Okay, improved the start, resulting in more than 2^^45 Thaumaturges before using Vault Robber for the first time. Not having Palladium Myr greatly reduces the efficiency of the trigger cycles, but it doesn't matter much; getting another exponentiation is more important.
Turn 1:
Tapped Land, go.
Turn 2:
Draw (7 cards in hand, 52 cards in library)
Play Island.
Play Stonecoil Serpent with X=0.
Play Tibalt's Trickery counters Serpent, mills 1 card and casts Genesis Ultimatum. (4 cards in hand, 50 cards in library)
Ultimatum puts Xorn, Purphoros, Bronze-Blooded, Tyvar Kell, Woe Strider and Gyruda, Doom of Depths into play. (45 cards in library)
Gyruda mills 4 cards and puts Luminous Broodmoth into play. (41 cards in library)
Woe Strider sacrifices Gyruda. Broodmoth brings it back.
Gyruda mills 4 cards and puts another Gyruda into play. Legend rule kills the one with flying counter. (37 cards in library)
Gyruda mills 4 cards and puts Kinnan, Bonder Prodigy into play. (33 cards in library)
Woe Strider sacrifices Gyruda. Broodