Moraug triggers)
Play Mox Sapphire, pay for 4 copies, tap for mana. (18 cards used, 5 blue mana, 64 red mana, 52 artifacts, 22 Moraug triggers)
Activate Marchesa's Smuggler to give a Master Transmuter haste (4 blue mana, 62 red mana)
Activate Master Transmuter, bounce Panharmonicon, put Vault of Whispers into play. (18 cards used, 3 blue mana, 62 red mana, 52 artifacts, 47 Moraug triggers, 20 Master Transmuters)
Pay for 4 copies of Vault of Whispers. Tap the Vaults for mana. (3 blue mana, 58 red mana, 1 black mana, 56 artifacts, 147 Moraug triggers)
Play Panharmonicon, pay for 4 copies. (3 blue mana, 50 red mana, 1 black mana, 61 artifacts, 147 Moraug triggers)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Mox Sapphire, pay for 8 copies, tap 8 Moxen. (9 blue mana, 32 red mana, 1 black mana, 69 artifacts, 147 Moraug triggers, 19 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. Tap Vaults for mana. (7 blue mana, 23 red mana, 1 black mana, 77 artifacts, 372 Moraug triggers, 18 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (5 blue mana, 14 red mana, 1 black mana, 85 artifacts, 597 Moraug triggers, 17 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 7 copies. (0 blue mana, 9 red mana, 1 black mana, 92 artifacts, 797 Moraug triggers, 16 Master Transmuters)
Tap Tolarian Academy for 92 blue mana.(92 blue mana, 9 red mana, 1 black mana, 93 artifacts, 797 Moraug triggers, 16 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (82 blue mana, 8 red mana, 1 black mana, 1022 Moraug triggers, 15 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (72 blue mana, 7 red mana, 1 black mana, 1247 Moraug triggers, 14 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (62 blue mana, 6 red mana, 1 black mana, 1472 Moraug triggers, 13 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (52 blue mana, 5 red mana, 1 black mana, 1697 Moraug triggers, 12 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (42 blue mana, 4 red mana, 1 black mana, 1922 Moraug triggers, 11 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. Do not tap Vault copies. (25 blue mana, 3 red mana, 2147 Moraug triggers, 10 Master Transmuters, 8 untapped Vaults)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. Do not tap Vault copies. (7 blue mana, 2 red mana, 2372 Moraug triggers, 9 Master Transmuters, 16 untapped Vaults)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 2 copies. Tap 2 Vaults. (2 blue mana, 1 red mana, 2447 Moraug triggers, 9 Master Transmuters, 17 untapped Vaults)
Spend the remaining mana to give Moraug, Fury of Akoum haste.
End the precombat main phase, we get 2448 combat phases.
Begin the first combat phase.
Attack with Moraug, the Night Dealings gets 7 Thief counters.
Tap 12 untapped Vaults.
Use Night Dealings to fetch Spellweaver Helix. Play it to imprint Prosperity and Acorn Harvest.
Use Night Dealings to fetch Riftsweeper. Play it and shuffle our exiled cards into our library.
Use Night Dealings to fetch Prosperity.
Tap Mox Sapphire.
Prosperity for up to 5.
Play Mox Pearl, Mox Sapphire, Tolarian Academy, tap them. (3u, 1w, 4 cards)
Play Show and Tell, put Omniscience into play. (1u, 2 cards)
Play Channel, convert 19 life into mana. (1u, 19c, 1 card)
Play Prosperity with X=19. (19 cards)
Play Vedalken Orrery. (18 cards)
Play Mirrorworks. (17 cards)
Play Panharmonicon. Leave 2 Mirrorwork triggers on the stack (16 cards)
Play Opalescence. (15 cards)
Play Dual Nature, get 2 copies. (14 cards)
Play Sea Gate Stormcaller. 3 Dual Natures trigger 2 times each. 7 Sea Gate Stormcaller enter the battlefield, each triggering 2 times. Create 14 delayed triggers. (13 cards)
Play Gravebreaker Lamia. Leave 1 Dual Nature Trigger and 2 etb triggers on the stack. Resolve 10 etb triggers from the copies and put 10 cards into the graveyard. Among them: Mystical Teachings, Riftsweeper, Siege of Towers, Mobilize, 2x Acorn Harvest and Wood Elves. (12 cards)
Play Eureka, leave it on the stack. (11 cards)
Play Worldpurge, leave it on the stack. (10 cards)
Play Wormfang Behemoth, let it exile your hand. (9 cards exiled)
Resolve Worldpurge. It bounces Mox Pearl, Mox Sapphire, Tolarian Academy, Omniscience, Vedalken Orrery, Mirrorworks, Panharmonicon, Opalescence, Dual Nature, Sea Gate Stormcaller, Gravebreaker Lamia and Wormfang Behemoth. Shuffle Mox Pearl, Mox Sapphire, Sea Gate Stormcaller, Gravebreaker Lamia and Wormfang Behemoth into the library.
Wormfang Behemoth trigger returns the exiled cards to hand. (16 cards)
Resolve Eureka, put Omniscience, Vedalken Orrery, Tolarian Academy, Mirrorworks, Opalescence, Vault of Whispers, Spellweaver Helix, Rings of Brighthearth and Blighted Steppe into play. (7 cards)
Resolve the Gravebreaker Lamia triggers. Put Gravebreaker Lamia and Sea Gate Stormcaller into the graveyard. (7 cards)
Play Panharmonicon. Leave 2 Mirrorwork triggers on the stack. (1 PH, 6 cards)
Play Dual Nature, get 2 copies (1 PH, 5 cards)
Play Myr Battlesphere, get 6 copies, create 56 myr tokens. (1 PH, 4 cards)
Tap Tolarian Academy for mana. We have 69 artifacts. (1 PH, 4 cards, 69u)
Pay for the 4 Mirrorworks(Panharmonicon) triggers. (5 PH, 4 cards, 61u)
Tap Vault of Whispers to flashback Mystical Teachings and fetch Battly Hymn. (5 PH, 5 cards, 56u)
Play The Scarab God. Get 18 Dual Nature copies. (5 PH, 4 cards, 56u)
Play Marchesa's Smuggler. Get 18 Dual Nature copies. (5 PH, 3 cards, 56u)
Play Master Transmuter. Get 18 Dual Nature copies. (5 PH, 2 cards, 56u)
Play Night Dealings. Get 18 Dual Nature copies. (5 PH, 1 card, 56u)
Play Battle Hymn. Get 14 copies from Sea Gate Stormcaller triggers. (5 PH, 56u)
Resolve the first Battly Hymn copy. We have 143 creatures. (5 PH, 56u, 143r)
Use the mana to create more Panharmonicons: Marchesa's Smuggler gives haste to a Master Transmuter. Master transmuter returns Panharmonicon to hand. Replay it and pay for Mirrorworks triggers.
1st time costs 2u,1r,1c for 5 Mirrorworks triggers. Pay for them. (10 PH, 54u, 131r)
2nd time costs 2u,1r,1c for 10 Mirrorworks triggers. Pay for them. (20 PH, 52u, 109r)
3rd time costs 2u,1r,1c for 20 Mirrorworks triggers. Pay for them. (40 PH, 50u, 67r)
4th time costs 2u,1r,1c for 40 Mirrorworks triggers. Pay for them. (80 PH, 16u, 17r)
5th time costs 2u,1r,1c for 80 Mirrorworks triggers. Pay for 22 of them. (102 PH, 4u, 3r)
Use Marchesa's Smuggler + Master Transmuter to bounce Myr Battlesphere. Dual Nature exiles the token copies. (102 PH, 2u, 1r)
Play Myr Battlesphere. Don't pay for the Mirrorworks triggers. Dual Nature triggers 3*103 times for a total of 310 Myr Battlespheres entering the battlefield. Each one triggers its etb 103 times and we create 127720 Myrs. (102 PH, 2u, 1r)
Resolve a Battle Hymn copy. The Number of creatures is big enough that I'm going to start estimating. The last step gave us over 128000 creatures. Let's go with that. (102 PH, 2u, >128000r)
Use Marchesa's Smuggler + Master Transmuter to bounce Vault of Whispers. Put it back into play. Pay for 1 copy. (102 PH, >128000r)
Tap the Vault of Whispers to activate Night Dealings. Find Mox Sapphire. (102 PH, >128000r)
Play Mox Sapphire. Pay for some copies. Tap them. We need roughly 2*log_2(red mana) of them so about 36... not enough to make a dent in our red mana estimate. (102 PH, >128000r, ~36u)
Now turn the red mana into Panharmonicon copies again. We need to pay 2r per copy plus some overhead to generate new triggers, plus some overhead overhead to generate more blue mana and untapped Master Transmuters. The overhead is roughly at log_2 of the red mana, so we can keep ignoring that for the estimate.
After spending most of the mana we have 64000 Panharmonicons. (>64000 PH, 4u, 2r)
Use the last mana to bounce and replay Myr Battlesphere. We get (1+DN*PH)*(1+PH)*4 Myrs. (>64000 PH, 2u)
Resolve another Battle Hymn. If we have X Panharmonicons we get >12*X^2 mana.
Turn the mana into more Panharmonicons. We get more than >6*X^2 copies. So 6*64000^2 > 2^2*64000^2 = 128000^2 > (2^16)^2 = 2^32
Repeat for the other 12 Battle Hymn copies on the stack. Get a huge amount of anything we can create here: Panharmonicons, other artifacts, red mana, blue mana, black mana and white mana (Night Dealings can fetch Mox Pearl)
How much? We more than square the number of Panharmonicons 12 more times, so we get more than (2^32)^(2^12) = 2^(32*2^12) > 2^(2^4*2^12) = 2^(2^16) = 2^^5
Specifically we turn most of those resources into Panharmonicon copies, leaving just enough operating mana to get through the next few steps.
Activate The Scarab God to create a copy of Sea Gate Stormcaller. Get >2^^5 delayed triggers.
Activate The Scarab God to create a copy of Gravebreaker Lamia. Leave the triggers on the stack.
Activate The Scarab God to create a copy of Riftsweeper. Put the exiled creatures and Mystical Teachings back into the library.
Resolve a few Gravebreaker Lamia triggers to put those cards into the graveyard again. Leave the rest on the stack, we don't want to empty our library yet.
Flashback Mystical Teachings and fetch the second Battly Hymn.
Cast Battle Hymn, getting 2^^5 copies.
Again each copy more than squares the number of creatures. We end up with more than 2^(2^(2^^5)) = 2^^7 artifacts.
This time we turn most of those resources into Rings of Brighthearth copies, leaving just enough operating mana to get through the next few steps.
Sacrifice Blighted Steppe, get more than 2^^7 Ring of Brighthearth triggers for the ability.
Pay for one of the Ring of Brighthearth triggers and get 2^^7 life.
Bounce and replay Spellweaver Helix. Exile Siege of Towers, Mobilize and Acorn Harvest.
Activate The Scarab God to create a copy of Sea Gate Stormcaller. Get >2^^7 delayed triggers.
Activate The Scarab God to create a copy of Wood Elves. Find Stomping Ground and pay 2 life to let it come into play untapped. Tap for green.
Flashback Acorn Harvest.
Spellweaver Helix triggers. When resolving cast Mobilize first. The Sea Gate Stormcallers trigger and wait to be put on the stack. Then cast Siege of Towers and pay the replicate cost once. Replicate triggers and waits to be put on the stack. After that we finish resolving Spellweaver Helix and put the new triggers on the stack. Order them so that we resolve replicate first.
Resolve replicate and turn Stomping Ground into a creature.
Resolve the >2^^7 Mobilizes to untap Stomping Ground and tap for r/g every time.
Activate The Scarab God to create a copy of Gravebreaker Lamia. Leave the triggers on the stack.
Activate The Scarab God to create a copy of Riftsweeper. Put all the exiled sorceries and creatures back into the library.
Resolve the Gravebreaker Lamia triggers, putting the entire library into the graveyard. (We can't fail to find a card, so unless we get rid of most Panharmonicons the library is now empty. But I don't think that is a problem.)
Turn the mana into more copies of artifacts and creatures again.
Repeat for all of the life we have, each time roughly doubling the number of artifacts. We end up with more than 2^(2^^7) = 2^^8 creatures.
Then we resolve the next copy of the Blighted Steppes ability, this time gaining 2^^8 life, which we turn into 2^(2^^8) = 2^^9 creatures.
After all 2^^7 copies of the Blighted Steppes ability we have more than 2^^(2^^7) artifacts/life/mana. We can also create The Scarab God copies of our creatures in the graveyard.
Create a copy of Moraug, Fury of Akoum.
Bounce Vault of Whispers and put it back onto the battlefield, triggering Moraug, Fury of Akoum 2^^2^^7 times thanks to Panharmonicon copies.
Exile Prosperity with Spellweaver Helix and put it in the library with a Riftsweeper copy. (also put in the Riftsweeper and anything else we want to draw.)
Go to combat with a hasty Myr Battlesphere, attack and damage the opponent with the trigger. Get some counters on Night Dealings.
Activate Night Dealings with X=1 to grab Prosperity. (Get mana from Vault of Whisper and Mox Sapphire copies)
Create a Sea Gate Stormcaller copy to get 2^^2^^7 delayed triggers.
Cast Prosperity with X=1 to draw 1 card 2^^2^^7 times.
I have no doubt we can access the full combo from there
Edit: With the mana from Stomping Ground, we can activate Temur Sabertooth X times, and turn C Dual Natures into C * (PH+2)^X Dual Natures. The problem is that that puts Dual Nature destruction triggers on the stack. But, we can use the opportunity to make permanent copies of other creatures (like Sea Gate Stormcaller, not that those tokens need to be permanent) into play, using the interrupt trick. So, I think we can get triple arrows with your setup.
hmm, using Dual Nature like that is a great idea! I haven't thought about that.
Currently the problem would be that Sea Gate Stormcaller ended up in the graveyard and creating The Scarab God copies of it doesn't take advantage of Dual Nature. Dual Nature also doesn't help to create more Panharmonicons, so I don't see how to turn it into more copies of Mobilize on the next flashback.
To make it work we need Sea Gate Stormcaller in hand. That is probably doable, but requires some shuffling around. We need to have Sea Gate Stormcaller triggers ready when we flashback Acorn Harvest, since without Mobilize copies we only get the one green back that we payed for the flashback.
So either we don't use the Stormcaller before that or we use an extra card in hand for Elvish Spirit Guide and bounce it once. Room in hand after Worldpurge is also tight if we want to sneak in extra Stormcaller triggers from that.
For freeing up the extra card slot I was thinking about skipping Wormfang Behemoth. Most of the cards can be put on the stack before we cast Eureka and Worldpurge, so exiling the hand might be unnecessary. Of course that makes it impossible to react to some triggers, which loses some Panharmonicon copies at the start.
So we'll need to make some early changes and go through everything again to make sure we don't lose too much to get started. But getting that extra layer seems doable
Edit:
Yep, I've successfully modified my start to include the Dual Nature layer:
Play Mox Pearl, Mox Sapphire, Tolarian Academy, tap them. (3u, 1w, 4 cards)
Play Show and Tell, put Omniscience into play. (1u, 2 cards)
Play Channel, convert 19 life into mana. (1u, 19c, 1 card)
Play Prosperity with X=19. (19 cards)
Play Vedalken Orrery. (18 cards)
Play Opalescence. (17 cards)
Play Dual Nature. Leave 2 Dual Nature triggers on the stack. (16 cards)
Play Mirrorworks. (15 cards)
Play Panharmonicon. Leave 2 Mirrorwork triggers on the stack (14 cards)
Play Eureka, leave it on the stack. (13 cards)
Play Worldpurge, leave it on the stack. (12 cards)
Play Wormfang Behemoth, let it exile your hand. (11 cards exiled)
Resolve Worldpurge. It bounces Mox Pearl, Mox Sapphire, Tolarian Academy, Omniscience, Vedalken Orrery, Mirrorworks, Panharmonicon, Opalescence, Dual Nature and Wormfang Behemoth. Shuffle Mox Pearl, Mox Sapphire and Wormfang Behemoth into the library.
Wormfang Behemoth trigger returns the exiled cards to hand. (18 cards)
Resolve Eureka, put Omniscience, Vedalken Orrery, Tolarian Academy, Blighted Steppe, Spellweaver Helix, Rings of Brighthearth, Opalescence, Mirrorworks and Vault of Whispers into play. Leave the Mirrorworks trigger for Vault of Whispers on the stack. (9 cards)
Play Panharmonicon. Leave 2 Mirrorwork triggers on the stack. (1 PH, 8 cards)
Play Dual Nature, get 2 copies (1 PH, 7 cards)
Play Myr Battlesphere, get 6 copies, create 56 myr tokens. (1 PH, 6 cards)
Tap Tolarian Academy for mana. We have 69 artifacts. (1 PH, 6 cards, 69u)
Pay for the 4 Mirrorworks(Panharmonicon) and the Mirrorworks(Vault of Whispers) triggers. (5 PH, 6 cards, 59u)
Resolve the 2 Dual Nature triggers. We now have 5 Dual Natures. (5 PH, 6 cards, 59u)
Play The Scarab God. Get 30 Dual Nature copies. (5 PH, 5 cards, 59u)
Play Master Transmuter. Get 30 Dual Nature copies. (5 PH, 4 cards, 59u)
Play Night Dealings. Get 30 Dual Nature copies. (5 PH, 3 cards, 59u)
Play Sea Gate Stormcaller kicked. Get 30 Dual Nature copies. Each triggers 6 times for a total of 186 delayed triggers, 6 of which are kicked. (5 PH, 2 cards, 54u)
Play Gravebreaker Lamia. Put the 6 etb triggers on the stack first, then the 30 Dual Nature triggers. Resolve 6 Dual Nature triggers, resolving the 30 etb's for the first 5 copies. This leaves us with 7 cards in the library. We fetch 5 of those later, so we can't resolve more etbs to get more Dual Nature copies yet. (5 PH, 1 card, 54u)
Exile Elvish Spirit Guide from hand. Save the green mana for later. I just don't want to keep track of cards in hand anymore ^^ (5 PH, 54u)
Tap one Vault of Whispers to activate The Scarab God and get a copy of Marchesa's Smuggler. (5 PH, 51u)
Tap the other Vault of Whispers to flashback Mystical Teachings and fetch Battle Hymn. (5 PH, 51u)
Play Battle Hymn. Get 192 copies from Sea Gate Stormcaller triggers. (5 PH, 51u)
Resolve the first Battly Hymn copy. We have 201 creatures. (5 PH, 51u, 201r)
Use the mana to create more Panharmonicons: Marchesa's Smuggler gives haste to a Master Transmuter. Master transmuter returns Panharmonicon to hand. Replay it and pay for Mirrorworks triggers.
1st time costs 2u,1r,1c for 5 Mirrorworks triggers. Pay for them. (10 PH, 49u, 189r)
2nd time costs 2u,1r,1c for 10 Mirrorworks triggers. Pay for them. (20 PH, 47u, 167r)
3rd time costs 2u,1r,1c for 20 Mirrorworks triggers. Pay for them. (40 PH, 45u, 125r)
4th time costs 2u,1r,1c for 40 Mirrorworks triggers. Pay for them. (80 PH, 43u, 43r)
5th time costs 2u,1r,1c for 80 Mirrorworks triggers. Pay for 36 of them. (116 PH, 4u, 2r)
Use Marchesa's Smuggler + Master Transmuter to bounce Myr Battlesphere. Dual Nature exiles the token copies. (116 PH, 2u)
Play Myr Battlesphere. Don't pay for the Mirrorworks triggers. Dual Nature triggers 5*117 times for a total of 586 Myr Battlespheres entering the battlefield. Each one triggers its etb 117 times and we create 274284 Myrs. (116 PH, 2u)
Resolve a Battle Hymn copy. The Number of creatures is big enough that I'm going to start estimating. The last step gave us over 270000 creatures. Let's go with that. (116 PH, 2u, >270000r)
Use Marchesa's Smuggler + Master Transmuter to bounce Vault of Whispers. Put it back into play. Pay for 1 copy. (116 PH, >270000r)
Tap the Vault of Whispers to activate Night Dealings. Find Mox Sapphire. (116 PH, >270000r)
Play Mox Sapphire. Pay for some copies. Tap them. We need roughly 2*log_2(red mana) of them so about 40... not enough to make a dent in our red mana estimate. (116 PH, ~40u, >270000r)
Now turn the red mana into Panharmonicon copies again. We need to pay 2r per copy plus some overhead to generate new triggers, plus some overhead overhead to generate more blue mana and untapped Master Transmuters. The overhead is roughly at log_2 of the red mana, so we can keep ignoring that for the estimate.
After spending most of the mana we have more than 135000 Panharmonicons. (>135000 PH, 4u, 2r)
Use the last mana to bounce and replay Myr Battlesphere. We get (1+DN*PH)*(1+PH)*4 Myrs. (>135000 PH, 2u)
Resolve another Battle Hymn. If we have X Panharmonicons we get >20*X^2 mana.
Turn the mana into more Panharmonicons. We get more than >20*X^2 copies. So 20*135000^2 > 4^2*135000^2 = 540000^2 > (2^19)^2 = 2^38
Repeat for the other 190 Battle Hymn copies on the stack. Get a huge amount of anything we can create here: Panharmonicons, other artifacts, red mana, blue mana, black mana and white mana (Night Dealings can fetch Mox Pearl)
How much? We more than square the number of Panharmonicons 190 more times, so we get more than (2^38)^(2^190) = 2^(38*2^190) > 2^(2^5*2^190) = 2^(2^195) > 2^^5
Specifically we turn most of those resources into Panharmonicon copies, leaving just enough operating mana/artifacts to get through the next few steps.
Activate The Scarab God to create a copy of Riftsweeper. Put the exiled creatures and Mystical Teachings back into the library.
Resolve a few Gravebreaker Lamia triggers to put those cards into the graveyard again. Leave the rest on the stack, we still don't want to empty our library.
Flashback Mystical Teachings and fetch the second Battly Hymn.
Activate The Scarab God to create a copy of Temur Sabertooth.
Use the one green mana we still have saved to activate it, getting a Rings of Brighthearth trigger.
Pay for the trigger to bounce Sea Gate Stormcaller.
Play Sea Gate Stormcaller and get 2^^5 delayed triggers.
Resolve the Temur Sabertooth ability to bounce Sea Gate Stormcaller again. We can do that because the ability doesn't target. Keep it in hand for later.
Cast Battle Hymn, getting 2^^5 copies.
Again each copy more than squares the number of creatures. We end up with more than 2^(2^(2^^5)) = 2^^7 artifacts.
This time we turn most of those resources into Rings of Brighthearth copies, leaving just enough operating mana to get through the next few steps.
Sacrifice Blighted Steppe, get more than 2^^7 Ring of Brighthearth triggers for the ability.
Pay for one of the Ring of Brighthearth triggers and get 2^^7 life.
Bounce and replay Spellweaver Helix. Exile Siege of Towers, Mobilize and Acorn Harvest.
Play Sea Gate Stormcaller. Get >2^^7 delayed triggers.
Activate The Scarab God to create a copy of Wood Elves. Find Stomping Ground and pay 2 life to let it come into play untapped. Tap for green. (We have now fetched everything we needed from the library)
Flashback Acorn Harvest.
Spellweaver Helix triggers. When resolving cast Mobilize first. The Sea Gate Stormcallers trigger and wait to be put on the stack. Then cast Siege of Towers and pay the replicate cost once. Replicate triggers and waits to be put on the stack. After that we finish resolving Spellweaver Helix and put the new triggers on the stack. Order them so that we resolve replicate first.
Resolve replicate and turn Stomping Ground into a creature.
Resolve the >2^^7 Mobilizes to untap Stomping Ground and tap for r/g every time.
Use 2 mana to bounce Dual Nature. Leave the token destruction triggers on the stack.
Replay Dual Nature. All Dual Natures trigger many times. The important part is that we more than double the amount of Dual Nature tokens once we resolve all the token creation trigger.
Repeat the last two steps X times to get more than 2^X Dual Natures. Leave just enough operating mana to get through the few steps until more mana is generated.
Bounce and replay Sea Gate Stormcaller to get 2^X delayed triggers.
Let the destructive Dual Nature triggers resolve. We lose all the created creature tokens, but those are not important anymore.
Activate The Scarab God to create a copy of Riftsweeper. Put the exiled Acorn Harvest and Riftsweeper back into the library.
Bounce and replay Gravebreaker Lamia to put the library back into the graveyard.
Pay 3 life to flashback Acorn Harvest again, triggering a cast of Mobilize with 2^X copies, giving us 2^X mana.
Repeat the last few steps. First repeat gets us to 2^(2^^7)=2^^8, second to 2^(2^^8)=2^^9. After 2^^7 repeats we get 2^^(2^^7). In general we can turn X life into 2^^X mana/artifacts/creatures/enchantments.
Specifically we want creatures because we still have 2^^7 Rings of Brighthearth copies for Blighted Steppes ability on the stack. Resolve them one at a time, each time turning X life into 2^^X creatures. The first gets more than 2^^(2^^7) > 2^^(2^^4) = 2^^^4. The second gets 2^^(2^^^4) = 2^^^5. So we can turn X Blighted Steps abilities into 2^^^X artifacts/creatures/enchantments/mana/life
After all 2^^7 copies of the Blighted Steppes ability we have more than 2^^^(2^^7) of anything we can produce. It is time to get access to the real combo.
Use The Scarab God to create a copy of Moraug, Fury of Akoum.
Bounce Vault of Whispers and put it back onto the battlefield, triggering Moraug, Fury of Akoum 2^^^(2^^7) times thanks to Panharmonicon copies.
Exile Prosperity with Spellweaver Helix and put it in the library with a Riftsweeper copy. Also put in the Riftsweeper and anything else we want to draw.
Go to combat with a hasty Myr Battlesphere, attack and damage the opponent with the trigger. Get some counters on Night Dealings.
Activate Night Dealings with X=1 to grab Prosperity. (Get mana from Vault of Whisper and Mox Sapphire copies)
Create a Sea Gate Stormcaller copy to get 2^^^(2^^7) delayed triggers.
Cast Prosperity with X=1 to draw 1 card 2^^^(2^^7) times.
I have no doubt we can access the full combo from there
I thought a bit about replacing Elvish Spirit Guide with Acorn Havest, to get a bunch of green mana with Mobilize rather than one. That would most conveniently and effectively be done after the first Battle Hymn; the problem is at that point the Sea Gate Stormcaller is on the battlefield. So it seems like we would want to do this before the first Battle Hymn; we could then put Stormcaller triggers on the stack for the first Battle Hymn, then have a bounce waiting to put Stormcaller in play before the second Battle Hymn. But, before the first Battle Hymn means we have to cast Siege of Towers separately, since we don't yet have red mana to cast the Replicate cost. So we would need to replace one more card. Also, we need one more black mana to use Scarab God to fetch Wood Elves and Stomping Ground.
Actually, at this point, it would be easier just to have the Elvish Spirit Guide since we need to replace another card anyway, and cast Acorn Harvest between the Battle Hymns. But I don't know what we would replace.
Anyway, this is looking good! I suppose there is no chance of fitting in a stage?
Edit: Hmmm, instead of Siege of Towers, would Living Lands be more convenient? Living Lands will get bounced by Worldpurge, so I don't think it would allow us to put Mobilize below Worldpurge. Living Lands would free us from needing a Mountain, and we wouldn't have to pay the Replicate cost for Siege of Towers.
I imagine this doesn't save us a card, as you already pointed out that we can't use the land to pay for Deathgrip. Would it free us from needing a second Battle Hymn? Probably not.
Still, we could replace Stomping Ground with Temple Garden to get white mana, and then Mox Pearl could go back to Mana Crypt. That would get us another colorless mana, which I imagine we would use to draw another card in the opening.
Burnt Offering looks good! Is there any way we can turn an extra card slot into another layer? If not, then we can use it to improve the start. For example Master Skald could give us access to all the artifacts and enchantments we cannot draw. That means we could potentially go through the entire hyperstage including BB calculations in the first main phase. Though I will wait for a while before I try to work out the start with that.
A while back, we used damage bouncers to efficiently gain more layers - I haven't really looked at them, because they were mostly about dealing damage to creatures, but it looks like we can still use Justice and Backfire. Both of those can get double layers for dealing 1-2 damage and dealing 3 damage. So, how about:
Backfire won't add a layer because on every iteration but the first the creature that deals damage will already be gone from the battlefield from all the Worldpurges. So we can't enchant it to create a bigger number of Backfire triggers.
The Justice layer should work out though. As long as we make sure the damage is dealt from red creatures under the correct persons control. For the discard to draw sequence that should be fine as we can use Brallin, Skyshark Rider to deal damage and Night Dealings/Angelheart Vial to draw, depending on where the damage ends up/who discards.
For the attack to discard sequence we need to find a working red source. Unfortunately Awaken the Blood Avatar can't be used with the combat layers because the token it creates has haste. It can be blocked and start a BB computation without clearing our side of the battlefield. Mage Slayer looks like it would work.
So we attack with a equipped red creature. It deals >3 damage to the opponent X times. Every time Justice deals >3 damage to us X times. Every time we have to discard a card X times. Every time Brallin damages the opponent X times. Every time Justice damages us X times.
To me it looks like that sequence works, and we end in Angelheart Vial.
So we get 2 extra layers from Justice. That was a great idea! Too bad about the Backfire, I guess we'll keep World at War again.
Ah, right. It looks like losing Backfire means we don't have the option to end on Night Dealings, so the start has to be amended a bit, but hopefully it should get up to about the same amount.
With the extra card at the start, maybe I will look into the unlikely possibility of getting a stage going. Getting a decent BB computation looks hard, since we have to give the opponent creatures one at a time with Fractured Identity, so I guess we will have to have a lot of life and green mana to get it working. The normal stage also seems problematic, since it requires black mana to counter our creature casts, so it seems to only work when there is a Worldfire stage we can transition into. You mentioned a janky life stage, but I realize I don't know how that works. Can you explain the life stage?
The janky life stage is basically our hyperstage, except that the substages don't work. So for 3 life you put the hyperstage transition on the stack to generate X mana, turn that into a layer of Bloodbond March triggers on Elvish Spirit Guide. Later you resolve the transition to gain the life back. Then you put it on the stack again, but get a bigger layer, thanks to more Sea Gate Stormcaller triggers.
This requires the ability to put a transition on the stack again without the instants and using just Bloodbond March triggers of Elvish Spirit Guide. We might get enough mana for that from Tolarian Academy and the other lands. But it is pretty tough.
We can't use a creature bounce layer since we need to return the Elvish Spirit Guide from the graveyard to generate green mana and without black from the instants we can't counter it to get useful Bloodbond March triggers. We also can't keep Mobilize on the stack from the lower transition to get colored mana, since the land won't be animated and we can't mix any Siege of Towers between the Mobilize copies.
Honestly, I think getting BB calculations (or some smaller useful Waterfall program) would require less extra cards.
Edit: And I just noticed that the janky stage would be completely impossible now that we get all our black mana from an instant.
Hmm, can we get something decent off of a BB calculation? I suppose with Rotlung Reanimators we can use the creatures on our side, triggering the opponent's RRs when they are killed by Kaervek's Spite. So let R be the number of enemy Reanimators, and C be the total number of creatures that we can use as inputs. How high can we get R and C to be in the opening?
I suppose this could be a case where, when we write this up, we present both the noncomputation opening, and a computation opening (or a set of computational openings with various R's and C's), and leave it open which one is bigger. Might as well cover all bases.
Of course, it would be nice to actually demonstrate a good lower bound for the computation. So, it may be fruitful to look at simple Waterfall programs. My first thought is just turning A's into B's, B's into C's, to get something like c^N as the output. That's completely weaksauce though, considering we're competing against something like 2^^^2^^7. I understand how to do Knuth arrows with counters:
-have counters 1 through N
-we can decrease counter 2 by 1 to increase counter 1 by more (increase by 2 is fine)
-we can decrease counter X (for X > 2) by 1 to convert/add a lower counter (counter 1 is fine) to counter X-1.
If decreasing counter 2 increases counter 1 by 2, than Y in counter X can turn into roughly 2 -> Y -> X-2 in counter 1.
Of course, this is a different sort of counter computational model than the Waterfall model. But this would be an instructive thing to try to translate into the Waterfall model.
I just had some fun implementing a layer system in the waterfall model. I can get 2^X with 5 clocks and then need 3 additional clocks for each layer. We'd need constant*layers^2 donations to make it work, so very much something we could potentially implement at the start. (Though limited by creature types)
(use 4,4 as input for the last 2 clocks to get a long run that you can still watch to the end)
For an extra layer I need 3 additional clocks:
- 1 clock for the layer counter
- 1 clock for the transfer state that will move the output to the layer counter below it
- 1 clock that will be another copy of the output. I found that necessary to make the state switch after emptying the output work correctly
Oh, very nice! So, 42 layers would require 128 clocks, which work out to 256 creature types, (or 255 since the last clock seems to not produce anything) less than the 261 we currently have. 128 clocks seem to take about 2*128*127 ~ 32,000 donations, seems reasonable.
Edit: Hmm, I think Mage Slayer is problematic, because of the need to equip. I think Emberwilde Captain works? Emberwilde Captain switches around who takes and who deals damage, so it's back to Night Dealings, which is just as well probably.
Edit: Okay, this start is triggering me. I believe I know how to get to Mobilize / Blighted Steppe / Rings of Brighthearth combo and get a decent triple arrow number, then go to the computation. The problem is that we won't have much black mana. Even if we can keep Iijil's start, and then cast a Burnt Offering, sacrificing a Gravebreaker Lamia say, we will only get 900+ black/red mana, and we have to use that mana if we want to build up more. So, if we need to use The Scarab God for our Rotlung Reanimators, we can only get about 900 of them perhaps. If we can cast Rotlung Reanimator from our hand, we could potentially get a lot more, but of course this wouldn't give precisely the Waterfall Model, as Iijil pointed out earlier.
Ideally, we would want to delay the casting of Burnt Offering until we cast some other buildup spells, like Battle Hymn or Acorn Harvest. But, we are using our black mana for a lot of the card fetches, using The Scarab God and Mystical Teachings. So, delaying Burnt Offering means we have to have drawn those cards. I'm having trouble making do with the card slots we have again.
Edit: Hmmm, do we really need Wood Elves? When Temple Garden is a creature, we can use Temur Sabertooth to bring it back to our hand, then Wormfang Behemoth can protect it from [c}Worldfire[/c]. After Worldpurge, we can use Show and Tell to put it back on the battlefield. (I don't think we currently need Show and Tell for anything else?)
If Wood Elves can be removed, then we have another card slot. I'm thinking about using Silkbind Faerie. When we resolve a Tolarian Kraken trigger, we can tap a Silkbind Faerie. We can then untap the Silkbind Faerie to put a lot of Rings of Brighthearth triggers on the stack, each of which can tap an Arbiter of the Ideal, which we can then untap with Mobilize. So I think that's another layer.
We can use two Silkbind Faeries to repeatedly tap each other and get more RoB triggers, but each time it costs mana, and I don't think we get any benefit from this procedure until we resolve Mobilize to untap an Arbiter of the Ideal, at which point the party stops.
Edit: Oh, I guess the party doesn't have to stop; after a Mobilize, we can use a RoB trigger to tap a Silkbind Faerie, then create more RoB triggers again. So this goes infinite.
Edit: Instead of Silkbind Faerie, I'm contemplating having a Gilder Bairn and using it to get to the second stage of Kiora Bests the Sea God, which can tap Gilder Bairns under the opponent's control. To keep this from going infinite, we can have something sufficiently expensive to gain control of the tapped Gilder Bairns. (Mass Manipulation?) It doesn't look like this is worth the cards though.
Edit: It occurred to me it would be okay to damage animated enchantments, since if we dealt damage to an animated enchantment with Arcbond on it, it would quickly die and the computation would stop. So, that opens up the possibility of using the cards that required dealing damage to creatures, like Guilty Conscience and Spiteful Shadows. But, it looks like those particular cards don't add any layers, for the same reason that Backfire doesn't: the enchanted creature goes away once we try to make use of the damage, and the triggers that we have are only worth one layer. Looking at global enchantments, we have Repercussion and Mangara's Equity. Those two seem to go infinite together though. Repercussion could perhaps combo very well with Justice, but it has to start with damage dealt to a creature, and to be safe we want to deal damage to an animated enchantment. However, I'm not sure how we would restrict to just damaging animated enchantments, unless we use a damage bouncer, and the damage bouncers that I know (Guilty Conscience and Mangara's Equity) seem to go infinite with Repercussion. So, no progress here.
Edit: I was wondering if we could get something off of Proliferate, like using Thrummingbird. I was thinking Thrummingbird could get us to the fourth stage of The Akroan War, causing all our tapped creatures to damage themselves. But, not all creatures would kill themslves this way. In particular, Master Transmuter wouldn't kill itself with the damage, and we can make it tapped even without Tolarian Kraken, if we were to remove that. So presumably we can get an infinite computation started that way.
Another idea is to get to the final stage of Tymaret Calls the Dead, and give the opponent life. Then we can use something like Kaboom! to deal damage to them, and trigger Justice and the rest, adding two additional layers. But, due to not being able to damage the opponent lower down, we have to replace Brallin, Skyshark Rider with Megrim, which we can't link into Justice, so we lose a layer. Also, we're one card over, so we're going to lose another layer. But, we can drop World at War, so that we end in Moraug for BB_{w^2+13} (BB_{w^2+13} (X)) damage.
Edit: Oh, I had a very nice idea that I really hoped would work out, but it doesn't quite work out yet. We saw that we were able to double up on Justice, once for dealing 3 or more damage, and once for dealing 1-2 damage. I was thinking perhaps we could double up again, by which players used and got affected by which effects. In particular, perhaps we could have Megrim or Brallin, Skyshark Rider be able to deal 3+ damage, but only one way. So, we could use cards that increased damage that our sources deal, but not the opponent's, so we that we can re-trigger Pain Magnification when the sources are on our side, then they will go on to the other side, and we can't trigger again.
Using Brallin nicely switches who takes damage, but unfortunately Justice switches it back, so with Brallin + Justice we'll keep having Brallin on our side, which is no good. With Brallin and no Justice, we'll gain two layers, with the repeat, but losing Justice costs us two layers, and we need a card to increase Brallin's damage, so we wind up with the same number of layers and the same number of cards as a previous layer sequence. (Not the most recent one with Thrummingbird, which seems to be better)
Megrim + Justice would switch, if Justice was triggered by Megrim. I don't know of a way to make Megrim trigger Justice that wouldn't also allow Justice to trigger itself and go infinite. (e.g. Sleight of Mind or Chaoslace) I tried to think of ways to replace Justice, but anything that enchants or deals damage to a Megrim will stop being useful once Megrim goes away, so I didn't see a way to add a layer with cards like Mangara's Equity or Backfire.
Spiteful Visions has the characteristics to work with Justice, but I don't know of a damage mechanic like Pain Magnfication for drawing.
So yeah, not an improvement yet with this idea. If we could somehow get the repeat and keep Justice, that could potentially add 3 layers.
Edit: Oh, I guess with Megrim we wouldn't have to rely on Justice or whatever we used to add another layer, we could get the infinite with just Megrim. So yeah, it looks like we can only use Brallin.
Sorry for being a bit absent from discussions, and missing the standard deadline. Maybe I can still shape it up enough to post but it kind of doesn't matter...
Looks like I've missed some serious developments in the deck, before I try and get caught up I just want to chime in that 6 waterclocks (+halting flooding clock) is enough to implement a UTM, though it needs something like x^^^^x (maybe x^^^x) tokens to make a machine of size x, (via https://esolangs.org/wiki/Spiral_Rise into a bitwise cyclic tag system [there's a proof for that somewhere...], and there into something more efficient, losing about an arrowsworth of efficiency each translation.)
Given that flooding clocks are still plentiful (and fast growing!), it seems likely that we can do much better than tetration with very few proper waterclocks.
No worries! I feel like writing up the article does matter, to have it for the historical record at least - the previous articles are still interesting, at least to me, and I feel like if we went to the effort to make the deck, we should finish and write it up. Of course, you have been doing most of the work with the writeups, so I appreciate that very much! I can try to do some more editing going forward, and hopefully we can finish this off. I added sections for the setup, the layer sequence, and the final damage, so I think that should take care of nearly all the content we need. Just needs to be updated to the most recent version of the deck, and edited and prettified. We can lower our standards to get it done, I suppose.
How many Rotlung Reanimators are needed for the UTM? That's the crucial number; the number of clocks don't really matter, except indirectly in affecting how many Reanimators (and Dralnu's Crusades, but we only need a few Dralnu's Crusades) we need.
The start will depend on whether we have any extra card slots left over from the layer sequence. If we have at least one slot, we can add Master Skald, which along with our other card fetchers will allow us to access the entire deck before combat. So we should be able to generate BB_{w^2 + 1}(X) Moraug triggers before combat, where X is how many Rings of Brighthearth triggers we can get when we finally activate our Blighted Steppe. So this will be large regardless, however the value of X may very well depend on the output of a Waterfall computation, so even here we may need to an estimate or lower bound as to the size of it. (I haven't looked into this enough to give more details.)
If we don't have any more space left, than the best I was able to do was to generate about 1900 black mana, and then, depending on how much of that mana we are willing to give up, generate something like 2^^^X of other resources, like other colors of mana and Panharmonicons and Sea Gate Stormcallers. So we will be able to generate around 1900 - Y Rotlung Reanimators and 2^^^X token creatures.
So, then it matters whether we need X^^^^X or X^^^X tokens to make a machine of size X. Precise bounds will be very helpful, since even with X^^^X we will be cutting it close. We will also need to be able to code the UTM with 1900 - Y Reanimators, of course.
So yeah, precise details with regard to the translation to UTM's and the normal Busy Beaver function would be of great help!
I think that perhaps when we write this up, we could include both the lower bound in terms of a Waterfall Busy Beaver function (perhaps we can define WBB(R,C) to be the largest output that we can get from a halting computation that requires no more than R Rotlung Reanimators and C input creatures), and then possibly also in other terms, like a computational bound, and/or a standard Busy Beaver bound, so that we have a bound in whatever version the reader prefers.
Using flooding clocks to help cut down on resources when we program actual Waterfall programs could be useful, as could ignoring the rule that waterclocks can't zero at the same time. I'm not sure about doing much better than tetration with very few proper waterclocks though - I would theorize that the actual Busy Beaver Waterfall programs will be amazingly good, but in terms of what we can actually program, I'm not sure if we will be able to implement say the Ackermann function with just a few waterclocks. Did you have something in mind?
What about a creature supplying black mana, like Witch Engine?
What about Marchesa's Smuggler, or a hacked Battle Cry Goblin? That would free us up from needing a Mountain, so we could replace Stomping Ground and Reality Twist with Temple Garden, saving a card.
Edit: Nah, Seige of Towers requires a Mountain.
(I think it is still impossible to use the same instant card to catch up on progress after Worldpurge and BB-Computations, so this can't replace the Brightstone Ritual.)
So by using Marchesa's Smuggler instead of Anger we lose a card slot. But now all our hasty creatures can't be blocked! That means we can't use combat damage to trigger Arcbond. That opens up layers from additional combats.
2 Opalescence
3 Dual Nature
4 Vedalken Orrery
5 Riftsweeper
6 Watcher in the Mist
7 Marchesa's Smuggler
8 Coat of Arms
9 Rotlung Reanimator
10 Dralnu's Crusade
11 Arcbond
12 Arcbond
13 Fractured Identity
14 Artificial Evolution
15 Sea Gate Stormcaller
16 Avacyn, Guardian Angel
17 Kaervek's Spite
18 Amulet of Safekeeping
19 Goblin Boom Keg
20 Brightstone Ritual
21 Mirrorworks
22 Master Transmuter
23 Mox Sapphire
25 The Scarab God
26 Rings of Brighthearth
27 Temur Sabertooth
28 Elvish Spirit Guide
29 Mobilize
30 Siege of Towers
31 Worldfire
32 Worldpurge
33 Acorn Harvest
34 Acorn Harvest
35 Radiant Fountain
36 Akoum Refuge
37 Eureka
38 Show and Tell
39 Wood Elves
40 Battle Hymn
41 Dark Ritual
42 Panharmonicon
43 Spellweaver Helix
44 Wormfang Behemoth
45 Deathgrip
46 Mystical Teachings
48 Reality Twist
49 Mana Crypt
50 Tolarian Academy
51 Channel
52 Blighted Steppe
53 Arbiter of the Ideal
54 Tolarian Kraken
55 Prosperity
56 Farsight Mask
57 Brallin, Skyshark Rider
58 Pain Magnification
59 Righteous Cause
60 Moraug, Fury of Akoum
61 World at War
62 Harmonic Prodigy
63 Kaboom!
my first thought is to replace Pain Magnfication, Righteous Cause, and Kaboom! with Shrieking Specter. We can then drop World at War, resulting in BB_{w^2+9}(BB_{w^2+9}(BB... instead of BB_{w^2+9}(BB_{w^2+8}(BB... . Not bad considering we lose a card slot for Battle Hymn.
Looking for further improvements, in addition to the inefficiency of needing Harmonic Prodigy as a support card, I believe Reality Twist is only used to provide mana for [c}Avacyn Guardian Angel[/c] and Blighted Steppe. So, if we can integrate white mana into the layer sequence, we can drop Reality Twist. But again, the Blighted Steppe start is really nice.
Then, there is the possibility of getting more than one layer per card, as we see with Blighted Steppe, and we previously saw with Black Lotus aided by Dual Nature and Doubling Season. Creating Clue tokens seems to be a nice possibility for a double layer. Search the Premises should get us two layers; unfortunately, it hooks directly from combat to our drawing, so even if we add World at War, we only get 9 layers.
I'll definitely think about it some more!
Another possibility is simply a replacement for Avacyn, but I haven't found one yet.
Edit: Hmm, perhaps Platinum Emperion will work?
So:
2 Opalescence
3 Dual Nature
4 Vedalken Orrery
5 Riftsweeper
6 Watcher in the Mist
7 Marchesa's Smuggler
8 Coat of Arms
9 Rotlung Reanimator
10 Dralnu's Crusade
11 Arcbond
12 Arcbond
13 Fractured Identity
14 Artificial Evolution
15 Sea Gate Stormcaller
16 Kaervek's Spite
17 Platinum Emperion
18 Safe Passage
19 Goblin Boom Keg
20 Brightstone Ritual
21 Mirrorworks
22 Master Transmuter
23 Mox Sapphire
25 The Scarab God
26 Rings of Brighthearth
27 Temur Sabertooth
28 Elvish Spirit Guide
29 Mobilize
30 Siege of Towers
31 Worldfire
32 Worldpurge
33 Acorn Harvest
34 Acorn Harvest
35 Radiant Fountain
36 Akoum Refuge
37 Eureka
38 Show and Tell
39 Wood Elves
40 Battle Hymn
41 Dark Ritual
42 Panharmonicon
43 Spellweaver Helix
44 Wormfang Behemoth
45 Deathgrip
46 Mystical Teachings
48 Mox Pearl
49 Tolarian Academy
50 Channel
51 Blighted Steppe
52 Arbiter of the Ideal
53 Tolarian Kraken
54 Prosperity
55 Night Dealings
56 Megrim
57 Pain Magnification
58 Tectonic Giant
59 Moraug, Fury of Akoum
60 Harmonic Prodigy
If this works, we will deal more than BB_{w^2+10} (BB_{w^2+10} (BB(X))) damage.
Tectonic Giant would go infinite because the opponent can target it with a Fractured Identity from a donated Spellweaver Helix. But Myr Battlesphere doesn't have that problem and gets us that layer.
A lifelinker would have no problem keeping the opponent alive. The Kaervek's Spite always resolves after our BB computations, because those get triggered from the sacrifice cost when we put the spell on the stack.
That means we can replace Platinum Emperion and Watcher in the Mist with Gravebreaker Lamia, saving another card.
Adding World at War we would get BB_{w^2+11}(BB_{w^2+10}(X)) damage. X would be rather small because it's the number of Moraug, Fury of Akoum triggers we get in the first main phase. That means we only get that one big draw from the first Prosperity to try and get that as high as possible, while also making sure that we can continue to draw the deck once we go to the combats.
A couple of things I noted: Since Battle Hymn recovers our progress after a Worldpurge, we don't need Dark Ritual to do so. So, we could perhaps replace Dark Ritual with something like Witch Engine, if it worked out better. Also, since we need red mana to give Master Transmuter haste, there isn't an infinite from Doubling Season, so we could put that in if it helped. Unfortunately, it doesn't seem to add a layer anywhere - For Blighted Steppe and the counters of Night Dealings, the layer that we get from Doubling Season doesn't stack with what we already get from Rings of Brighthearth, because we have to activate everything before they get destroyed by Worldpurge et al. Same for any Clue tokens we would generate I believe. Since the deck is full, there's no room for Doubling Season.
Maximizing the start should be interesting. It doesn't look like we have a way to reacquire Prosperity or draw in some other way prior to the combat phases. So, we can get the up to 19 cards we get from Prosperity, and maybe mill a few cards due to Gravebreaker Lamia. We could try to save some life to pay for Acorn Harvest, but at 3 life per cast, that's a pretty steep price at this point. There is also the question of whether we want to try to do a BB computation this early... perhaps it's just not possible with the amount of resources we have access to at this point.
Edit: Hmmm, mana is kind of a pain in the start. We blew our blue mana cards at the beginning, so I don't see how we would get blue mana now. That keeps us from copying Panharmonicon beyond the two Mirrorworks triggers we get when we play it. It also seems to kill the idea of replacing Tolarian Kraken with Gridlock or Glimpse of the Sun God to get some usage out of Arbiter of the Ideal at the beginning.
We also need some mana at the beginning for the Panharmonicon copies - could we replace Vedalken Orrery with Leyline of Anticipation? I would like to use it to have another creature on the battlefield, for an early Battle Hymn. (it still seems like a waste of a Battle Hymn, but I'm having trouble getting early mana.)
Edit: Quick rules question: If I use Eureka to put Radiant Fountain and Stomping Ground onto the battlefield, can I gain the life from Radiant Fountain before having to pay the cost for Stomping Ground?
Edit: Oh, there's a problem. With the current start, we don't have any blue mana after we cast Prosperity for the first time. I don't see how to get any more blue mana, other than by exiling the Mox Sapphire, putting it into the library with Riftsweeper, and either drawing it or fetching it with Arbiter of the Ideal or Night Dealings. But, to do any of those, we need to attack with a creature first. Right now, we need to activate Marchesa's Smuggler, which requires a blue mana. So we're kind of stuck, I think.
One possibility is to use Break through the Line rather than Marchesa's Smuggler, but that unfortunately that can't target Myr Battleshpere. I was contemplating perhaps replacing Safe Passage with something that doesn't completely prevent damage to ourselves, but the only creature I saw that dealt 3+ damage to ourselves was Hasran Ogress, which also has 3+ power.
One option for the start is to use Vault of Whispers instead of Dark Ritual for our black mana. That can be bounced and replayed by Master Transmuter but not donated with Fractured Identity and might help out with triggering Moraug, Fury of Akoum.
If mana at the start turns out to be the bottleneck, then we can play a second Battle Hymn instead of Brightstone Ritual.
For Eureka, Radiant Fountain and Stomping Ground: I don't think you can gain the life before paying for Stomping grounds. The payment on that is part of a replacement effect that happens during Eureka's resolution. Radiant Fountain's lifegain is a trigger and goes on the stack after Eureka finishes resolving.
Play Vedalken Orrery. (1 card used)
Cast Eureka. (2 cards used)
Respond by casting Worldpurge. (3 cards used)
Respond by playing Wormfang Behemoth, exiling our hand.
Resolve Worldpurge, bringing Omniscience, Mox Pearl, Mox Sapphire, Tolarian Academy, Vedalken Orrery, and Wormfang Behemoth back to our hand.
Wormfang Behemoth triggers, and brings 16 other cards back to our hand.
Eureka resolves, put into play:
Moraug, Fury of Akoum (4 cards used)
Omniscience
Mox Pearl
Mox Sapphire
Vedalken Orrery
Play Mirrorworks. (5 cards used)
Play Opalescence. (6 cards used)
Play Gravebreaker Lamia, mill Acorn Harvest (7 cards used)
Play Marchesa's Smuggler. (8 cards used)
Play Night Dealings. (9 cards used)
Play Battle Hymn, get 5 red mana. (10 cards used)
Play Panharmonicon, pay for 2 copies. (11 cards used)
Play Dual Nature, get 4 copies. (12 cards used)
Play Harmonic Prodigy, get 20 copies. (13 cards used)
Play Artificial Evolution, turning Moraug into a Wizard or Shaman. (14 cards used)
Play Spellweaver Helix, imprinting Acorn Harvest, Eureka, Prosperity, and 1 or 3 of the other sorceries. (15 cards used)
Play Acorn Harvest, triggering Spellweaver Helix (16 cards used)
Put Tolarian Academy, Vault of Whispers into play. (17 cards used, 47 Moraug triggers)
Tap Mox Sapphire, Mox Pearl, Vault of Whispers for mana. (1 red, 1 blue, 1 white, 1 black mana)
Pay for two copies of Vault of Whispers. (97 Moraug triggers)
Play Riftsweeper, get 20 copies. Shuffle Acorn Harvest, Eureka, Prosperity, and 1 or 3 of the other sorceries into the library. (18 cards)
Have Battle Hymn remaining in hand.
End precombat main phase, get 98 combat phases.
Enter first combat phase.
Cast Battle Hymn for 52 red mana.
Tap Tolarian Academy for 11 blue mana.
Pay a blue and two red to give a Gravewalker Lamia haste. Attack with it. (5 life, opponent 16 life, 50 red, 10 blue)
Put 4 Theft tokens on Night Dealings.
Tap the Vaults for 2 black mana.
Pay 2 red and 2 black, and remove a Theft token to fetch Prosperity. (48 red, 10 blue, 3 Theft tokens left)
Prosperity. (We have 38 or 40 cards left in our library, depending on what Spellweaver Helix imprinted.)
We should continue this, but with access to our entire deck now, and some spare mana to keep us going, we should be able to continue, and attack with more than 97 Myr Battlespheres next combat phase. So this should get us to BB_{w^2+11}(BB_{w^2+10}(97)).
Can we do better?
Edit: An improved start:
Play Vedalken Orrery (1 card used)
Play Opalescence (2 cards used)
Play Dual Nature (3 cards used)
Play Gravebreaker Lamia, get 2 copies, mill Acorn Harvest, Eureka, and Worldpurge. (4 cards used.)
Play Panharmonicon (5 cards used)
Play Spellweaver Helix, imprint Acorn Harvest, Eureka, Worldpurge, and Show and Tell. (6 cards used)
Play Acorn Harvest, triggering Spellweaver Helix (7 cards used)
Play Wormfang Behemoth, exiling our hand. (8 cards used)
Resolve Worldpurge. Return Omniscience, Mox Sapphire, Tolarian Academy, Vedalken Orrery, Opalescence, Dual Nature, and Panharmonicon to our hand. Gravebreaker Lamia, Spellweaver Helix, Wormfang Behemoth, and Mox Pearl get shuffled into the library.
Wormfang Behemoth triggers, returning our other cards back to our hand.
Resolve Eureka, put Omniscience and Vedalken Orrery back into play.
Play Mirrorworks. (9 cards used, 2 artifacts)
Play Opalescence.
Play Panharmonicon, getting two Mirrorworks triggers.
Play Dual Nature, getting two copies.
Play Moraug, getting copies that die. (10 cards used, 5 creatures)
Play Marchesa's Smuggler, getting 6 copies. (11 cards used, 12 creatures)
Play Night Dealings, getting 6 copies. (12 cards used, 19 creatures)
Play Master Transmuter, getting 6 copies. Ignore the Mirrorworks triggers. (13 cards used, 26 creatures)
Play Battle Hymn, get 26 red mana. (14 cards used, 26 red mana)
Pay for the two Panharmonicon triggers. (22 red mana, 5 artifacts)
Play Harmonic Prodigy, get 12 copies. (15 cards used)
Play Artificial Evolution, turn Moraug into a Wizard or Shaman. (16 cards used)
Resolve Show and Tell, put Tolarian Academy into play. (16 cards used, 14 Moraug triggers)
Play Mox Sapphire, pay for 4 copies, tap for mana. (16 cards used, 5 blue mana, 14 red mana, 10 artifacts)
Activate Marchesa's Smuggler to give a Master Transmuter haste (4 blue mana, 12 red mana)
Activate Master Transmuter, bounce Mox Sapphire, put Vault of Whispers into play. (17 cards used, 3 blue mana, 12 red mana, 31 Moraug triggers, 10 artifacts)
Pay for 4 copies of Vault of Whispers. Tap the Vaults for mana. (1 blue mana, 6 red mana, 5 black mana, 99 Moraug triggers, 14 artifacts)
Play Mox Sapphire, pay for 4 copies, tap 3 for mana. (1 blue mana, 6 red mana, 19 artifacts)
Tap Tolarian Academy for 19 blue mana. (20 blue mana, 6 red mana, 99 Moraug triggers)
Activate Marchesa's Smuggler and Master Trasmuter to bounce and replay Vault of Whispers, pay for 4 copies and tap them. (13 blue mana, 5 red mana, 1 black mana, 184 Moraug triggers)
Activate Marchesa's Smuggler and Master Trasmuter to bounce and replay Vault of Whispers, pay for 4 copies and tap them. (7 blue mana, 4 red mana, 1 black mana, 269 Moraug triggers)
Activate Marchesa's Smuggler and Master Trasmuter to bounce and replay Vault of Whispers, pay for 4 copies. (0 mana, 354 Moraug triggers)
We have Battle Hymn and Riftsweeper in our hand.
End precombat main phase, get 355 combat phases.
Cast Battle Hymn, get 39 red mana.
Tap two Mox Sapphire for 2 blue mana.
Give a Night Dealings haste and attack. (37 red mana, 1 blue mana) (I'm not sure which creature to attack with, Moraug gets us more Theft tokens, but we might want to save our opponent's life.)
Each Night Dealings gets 5 Theft tokens.
Tap 5 Vault of Whispers for mana. (37 red mana 1 blue mana, 5 black mana)
Use Night Dealings to fetch Spellweaver Helix. (35 red mana, 1 blue mana, 3 black mana)
Play Spellweaver Helix, exile Prosperity and Acorn Harvest.
Play Riftsweeper, get 12 copies, shuffle all our exiled cards into our library.
Use Night Dealings to fetch Prosperity. (33 red mana, 1 blue mana, 1 black mana)
Cast Prosperity for up to 34.
I'm hoping we can get going with this Prosperity cast, we get most but not all of the deck. The biggest issue seems to be we don't get red mana anymore without Worldfire, but we should be able to incorporate Worldfire now?
Edit: Improved the start more. Got pretty greedy; I got 1795 combat phases, but we have to see whether we can continue with a Prosperity for up to 9.
Play Vedalken Orrery (1 card used)
Play Opalescence (2 cards used)
Play Dual Nature (3 cards used)
Play Gravebreaker Lamia, get 2 copies, mill Acorn Harvest, Eureka, and Worldpurge. (4 cards used.)
Play Panharmonicon (5 cards used)
Play Spellweaver Helix, imprint Acorn Harvest, Eureka, Worldpurge, and Show and Tell. (6 cards used)
Play Acorn Harvest, triggering Spellweaver Helix (7 cards used)
Play Wormfang Behemoth, exiling our hand. (8 cards used)
Resolve Worldpurge. Return Omniscience, Mox Sapphire, Tolarian Academy, Vedalken Orrery, Opalescence, Dual Nature, and Panharmonicon to our hand. Gravebreaker Lamia, Spellweaver Helix, Wormfang Behemoth, and Mox Pearl get shuffled into the library.
Wormfang Behemoth triggers, returning our other cards back to our hand.
Resolve Eureka, put Omniscience and Vedalken Orrery back into play.
Play Mirrorworks. (9 cards used, 2 artifacts)
Play Opalescence.
Play Moraug, Fury of Akoum. (10 cards used, 2 creatures)
Play Marchesa's Smuggler. (11 cards used, 3 creatures)
Play Night Dealings. (12 cards used, 4 creatures)
Play Battle Hymn, getting 4 red mana. (13 cards used, 4 red mana, 4 creatures)
Play Panharmonicon, and pay for two Mirrorworks triggers. (13 cards used, 0 red mana, 4 creatures, 5 artifacts)
Play Dual Nature, getting four copies. (13 creatures used, 0 mana, 9 creatures, 5 artifacts)
Play Master Transmuter, getting 20 copies. Ignore the Mirrorworks triggers. (14 cards used, 30 creatures, 26 artifacts)
Play Harmonic Prodigy, get 20 copies. (15 cards used, 51 creatures, 26 artifacts)
Play Artificial Evolution, turn Moraug into a Wizard or Shaman. (16 cards used, 51 creatures, 26 artifacts)
Play Wood Elves, get 20 copies, fetch Stomping Ground from the library and put it in play. (17 cards, 72 creatures, 26 artifacts, 22 Moraug triggers)
Resolve Show and Tell, put Tolarian Academy into play. (17 cards used, 72 creatures, 26 artifacts, 44 Moraug triggers)
Play Battle Hymn, getting 72 red mana. (18 cards used, 72 red mana, 26 artifacts, 44 Moraug triggers)
Play Mox Sapphire, pay for 4 copies, tap for mana. (18 cards used, 5 blue mana, 64 red mana, 31 artifacts, 44 Moraug triggers)
Activate Marchesa's Smuggler to give a Master Transmuter haste (4 blue mana, 62 red mana)
Activate Master Transmuter, bounce Mox Sapphire, put Vault of Whispers into play. (18 cards used, 3 blue mana, 62 red mana, 31 artifacts, 69 Moraug triggers, 20 Master Transmuters)
Pay for 4 copies of Vault of Whispers. Tap the Vaults for mana. (3 blue mana, 58 red mana, 1 black mana, 35 artifacts, 169 Moraug triggers)
Play Mox Sapphire, pay for 4 copies, tap for mana. (8 blue mana, 50 red mana, 1 black mana, 40 artifacts, 169 Moraug triggers)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. (6 blue mana, 45 red mana, 1 black mana, 44 artifacts, 294 Moraug triggers, 19 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. (4 blue mana, 40 red mana, 1 black mana, 48 artifacts, 419 Moraug triggers, 18 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. (2 blue mana, 35 red mana, 1 black mana, 52 artifacts, 544 Moraug triggers, 17 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Mox Sapphire, pay for 4 copies, tap 4 of them. (4 blue mana, 25 red mana, 1 black mana, 56 artifacts, 544 Moraug triggers, 16 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. (2 blue mana, 20 red mana, 1 black mana, 60 artifacts, 669 Moraug triggers, 15 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. (0 blue mana, 15 red mana, 1 black mana, 64 artifacts, 794 Moraug triggers, 14 Master Transmuters)
Tap Tolarian Academy for 64 blue mana.
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. (58 blue mana, 14 red mana, 1 black mana, 919 Moraug triggers, 13 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. (52 blue mana, 13 red mana, 1 black mana, 1044 Moraug triggers, 12 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. (46 blue mana, 12 red mana, 1 black mana, 1169 Moraug triggers, 11 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. Do not tap the Vault copies (37 blue mana, 11 red mana, 1294 Moraug triggers, 10 Master Transmuters, 4 untapped Vaults)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. Do not tap the Vault copies (28 blue mana, 9 red mana, 1419 Moraug triggers, 9 Master Transmuters, 8 untapped Vaults)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. Do not tap the Vault copies. (19 blue mana, 7 red mana, 1544 Moraug triggers, 8 Master Transmuters, 12 untapped Vaults)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. Do not tap the Vault copies. (10 blue mana, 5 red mana, 1669 Moraug triggers, 7 Master Transmuters, 16 untapped Vaults)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 4 copies. Do not tap any Vaults. (2 blue mana, 1 red mana, 1794 Moraug triggers, 6 Master Transmuters, 21 untapped Vaults)
Spend the remaining mana to give Moraug, Fury of Akoum haste.
End the precombat main phase, we get 1795 combat phases.
Begin the first combat phase.
Attack with Moraug, the Night Dealings gets 7 Thief counters.
Tap 12 untapped Vaults.
Use Night Dealings to fetch Spellweaver Helix. Play it to imprint Prosperity and Acorn Harvest.
Use Night Dealings to fetch Riftsweeper. Play it and shuffle our exiled cards into our library.
Use Night Dealings to fetch Prosperity.
Tap Mox Sapphire.
Prosperity for up to 9.
Edit: Even greedier, gets 2045 combat phases, but can only Prosperity for 6.
Play Vedalken Orrery (1 card used)
Play Opalescence (2 cards used)
Play Dual Nature (3 cards used)
Play Gravebreaker Lamia, get 2 copies, mill Acorn Harvest, Eureka, and Worldpurge. (4 cards used.)
Play Panharmonicon (5 cards used)
Play Spellweaver Helix, imprint Acorn Harvest, Eureka, Worldpurge, and Show and Tell. (6 cards used)
Play Acorn Harvest, triggering Spellweaver Helix (7 cards used)
Play Wormfang Behemoth, exiling our hand. (8 cards used)
Resolve Worldpurge. Return Omniscience, Mox Sapphire, Tolarian Academy, Vedalken Orrery, Opalescence, Dual Nature, and Panharmonicon to our hand. Gravebreaker Lamia, Spellweaver Helix, Wormfang Behemoth, and Mox Pearl get shuffled into the library.
Wormfang Behemoth triggers, returning our other cards back to our hand.
Resolve Eureka, put Omniscience and Vedalken Orrery back into play.
Play Mirrorworks. (9 cards used, 2 artifacts)
Play Opalescence.
Play Moraug, Fury of Akoum. (10 cards used, 2 creatures)
Play Marchesa's Smuggler. (11 cards used, 3 creatures)
Play Night Dealings. (12 cards used, 4 creatures)
Play Battle Hymn, getting 4 red mana. (13 cards used, 4 red mana, 4 creatures)
Play Panharmonicon, and pay for two Mirrorworks triggers. (13 cards used, 0 red mana, 4 creatures, 5 artifacts)
Play Dual Nature, getting four copies. (13 creatures used, 0 mana, 9 creatures, 5 artifacts)
Play Master Transmuter, getting 20 copies. Ignore the Mirrorworks triggers. (14 cards used, 30 creatures, 26 artifacts)
Play Harmonic Prodigy, get 20 copies. (15 cards used, 51 creatures, 26 artifacts)
Play Artificial Evolution, turn Moraug into a Wizard or Shaman. (16 cards used, 51 creatures, 26 artifacts)
Play Wood Elves, get 20 copies, fetch Stomping Ground from the library and put it in play. (17 cards, 72 creatures, 26 artifacts, 22 Moraug triggers)
Resolve Show and Tell, put Tolarian Academy into play. (17 cards used, 72 creatures, 26 artifacts, 44 Moraug triggers)
Play Battle Hymn, getting 72 red mana. (18 cards used, 72 red mana, 26 artifacts, 44 Moraug triggers)
Play Mox Sapphire, pay for 4 copies, tap for mana. (18 cards used, 5 blue mana, 64 red mana, 31 artifacts, 44 Moraug triggers)
Activate Marchesa's Smuggler to give a Master Transmuter haste (4 blue mana, 62 red mana)
Activate Master Transmuter, bounce Panharmonicon, put Vault of Whispers into play. (18 cards used, 3 blue mana, 62 red mana, 31 artifacts, 69 Moraug triggers, 20 Master Transmuters)
Pay for 4 copies of Vault of Whispers. Tap the Vaults for mana. (3 blue mana, 58 red mana, 1 black mana, 35 artifacts, 169 Moraug triggers)
Play Panharmonicon, pay for 4 copies. (3 blue mana, 50 red mana, 1 black mana, 40 artifacts, 169 Moraug triggers)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Mox Sapphire, pay for 8 copies, tap 8 Moxen. (9 blue mana, 32 red mana, 1 black mana, 48 artifacts, 169 Moraug triggers, 19 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. Tap Vaults for mana. (7 blue mana, 23 red mana, 1 black mana, 56 artifacts, 394 Moraug triggers, 18 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (5 blue mana, 14 red mana, 1 black mana, 64 artifacts, 619 Moraug triggers, 17 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (0 blue mana, 8 red mana, 1 black mana, 72 artifacts, 844 Moraug triggers, 16 Master Transmuters)
Tap Tolarian Academy for 72 blue mana.(72 blue mana, 8 red mana, 1 black mana, 72 artifacts, 844 Moraug triggers, 16 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (62 blue mana, 7 red mana, 1 black mana, 80 artifacts, 1069 Moraug triggers, 15 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (52 blue mana, 6 red mana, 1 black mana, 88 artifacts, 1294 Moraug triggers, 14 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (42 blue mana, 5 red mana, 1 black mana, 96 artifacts, 1519 Moraug triggers, 13 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. Do not tap Vault copies. (24 blue mana, 4 red mana, 1 black mana, 104 artifacts, 1744 Moraug triggers, 12 Master Transmuters, 8 untapped Vaults)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (6 blue mana, 3 red mana, 1 black mana, 112 artifacts, 1969 Moraug triggers, 11 Master Transmuters, 16 untapped Vaults)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 2 copies, tap 1 for mana (1 blue mana, 1 red mana, 1 black mana, 114 artifacts, 2044 Moraug triggers, 10 Master Transmuters, 18 untapped Vaults)
Spend the remaining mana to give Moraug, Fury of Akoum haste.
End the precombat main phase, we get 2045 combat phases.
Begin the first combat phase.
Attack with Moraug, the Night Dealings gets 7 Thief counters.
Tap 12 untapped Vaults.
Use Night Dealings to fetch Spellweaver Helix. Play it to imprint Prosperity and Acorn Harvest.
Use Night Dealings to fetch Riftsweeper. Play it and shuffle our exiled cards into our library.
Use Night Dealings to fetch Prosperity.
Tap Mox Sapphire.
Prosperity for up to 6.
Edit: Another improvement, 2448 combat phases, Prosperity for up to 5.
Play Vedalken Orrery (1 card used)
Play Opalescence (2 cards used)
Play Dual Nature (3 cards used)
Play Gravebreaker Lamia, get 2 copies, mill Acorn Harvest, Eureka, and Worldpurge. (4 cards used.)
Play Panharmonicon (5 cards used)
Play Spellweaver Helix, imprint Acorn Harvest, Eureka, Worldpurge, and Show and Tell. (6 cards used)
Play Acorn Harvest, triggering Spellweaver Helix (7 cards used)
Play Wormfang Behemoth, exiling our hand. (8 cards used)
Resolve Worldpurge. Return Omniscience, Mox Sapphire, Tolarian Academy, Vedalken Orrery, Opalescence, Dual Nature, and Panharmonicon to our hand. Gravebreaker Lamia, Spellweaver Helix, Wormfang Behemoth, and Mox Pearl get shuffled into the library.
Wormfang Behemoth triggers, returning our other cards back to our hand.
Resolve Eureka, put Omniscience and Vedalken Orrery back into play.
Play Mirrorworks. (9 cards used, 2 artifacts)
Play Opalescence.
Play Moraug, Fury of Akoum. (10 cards used, 2 creatures)
Play Marchesa's Smuggler. (11 cards used, 3 creatures)
Play Night Dealings. (12 cards used, 4 creatures)
Play Battle Hymn, getting 4 red mana. (13 cards used, 4 red mana, 4 creatures)
Play Panharmonicon, and pay for two Mirrorworks triggers. (13 cards used, 0 red mana, 4 creatures, 5 artifacts)
Play Dual Nature, getting four copies. (13 creatures used, 0 mana, 9 creatures, 5 artifacts)
Play Master Transmuter, getting 20 copies. Ignore the Mirrorworks triggers. (14 cards used, 30 creatures, 26 artifacts)
Play Harmonic Prodigy, get 20 copies. (15 cards used, 51 creatures, 26 artifacts)
Play Artificial Evolution, turn Moraug into a Wizard or Shaman. (16 cards used, 51 creatures, 26 artifacts)
Play Myr Battlesphere, get 20 copies. (17 cards, 72 creatures, 47 artifacts, 22 Moraug triggers)
Resolve Show and Tell, put Tolarian Academy into play. (17 cards used, 72 creatures, 47 artifacts, 22 Moraug triggers)
Play Battle Hymn, getting 72 red mana. (18 cards used, 72 red mana, 47 artifacts, 22 Moraug triggers)
Play Mox Sapphire, pay for 4 copies, tap for mana. (18 cards used, 5 blue mana, 64 red mana, 52 artifacts, 22 Moraug triggers)
Activate Marchesa's Smuggler to give a Master Transmuter haste (4 blue mana, 62 red mana)
Activate Master Transmuter, bounce Panharmonicon, put Vault of Whispers into play. (18 cards used, 3 blue mana, 62 red mana, 52 artifacts, 47 Moraug triggers, 20 Master Transmuters)
Pay for 4 copies of Vault of Whispers. Tap the Vaults for mana. (3 blue mana, 58 red mana, 1 black mana, 56 artifacts, 147 Moraug triggers)
Play Panharmonicon, pay for 4 copies. (3 blue mana, 50 red mana, 1 black mana, 61 artifacts, 147 Moraug triggers)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Mox Sapphire, pay for 8 copies, tap 8 Moxen. (9 blue mana, 32 red mana, 1 black mana, 69 artifacts, 147 Moraug triggers, 19 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. Tap Vaults for mana. (7 blue mana, 23 red mana, 1 black mana, 77 artifacts, 372 Moraug triggers, 18 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (5 blue mana, 14 red mana, 1 black mana, 85 artifacts, 597 Moraug triggers, 17 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 7 copies. (0 blue mana, 9 red mana, 1 black mana, 92 artifacts, 797 Moraug triggers, 16 Master Transmuters)
Tap Tolarian Academy for 92 blue mana.(92 blue mana, 9 red mana, 1 black mana, 93 artifacts, 797 Moraug triggers, 16 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (82 blue mana, 8 red mana, 1 black mana, 1022 Moraug triggers, 15 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (72 blue mana, 7 red mana, 1 black mana, 1247 Moraug triggers, 14 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (62 blue mana, 6 red mana, 1 black mana, 1472 Moraug triggers, 13 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (52 blue mana, 5 red mana, 1 black mana, 1697 Moraug triggers, 12 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. (42 blue mana, 4 red mana, 1 black mana, 1922 Moraug triggers, 11 Master Transmuters)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. Do not tap Vault copies. (25 blue mana, 3 red mana, 2147 Moraug triggers, 10 Master Transmuters, 8 untapped Vaults)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 8 copies. Do not tap Vault copies. (7 blue mana, 2 red mana, 2372 Moraug triggers, 9 Master Transmuters, 16 untapped Vaults)
Activate Marchesa's Smuggler and Master Transmuter, bounce and replay Vault of Whispers, pay for 2 copies. Tap 2 Vaults. (2 blue mana, 1 red mana, 2447 Moraug triggers, 9 Master Transmuters, 17 untapped Vaults)
Spend the remaining mana to give Moraug, Fury of Akoum haste.
End the precombat main phase, we get 2448 combat phases.
Begin the first combat phase.
Attack with Moraug, the Night Dealings gets 7 Thief counters.
Tap 12 untapped Vaults.
Use Night Dealings to fetch Spellweaver Helix. Play it to imprint Prosperity and Acorn Harvest.
Use Night Dealings to fetch Riftsweeper. Play it and shuffle our exiled cards into our library.
Use Night Dealings to fetch Prosperity.
Tap Mox Sapphire.
Prosperity for up to 5.
Using The Scarab God and Mystical Teachings to access more cards. Fitting in a Blighted Steppe sacrifice, getting X copies of the ability, each giving us X life. 3 life give us X mana using Spellweaver Helix and the transition sorceries. We can convert mana into more of other stuff, i.e. 2 mana -> 1 Panharmonicon -> 1 additional Sea Gate Stormcaller trigger
Play Show and Tell, put Omniscience into play. (1u, 2 cards)
Play Channel, convert 19 life into mana. (1u, 19c, 1 card)
Play Prosperity with X=19. (19 cards)
Play Vedalken Orrery. (18 cards)
Play Mirrorworks. (17 cards)
Play Panharmonicon. Leave 2 Mirrorwork triggers on the stack (16 cards)
Play Opalescence. (15 cards)
Play Dual Nature, get 2 copies. (14 cards)
Play Sea Gate Stormcaller. 3 Dual Natures trigger 2 times each. 7 Sea Gate Stormcaller enter the battlefield, each triggering 2 times. Create 14 delayed triggers. (13 cards)
Play Gravebreaker Lamia. Leave 1 Dual Nature Trigger and 2 etb triggers on the stack. Resolve 10 etb triggers from the copies and put 10 cards into the graveyard. Among them: Mystical Teachings, Riftsweeper, Siege of Towers, Mobilize, 2x Acorn Harvest and Wood Elves. (12 cards)
Play Eureka, leave it on the stack. (11 cards)
Play Worldpurge, leave it on the stack. (10 cards)
Play Wormfang Behemoth, let it exile your hand. (9 cards exiled)
Resolve Worldpurge. It bounces Mox Pearl, Mox Sapphire, Tolarian Academy, Omniscience, Vedalken Orrery, Mirrorworks, Panharmonicon, Opalescence, Dual Nature, Sea Gate Stormcaller, Gravebreaker Lamia and Wormfang Behemoth. Shuffle Mox Pearl, Mox Sapphire, Sea Gate Stormcaller, Gravebreaker Lamia and Wormfang Behemoth into the library.
Wormfang Behemoth trigger returns the exiled cards to hand. (16 cards)
Resolve Eureka, put Omniscience, Vedalken Orrery, Tolarian Academy, Mirrorworks, Opalescence, Vault of Whispers, Spellweaver Helix, Rings of Brighthearth and Blighted Steppe into play. (7 cards)
Resolve the Gravebreaker Lamia triggers. Put Gravebreaker Lamia and Sea Gate Stormcaller into the graveyard. (7 cards)
Play Panharmonicon. Leave 2 Mirrorwork triggers on the stack. (1 PH, 6 cards)
Play Dual Nature, get 2 copies (1 PH, 5 cards)
Play Myr Battlesphere, get 6 copies, create 56 myr tokens. (1 PH, 4 cards)
Tap Tolarian Academy for mana. We have 69 artifacts. (1 PH, 4 cards, 69u)
Pay for the 4 Mirrorworks(Panharmonicon) triggers. (5 PH, 4 cards, 61u)
Tap Vault of Whispers to flashback Mystical Teachings and fetch Battly Hymn. (5 PH, 5 cards, 56u)
Play The Scarab God. Get 18 Dual Nature copies. (5 PH, 4 cards, 56u)
Play Marchesa's Smuggler. Get 18 Dual Nature copies. (5 PH, 3 cards, 56u)
Play Master Transmuter. Get 18 Dual Nature copies. (5 PH, 2 cards, 56u)
Play Night Dealings. Get 18 Dual Nature copies. (5 PH, 1 card, 56u)
Play Battle Hymn. Get 14 copies from Sea Gate Stormcaller triggers. (5 PH, 56u)
Resolve the first Battly Hymn copy. We have 143 creatures. (5 PH, 56u, 143r)
Use the mana to create more Panharmonicons: Marchesa's Smuggler gives haste to a Master Transmuter. Master transmuter returns Panharmonicon to hand. Replay it and pay for Mirrorworks triggers.
1st time costs 2u,1r,1c for 5 Mirrorworks triggers. Pay for them. (10 PH, 54u, 131r)
2nd time costs 2u,1r,1c for 10 Mirrorworks triggers. Pay for them. (20 PH, 52u, 109r)
3rd time costs 2u,1r,1c for 20 Mirrorworks triggers. Pay for them. (40 PH, 50u, 67r)
4th time costs 2u,1r,1c for 40 Mirrorworks triggers. Pay for them. (80 PH, 16u, 17r)
5th time costs 2u,1r,1c for 80 Mirrorworks triggers. Pay for 22 of them. (102 PH, 4u, 3r)
Use Marchesa's Smuggler + Master Transmuter to bounce Myr Battlesphere. Dual Nature exiles the token copies. (102 PH, 2u, 1r)
Play Myr Battlesphere. Don't pay for the Mirrorworks triggers. Dual Nature triggers 3*103 times for a total of 310 Myr Battlespheres entering the battlefield. Each one triggers its etb 103 times and we create 127720 Myrs. (102 PH, 2u, 1r)
Resolve a Battle Hymn copy. The Number of creatures is big enough that I'm going to start estimating. The last step gave us over 128000 creatures. Let's go with that. (102 PH, 2u, >128000r)
Use Marchesa's Smuggler + Master Transmuter to bounce Vault of Whispers. Put it back into play. Pay for 1 copy. (102 PH, >128000r)
Tap the Vault of Whispers to activate Night Dealings. Find Mox Sapphire. (102 PH, >128000r)
Play Mox Sapphire. Pay for some copies. Tap them. We need roughly 2*log_2(red mana) of them so about 36... not enough to make a dent in our red mana estimate. (102 PH, >128000r, ~36u)
Now turn the red mana into Panharmonicon copies again. We need to pay 2r per copy plus some overhead to generate new triggers, plus some overhead overhead to generate more blue mana and untapped Master Transmuters. The overhead is roughly at log_2 of the red mana, so we can keep ignoring that for the estimate.
After spending most of the mana we have 64000 Panharmonicons. (>64000 PH, 4u, 2r)
Use the last mana to bounce and replay Myr Battlesphere. We get (1+DN*PH)*(1+PH)*4 Myrs. (>64000 PH, 2u)
Resolve another Battle Hymn. If we have X Panharmonicons we get >12*X^2 mana.
Turn the mana into more Panharmonicons. We get more than >6*X^2 copies. So 6*64000^2 > 2^2*64000^2 = 128000^2 > (2^16)^2 = 2^32
Repeat for the other 12 Battle Hymn copies on the stack. Get a huge amount of anything we can create here: Panharmonicons, other artifacts, red mana, blue mana, black mana and white mana (Night Dealings can fetch Mox Pearl)
How much? We more than square the number of Panharmonicons 12 more times, so we get more than (2^32)^(2^12) = 2^(32*2^12) > 2^(2^4*2^12) = 2^(2^16) = 2^^5
Specifically we turn most of those resources into Panharmonicon copies, leaving just enough operating mana to get through the next few steps.
Activate The Scarab God to create a copy of Sea Gate Stormcaller. Get >2^^5 delayed triggers.
Activate The Scarab God to create a copy of Gravebreaker Lamia. Leave the triggers on the stack.
Activate The Scarab God to create a copy of Riftsweeper. Put the exiled creatures and Mystical Teachings back into the library.
Resolve a few Gravebreaker Lamia triggers to put those cards into the graveyard again. Leave the rest on the stack, we don't want to empty our library yet.
Flashback Mystical Teachings and fetch the second Battly Hymn.
Cast Battle Hymn, getting 2^^5 copies.
Again each copy more than squares the number of creatures. We end up with more than 2^(2^(2^^5)) = 2^^7 artifacts.
This time we turn most of those resources into Rings of Brighthearth copies, leaving just enough operating mana to get through the next few steps.
Sacrifice Blighted Steppe, get more than 2^^7 Ring of Brighthearth triggers for the ability.
Pay for one of the Ring of Brighthearth triggers and get 2^^7 life.
Bounce and replay Spellweaver Helix. Exile Siege of Towers, Mobilize and Acorn Harvest.
Activate The Scarab God to create a copy of Sea Gate Stormcaller. Get >2^^7 delayed triggers.
Activate The Scarab God to create a copy of Wood Elves. Find Stomping Ground and pay 2 life to let it come into play untapped. Tap for green.
Flashback Acorn Harvest.
Spellweaver Helix triggers. When resolving cast Mobilize first. The Sea Gate Stormcallers trigger and wait to be put on the stack. Then cast Siege of Towers and pay the replicate cost once. Replicate triggers and waits to be put on the stack. After that we finish resolving Spellweaver Helix and put the new triggers on the stack. Order them so that we resolve replicate first.
Resolve replicate and turn Stomping Ground into a creature.
Resolve the >2^^7 Mobilizes to untap Stomping Ground and tap for r/g every time.
Activate The Scarab God to create a copy of Gravebreaker Lamia. Leave the triggers on the stack.
Activate The Scarab God to create a copy of Riftsweeper. Put all the exiled sorceries and creatures back into the library.
Resolve the Gravebreaker Lamia triggers, putting the entire library into the graveyard. (We can't fail to find a card, so unless we get rid of most Panharmonicons the library is now empty. But I don't think that is a problem.)
Turn the mana into more copies of artifacts and creatures again.
Repeat for all of the life we have, each time roughly doubling the number of artifacts. We end up with more than 2^(2^^7) = 2^^8 creatures.
Then we resolve the next copy of the Blighted Steppes ability, this time gaining 2^^8 life, which we turn into 2^(2^^8) = 2^^9 creatures.
After all 2^^7 copies of the Blighted Steppes ability we have more than 2^^(2^^7) artifacts/life/mana. We can also create The Scarab God copies of our creatures in the graveyard.
Create a copy of Moraug, Fury of Akoum.
Bounce Vault of Whispers and put it back onto the battlefield, triggering Moraug, Fury of Akoum 2^^2^^7 times thanks to Panharmonicon copies.
Exile Prosperity with Spellweaver Helix and put it in the library with a Riftsweeper copy. (also put in the Riftsweeper and anything else we want to draw.)
Go to combat with a hasty Myr Battlesphere, attack and damage the opponent with the trigger. Get some counters on Night Dealings.
Activate Night Dealings with X=1 to grab Prosperity. (Get mana from Vault of Whisper and Mox Sapphire copies)
Create a Sea Gate Stormcaller copy to get 2^^2^^7 delayed triggers.
Cast Prosperity with X=1 to draw 1 card 2^^2^^7 times.
I have no doubt we can access the full combo from there
Edit: With the mana from Stomping Ground, we can activate Temur Sabertooth X times, and turn C Dual Natures into C * (PH+2)^X Dual Natures. The problem is that that puts Dual Nature destruction triggers on the stack. But, we can use the opportunity to make permanent copies of other creatures (like Sea Gate Stormcaller, not that those tokens need to be permanent) into play, using the interrupt trick. So, I think we can get triple arrows with your setup.
Currently the problem would be that Sea Gate Stormcaller ended up in the graveyard and creating The Scarab God copies of it doesn't take advantage of Dual Nature. Dual Nature also doesn't help to create more Panharmonicons, so I don't see how to turn it into more copies of Mobilize on the next flashback.
To make it work we need Sea Gate Stormcaller in hand. That is probably doable, but requires some shuffling around. We need to have Sea Gate Stormcaller triggers ready when we flashback Acorn Harvest, since without Mobilize copies we only get the one green back that we payed for the flashback.
So either we don't use the Stormcaller before that or we use an extra card in hand for Elvish Spirit Guide and bounce it once. Room in hand after Worldpurge is also tight if we want to sneak in extra Stormcaller triggers from that.
For freeing up the extra card slot I was thinking about skipping Wormfang Behemoth. Most of the cards can be put on the stack before we cast Eureka and Worldpurge, so exiling the hand might be unnecessary. Of course that makes it impossible to react to some triggers, which loses some Panharmonicon copies at the start.
So we'll need to make some early changes and go through everything again to make sure we don't lose too much to get started. But getting that extra layer seems doable
Edit:
Yep, I've successfully modified my start to include the Dual Nature layer:
Play Show and Tell, put Omniscience into play. (1u, 2 cards)
Play Channel, convert 19 life into mana. (1u, 19c, 1 card)
Play Prosperity with X=19. (19 cards)
Play Vedalken Orrery. (18 cards)
Play Opalescence. (17 cards)
Play Dual Nature. Leave 2 Dual Nature triggers on the stack. (16 cards)
Play Mirrorworks. (15 cards)
Play Panharmonicon. Leave 2 Mirrorwork triggers on the stack (14 cards)
Play Eureka, leave it on the stack. (13 cards)
Play Worldpurge, leave it on the stack. (12 cards)
Play Wormfang Behemoth, let it exile your hand. (11 cards exiled)
Resolve Worldpurge. It bounces Mox Pearl, Mox Sapphire, Tolarian Academy, Omniscience, Vedalken Orrery, Mirrorworks, Panharmonicon, Opalescence, Dual Nature and Wormfang Behemoth. Shuffle Mox Pearl, Mox Sapphire and Wormfang Behemoth into the library.
Wormfang Behemoth trigger returns the exiled cards to hand. (18 cards)
Resolve Eureka, put Omniscience, Vedalken Orrery, Tolarian Academy, Blighted Steppe, Spellweaver Helix, Rings of Brighthearth, Opalescence, Mirrorworks and Vault of Whispers into play. Leave the Mirrorworks trigger for Vault of Whispers on the stack. (9 cards)
Play Panharmonicon. Leave 2 Mirrorwork triggers on the stack. (1 PH, 8 cards)
Play Dual Nature, get 2 copies (1 PH, 7 cards)
Play Myr Battlesphere, get 6 copies, create 56 myr tokens. (1 PH, 6 cards)
Tap Tolarian Academy for mana. We have 69 artifacts. (1 PH, 6 cards, 69u)
Pay for the 4 Mirrorworks(Panharmonicon) and the Mirrorworks(Vault of Whispers) triggers. (5 PH, 6 cards, 59u)
Resolve the 2 Dual Nature triggers. We now have 5 Dual Natures. (5 PH, 6 cards, 59u)
Play The Scarab God. Get 30 Dual Nature copies. (5 PH, 5 cards, 59u)
Play Master Transmuter. Get 30 Dual Nature copies. (5 PH, 4 cards, 59u)
Play Night Dealings. Get 30 Dual Nature copies. (5 PH, 3 cards, 59u)
Play Sea Gate Stormcaller kicked. Get 30 Dual Nature copies. Each triggers 6 times for a total of 186 delayed triggers, 6 of which are kicked. (5 PH, 2 cards, 54u)
Play Gravebreaker Lamia. Put the 6 etb triggers on the stack first, then the 30 Dual Nature triggers. Resolve 6 Dual Nature triggers, resolving the 30 etb's for the first 5 copies. This leaves us with 7 cards in the library. We fetch 5 of those later, so we can't resolve more etbs to get more Dual Nature copies yet. (5 PH, 1 card, 54u)
Exile Elvish Spirit Guide from hand. Save the green mana for later. I just don't want to keep track of cards in hand anymore ^^ (5 PH, 54u)
Tap one Vault of Whispers to activate The Scarab God and get a copy of Marchesa's Smuggler. (5 PH, 51u)
Tap the other Vault of Whispers to flashback Mystical Teachings and fetch Battle Hymn. (5 PH, 51u)
Play Battle Hymn. Get 192 copies from Sea Gate Stormcaller triggers. (5 PH, 51u)
Resolve the first Battly Hymn copy. We have 201 creatures. (5 PH, 51u, 201r)
Use the mana to create more Panharmonicons: Marchesa's Smuggler gives haste to a Master Transmuter. Master transmuter returns Panharmonicon to hand. Replay it and pay for Mirrorworks triggers.
1st time costs 2u,1r,1c for 5 Mirrorworks triggers. Pay for them. (10 PH, 49u, 189r)
2nd time costs 2u,1r,1c for 10 Mirrorworks triggers. Pay for them. (20 PH, 47u, 167r)
3rd time costs 2u,1r,1c for 20 Mirrorworks triggers. Pay for them. (40 PH, 45u, 125r)
4th time costs 2u,1r,1c for 40 Mirrorworks triggers. Pay for them. (80 PH, 43u, 43r)
5th time costs 2u,1r,1c for 80 Mirrorworks triggers. Pay for 36 of them. (116 PH, 4u, 2r)
Use Marchesa's Smuggler + Master Transmuter to bounce Myr Battlesphere. Dual Nature exiles the token copies. (116 PH, 2u)
Play Myr Battlesphere. Don't pay for the Mirrorworks triggers. Dual Nature triggers 5*117 times for a total of 586 Myr Battlespheres entering the battlefield. Each one triggers its etb 117 times and we create 274284 Myrs. (116 PH, 2u)
Resolve a Battle Hymn copy. The Number of creatures is big enough that I'm going to start estimating. The last step gave us over 270000 creatures. Let's go with that. (116 PH, 2u, >270000r)
Use Marchesa's Smuggler + Master Transmuter to bounce Vault of Whispers. Put it back into play. Pay for 1 copy. (116 PH, >270000r)
Tap the Vault of Whispers to activate Night Dealings. Find Mox Sapphire. (116 PH, >270000r)
Play Mox Sapphire. Pay for some copies. Tap them. We need roughly 2*log_2(red mana) of them so about 40... not enough to make a dent in our red mana estimate. (116 PH, ~40u, >270000r)
Now turn the red mana into Panharmonicon copies again. We need to pay 2r per copy plus some overhead to generate new triggers, plus some overhead overhead to generate more blue mana and untapped Master Transmuters. The overhead is roughly at log_2 of the red mana, so we can keep ignoring that for the estimate.
After spending most of the mana we have more than 135000 Panharmonicons. (>135000 PH, 4u, 2r)
Use the last mana to bounce and replay Myr Battlesphere. We get (1+DN*PH)*(1+PH)*4 Myrs. (>135000 PH, 2u)
Resolve another Battle Hymn. If we have X Panharmonicons we get >20*X^2 mana.
Turn the mana into more Panharmonicons. We get more than >20*X^2 copies. So 20*135000^2 > 4^2*135000^2 = 540000^2 > (2^19)^2 = 2^38
Repeat for the other 190 Battle Hymn copies on the stack. Get a huge amount of anything we can create here: Panharmonicons, other artifacts, red mana, blue mana, black mana and white mana (Night Dealings can fetch Mox Pearl)
How much? We more than square the number of Panharmonicons 190 more times, so we get more than (2^38)^(2^190) = 2^(38*2^190) > 2^(2^5*2^190) = 2^(2^195) > 2^^5
Specifically we turn most of those resources into Panharmonicon copies, leaving just enough operating mana/artifacts to get through the next few steps.
Activate The Scarab God to create a copy of Riftsweeper. Put the exiled creatures and Mystical Teachings back into the library.
Resolve a few Gravebreaker Lamia triggers to put those cards into the graveyard again. Leave the rest on the stack, we still don't want to empty our library.
Flashback Mystical Teachings and fetch the second Battly Hymn.
Activate The Scarab God to create a copy of Temur Sabertooth.
Use the one green mana we still have saved to activate it, getting a Rings of Brighthearth trigger.
Pay for the trigger to bounce Sea Gate Stormcaller.
Play Sea Gate Stormcaller and get 2^^5 delayed triggers.
Resolve the Temur Sabertooth ability to bounce Sea Gate Stormcaller again. We can do that because the ability doesn't target. Keep it in hand for later.
Cast Battle Hymn, getting 2^^5 copies.
Again each copy more than squares the number of creatures. We end up with more than 2^(2^(2^^5)) = 2^^7 artifacts.
This time we turn most of those resources into Rings of Brighthearth copies, leaving just enough operating mana to get through the next few steps.
Sacrifice Blighted Steppe, get more than 2^^7 Ring of Brighthearth triggers for the ability.
Pay for one of the Ring of Brighthearth triggers and get 2^^7 life.
Bounce and replay Spellweaver Helix. Exile Siege of Towers, Mobilize and Acorn Harvest.
Play Sea Gate Stormcaller. Get >2^^7 delayed triggers.
Activate The Scarab God to create a copy of Wood Elves. Find Stomping Ground and pay 2 life to let it come into play untapped. Tap for green. (We have now fetched everything we needed from the library)
Flashback Acorn Harvest.
Spellweaver Helix triggers. When resolving cast Mobilize first. The Sea Gate Stormcallers trigger and wait to be put on the stack. Then cast Siege of Towers and pay the replicate cost once. Replicate triggers and waits to be put on the stack. After that we finish resolving Spellweaver Helix and put the new triggers on the stack. Order them so that we resolve replicate first.
Resolve replicate and turn Stomping Ground into a creature.
Resolve the >2^^7 Mobilizes to untap Stomping Ground and tap for r/g every time.
Use 2 mana to bounce Dual Nature. Leave the token destruction triggers on the stack.
Replay Dual Nature. All Dual Natures trigger many times. The important part is that we more than double the amount of Dual Nature tokens once we resolve all the token creation trigger.
Repeat the last two steps X times to get more than 2^X Dual Natures. Leave just enough operating mana to get through the few steps until more mana is generated.
Bounce and replay Sea Gate Stormcaller to get 2^X delayed triggers.
Let the destructive Dual Nature triggers resolve. We lose all the created creature tokens, but those are not important anymore.
Activate The Scarab God to create a copy of Riftsweeper. Put the exiled Acorn Harvest and Riftsweeper back into the library.
Bounce and replay Gravebreaker Lamia to put the library back into the graveyard.
Pay 3 life to flashback Acorn Harvest again, triggering a cast of Mobilize with 2^X copies, giving us 2^X mana.
Repeat the last few steps. First repeat gets us to 2^(2^^7)=2^^8, second to 2^(2^^8)=2^^9. After 2^^7 repeats we get 2^^(2^^7). In general we can turn X life into 2^^X mana/artifacts/creatures/enchantments.
Specifically we want creatures because we still have 2^^7 Rings of Brighthearth copies for Blighted Steppes ability on the stack. Resolve them one at a time, each time turning X life into 2^^X creatures. The first gets more than 2^^(2^^7) > 2^^(2^^4) = 2^^^4. The second gets 2^^(2^^^4) = 2^^^5. So we can turn X Blighted Steps abilities into 2^^^X artifacts/creatures/enchantments/mana/life
After all 2^^7 copies of the Blighted Steppes ability we have more than 2^^^(2^^7) of anything we can produce. It is time to get access to the real combo.
Use The Scarab God to create a copy of Moraug, Fury of Akoum.
Bounce Vault of Whispers and put it back onto the battlefield, triggering Moraug, Fury of Akoum 2^^^(2^^7) times thanks to Panharmonicon copies.
Exile Prosperity with Spellweaver Helix and put it in the library with a Riftsweeper copy. Also put in the Riftsweeper and anything else we want to draw.
Go to combat with a hasty Myr Battlesphere, attack and damage the opponent with the trigger. Get some counters on Night Dealings.
Activate Night Dealings with X=1 to grab Prosperity. (Get mana from Vault of Whisper and Mox Sapphire copies)
Create a Sea Gate Stormcaller copy to get 2^^^(2^^7) delayed triggers.
Cast Prosperity with X=1 to draw 1 card 2^^^(2^^7) times.
I have no doubt we can access the full combo from there
I thought a bit about replacing Elvish Spirit Guide with Acorn Havest, to get a bunch of green mana with Mobilize rather than one. That would most conveniently and effectively be done after the first Battle Hymn; the problem is at that point the Sea Gate Stormcaller is on the battlefield. So it seems like we would want to do this before the first Battle Hymn; we could then put Stormcaller triggers on the stack for the first Battle Hymn, then have a bounce waiting to put Stormcaller in play before the second Battle Hymn. But, before the first Battle Hymn means we have to cast Siege of Towers separately, since we don't yet have red mana to cast the Replicate cost. So we would need to replace one more card. Also, we need one more black mana to use Scarab God to fetch Wood Elves and Stomping Ground.
Actually, at this point, it would be easier just to have the Elvish Spirit Guide since we need to replace another card anyway, and cast Acorn Harvest between the Battle Hymns. But I don't know what we would replace.
Anyway, this is looking good! I suppose there is no chance of fitting in a stage?
Edit: Hmmm, instead of Siege of Towers, would Living Lands be more convenient? Living Lands will get bounced by Worldpurge, so I don't think it would allow us to put Mobilize below Worldpurge. Living Lands would free us from needing a Mountain, and we wouldn't have to pay the Replicate cost for Siege of Towers.
I imagine this doesn't save us a card, as you already pointed out that we can't use the land to pay for Deathgrip. Would it free us from needing a second Battle Hymn? Probably not.
Still, we could replace Stomping Ground with Temple Garden to get white mana, and then Mox Pearl could go back to Mana Crypt. That would get us another colorless mana, which I imagine we would use to draw another card in the opening.
Edit: Oh wait - I think we can replace a Battle Hymn and Dark Ritual/Vault of Whispers with a Burnt Offering.
Edit: Could we get anything positive out of replacing an Arcbond with Mirari?
Burnt Offering looks good! Is there any way we can turn an extra card slot into another layer? If not, then we can use it to improve the start. For example Master Skald could give us access to all the artifacts and enchantments we cannot draw. That means we could potentially go through the entire hyperstage including BB calculations in the first main phase. Though I will wait for a while before I try to work out the start with that.
2 Opalescence
3 Dual Nature
4 Vedalken Orrery
5 Riftsweeper
6 Gravebreaker Lamia
7 Marchesa's Smuggler
8 Coat of Arms
9 Rotlung Reanimator
10 Dralnu's Crusade
11 Arcbond
12 Arcbond
13 Fractured Identity
14 Artificial Evolution
15 Sea Gate Stormcaller
16 Kaervek's Spite
17 Avacyn, Guardian Angel
18 Goblin Boom Keg
19 Battle Hymn
20 Mirrorworks
21 Master Transmuter
22 Mox Sapphire
24 The Scarab God
25 Rings of Brighthearth
26 Temur Sabertooth
27 Elvish Spirit Guide
28 Mobilize
29 Ambush Commander
30 Worldfire
31 Worldpurge
32 Acorn Harvest
33 Acorn Harvest
34 Radiant Fountain
35 Akoum Refuge
36 Eureka
37 Show and Tell
38 Wood Elves
39 Burnt Offering
40 Panharmonicon
41 Spellweaver Helix
42 Wormfang Behemoth
43 Deathgrip
44 Mystical Teachings
46 Mana Crypt
47 Tolarian Academy
48 Channel
49 Blighted Steppe
50 Arbiter of the Ideal
51 Tolarian Kraken
52 Prosperity
53 Angelheart Vial
54 Backfire
55 Justice
56 Brallin, Skyshark Raider
57 Pain Magnification
58 Awaken the Blood Avatar
59 Moraug, Fury of Akoum
60 Harmonic Prodigy
If it all works, we can deal more than BB_{w^2+14} (BB_{w^2+14} (X)) damage.
The Justice layer should work out though. As long as we make sure the damage is dealt from red creatures under the correct persons control. For the discard to draw sequence that should be fine as we can use Brallin, Skyshark Rider to deal damage and Night Dealings/Angelheart Vial to draw, depending on where the damage ends up/who discards.
For the attack to discard sequence we need to find a working red source. Unfortunately Awaken the Blood Avatar can't be used with the combat layers because the token it creates has haste. It can be blocked and start a BB computation without clearing our side of the battlefield. Mage Slayer looks like it would work.
So we attack with a equipped red creature. It deals >3 damage to the opponent X times. Every time Justice deals >3 damage to us X times. Every time we have to discard a card X times. Every time Brallin damages the opponent X times. Every time Justice damages us X times.
To me it looks like that sequence works, and we end in Angelheart Vial.
So we get 2 extra layers from Justice. That was a great idea! Too bad about the Backfire, I guess we'll keep World at War again.
With the extra card at the start, maybe I will look into the unlikely possibility of getting a stage going. Getting a decent BB computation looks hard, since we have to give the opponent creatures one at a time with Fractured Identity, so I guess we will have to have a lot of life and green mana to get it working. The normal stage also seems problematic, since it requires black mana to counter our creature casts, so it seems to only work when there is a Worldfire stage we can transition into. You mentioned a janky life stage, but I realize I don't know how that works. Can you explain the life stage?
This requires the ability to put a transition on the stack again without the instants and using just Bloodbond March triggers of Elvish Spirit Guide. We might get enough mana for that from Tolarian Academy and the other lands. But it is pretty tough.
We can't use a creature bounce layer since we need to return the Elvish Spirit Guide from the graveyard to generate green mana and without black from the instants we can't counter it to get useful Bloodbond March triggers. We also can't keep Mobilize on the stack from the lower transition to get colored mana, since the land won't be animated and we can't mix any Siege of Towers between the Mobilize copies.
Honestly, I think getting BB calculations (or some smaller useful Waterfall program) would require less extra cards.
Edit: And I just noticed that the janky stage would be completely impossible now that we get all our black mana from an instant.
I suppose this could be a case where, when we write this up, we present both the noncomputation opening, and a computation opening (or a set of computational openings with various R's and C's), and leave it open which one is bigger. Might as well cover all bases.
Of course, it would be nice to actually demonstrate a good lower bound for the computation. So, it may be fruitful to look at simple Waterfall programs. My first thought is just turning A's into B's, B's into C's, to get something like c^N as the output. That's completely weaksauce though, considering we're competing against something like 2^^^2^^7. I understand how to do Knuth arrows with counters:
-have counters 1 through N
-we can decrease counter 2 by 1 to increase counter 1 by more (increase by 2 is fine)
-we can decrease counter X (for X > 2) by 1 to convert/add a lower counter (counter 1 is fine) to counter X-1.
If decreasing counter 2 increases counter 1 by 2, than Y in counter X can turn into roughly 2 -> Y -> X-2 in counter 1.
Of course, this is a different sort of counter computational model than the Waterfall model. But this would be an instructive thing to try to translate into the Waterfall model.
You can test the programs and see them in action on http://nethack4.org/esolangs/waterfall/. There is a nice interpreter at the bottom of the page.
Exponentiation program, use 2n as input for the last clock to get roughly 6*2^n:
[[1000,5,5,5,5,5],
[1,2,2,6,0,2],
[3,2,2,0,4,2],
[2,0,4,4,2,2],
[2,4,0,2,4,0],
[14,0,0,0,0,0]]
Tetration program, use 2n as input for the last clock to get 2^^n:
[[10000,8,8,8,8,8,8,8,8],
[1,2,2,2,6,6,0,2,2],
[3,2,2,2,0,0,4,2,2],
[3,2,2,2,0,0,2,4,2],
[2,0,4,2,4,2,2,2,2],
[2,0,2,4,2,4,2,2,2],
[2,4,0,2,2,4,4,0,2],
[2,2,4,0,4,0,2,4,0],
[4,0,0,0,0,0,0,0,0]]
(use 4,4 as input for the last 2 clocks to get a long run that you can still watch to the end)
For an extra layer I need 3 additional clocks:
- 1 clock for the layer counter
- 1 clock for the transfer state that will move the output to the layer counter below it
- 1 clock that will be another copy of the output. I found that necessary to make the state switch after emptying the output work correctly
Edit: Hmm, I think Mage Slayer is problematic, because of the need to equip. I think Emberwilde Captain works? Emberwilde Captain switches around who takes and who deals damage, so it's back to Night Dealings, which is just as well probably.
Edit: Okay, this start is triggering me. I believe I know how to get to Mobilize / Blighted Steppe / Rings of Brighthearth combo and get a decent triple arrow number, then go to the computation. The problem is that we won't have much black mana. Even if we can keep Iijil's start, and then cast a Burnt Offering, sacrificing a Gravebreaker Lamia say, we will only get 900+ black/red mana, and we have to use that mana if we want to build up more. So, if we need to use The Scarab God for our Rotlung Reanimators, we can only get about 900 of them perhaps. If we can cast Rotlung Reanimator from our hand, we could potentially get a lot more, but of course this wouldn't give precisely the Waterfall Model, as Iijil pointed out earlier.
Ideally, we would want to delay the casting of Burnt Offering until we cast some other buildup spells, like Battle Hymn or Acorn Harvest. But, we are using our black mana for a lot of the card fetches, using The Scarab God and Mystical Teachings. So, delaying Burnt Offering means we have to have drawn those cards. I'm having trouble making do with the card slots we have again.
Edit: Hmmm, do we really need Wood Elves? When Temple Garden is a creature, we can use Temur Sabertooth to bring it back to our hand, then Wormfang Behemoth can protect it from [c}Worldfire[/c]. After Worldpurge, we can use Show and Tell to put it back on the battlefield. (I don't think we currently need Show and Tell for anything else?)
If Wood Elves can be removed, then we have another card slot. I'm thinking about using Silkbind Faerie. When we resolve a Tolarian Kraken trigger, we can tap a Silkbind Faerie. We can then untap the Silkbind Faerie to put a lot of Rings of Brighthearth triggers on the stack, each of which can tap an Arbiter of the Ideal, which we can then untap with Mobilize. So I think that's another layer.
We can use two Silkbind Faeries to repeatedly tap each other and get more RoB triggers, but each time it costs mana, and I don't think we get any benefit from this procedure until we resolve Mobilize to untap an Arbiter of the Ideal, at which point the party stops.
Edit: Oh, I guess the party doesn't have to stop; after a Mobilize, we can use a RoB trigger to tap a Silkbind Faerie, then create more RoB triggers again. So this goes infinite.
Edit: Instead of Silkbind Faerie, I'm contemplating having a Gilder Bairn and using it to get to the second stage of Kiora Bests the Sea God, which can tap Gilder Bairns under the opponent's control. To keep this from going infinite, we can have something sufficiently expensive to gain control of the tapped Gilder Bairns. (Mass Manipulation?) It doesn't look like this is worth the cards though.
Edit: It occurred to me it would be okay to damage animated enchantments, since if we dealt damage to an animated enchantment with Arcbond on it, it would quickly die and the computation would stop. So, that opens up the possibility of using the cards that required dealing damage to creatures, like Guilty Conscience and Spiteful Shadows. But, it looks like those particular cards don't add any layers, for the same reason that Backfire doesn't: the enchanted creature goes away once we try to make use of the damage, and the triggers that we have are only worth one layer. Looking at global enchantments, we have Repercussion and Mangara's Equity. Those two seem to go infinite together though. Repercussion could perhaps combo very well with Justice, but it has to start with damage dealt to a creature, and to be safe we want to deal damage to an animated enchantment. However, I'm not sure how we would restrict to just damaging animated enchantments, unless we use a damage bouncer, and the damage bouncers that I know (Guilty Conscience and Mangara's Equity) seem to go infinite with Repercussion. So, no progress here.
Edit: I was wondering if we could get something off of Proliferate, like using Thrummingbird. I was thinking Thrummingbird could get us to the fourth stage of The Akroan War, causing all our tapped creatures to damage themselves. But, not all creatures would kill themslves this way. In particular, Master Transmuter wouldn't kill itself with the damage, and we can make it tapped even without Tolarian Kraken, if we were to remove that. So presumably we can get an infinite computation started that way.
Another idea is to get to the final stage of Tymaret Calls the Dead, and give the opponent life. Then we can use something like Kaboom! to deal damage to them, and trigger Justice and the rest, adding two additional layers. But, due to not being able to damage the opponent lower down, we have to replace Brallin, Skyshark Rider with Megrim, which we can't link into Justice, so we lose a layer. Also, we're one card over, so we're going to lose another layer. But, we can drop World at War, so that we end in Moraug for BB_{w^2+13} (BB_{w^2+13} (X)) damage.
Edit: Oh, I had a very nice idea that I really hoped would work out, but it doesn't quite work out yet. We saw that we were able to double up on Justice, once for dealing 3 or more damage, and once for dealing 1-2 damage. I was thinking perhaps we could double up again, by which players used and got affected by which effects. In particular, perhaps we could have Megrim or Brallin, Skyshark Rider be able to deal 3+ damage, but only one way. So, we could use cards that increased damage that our sources deal, but not the opponent's, so we that we can re-trigger Pain Magnification when the sources are on our side, then they will go on to the other side, and we can't trigger again.
Using Brallin nicely switches who takes damage, but unfortunately Justice switches it back, so with Brallin + Justice we'll keep having Brallin on our side, which is no good. With Brallin and no Justice, we'll gain two layers, with the repeat, but losing Justice costs us two layers, and we need a card to increase Brallin's damage, so we wind up with the same number of layers and the same number of cards as a previous layer sequence. (Not the most recent one with Thrummingbird, which seems to be better)
Megrim + Justice would switch, if Justice was triggered by Megrim. I don't know of a way to make Megrim trigger Justice that wouldn't also allow Justice to trigger itself and go infinite. (e.g. Sleight of Mind or Chaoslace) I tried to think of ways to replace Justice, but anything that enchants or deals damage to a Megrim will stop being useful once Megrim goes away, so I didn't see a way to add a layer with cards like Mangara's Equity or Backfire.
Spiteful Visions has the characteristics to work with Justice, but I don't know of a damage mechanic like Pain Magnfication for drawing.
So yeah, not an improvement yet with this idea. If we could somehow get the repeat and keep Justice, that could potentially add 3 layers.
Edit: Oh, I guess with Megrim we wouldn't have to rely on Justice or whatever we used to add another layer, we could get the infinite with just Megrim. So yeah, it looks like we can only use Brallin.
Looks like I've missed some serious developments in the deck, before I try and get caught up I just want to chime in that 6 waterclocks (+halting flooding clock) is enough to implement a UTM, though it needs something like x^^^^x (maybe x^^^x) tokens to make a machine of size x, (via https://esolangs.org/wiki/Spiral_Rise into a bitwise cyclic tag system [there's a proof for that somewhere...], and there into something more efficient, losing about an arrowsworth of efficiency each translation.)
Given that flooding clocks are still plentiful (and fast growing!), it seems likely that we can do much better than tetration with very few proper waterclocks.
How many Rotlung Reanimators are needed for the UTM? That's the crucial number; the number of clocks don't really matter, except indirectly in affecting how many Reanimators (and Dralnu's Crusades, but we only need a few Dralnu's Crusades) we need.
The start will depend on whether we have any extra card slots left over from the layer sequence. If we have at least one slot, we can add Master Skald, which along with our other card fetchers will allow us to access the entire deck before combat. So we should be able to generate BB_{w^2 + 1}(X) Moraug triggers before combat, where X is how many Rings of Brighthearth triggers we can get when we finally activate our Blighted Steppe. So this will be large regardless, however the value of X may very well depend on the output of a Waterfall computation, so even here we may need to an estimate or lower bound as to the size of it. (I haven't looked into this enough to give more details.)
If we don't have any more space left, than the best I was able to do was to generate about 1900 black mana, and then, depending on how much of that mana we are willing to give up, generate something like 2^^^X of other resources, like other colors of mana and Panharmonicons and Sea Gate Stormcallers. So we will be able to generate around 1900 - Y Rotlung Reanimators and 2^^^X token creatures.
So, then it matters whether we need X^^^^X or X^^^X tokens to make a machine of size X. Precise bounds will be very helpful, since even with X^^^X we will be cutting it close. We will also need to be able to code the UTM with 1900 - Y Reanimators, of course.
So yeah, precise details with regard to the translation to UTM's and the normal Busy Beaver function would be of great help!
I think that perhaps when we write this up, we could include both the lower bound in terms of a Waterfall Busy Beaver function (perhaps we can define WBB(R,C) to be the largest output that we can get from a halting computation that requires no more than R Rotlung Reanimators and C input creatures), and then possibly also in other terms, like a computational bound, and/or a standard Busy Beaver bound, so that we have a bound in whatever version the reader prefers.
Using flooding clocks to help cut down on resources when we program actual Waterfall programs could be useful, as could ignoring the rule that waterclocks can't zero at the same time. I'm not sure about doing much better than tetration with very few proper waterclocks though - I would theorize that the actual Busy Beaver Waterfall programs will be amazingly good, but in terms of what we can actually program, I'm not sure if we will be able to implement say the Ackermann function with just a few waterclocks. Did you have something in mind?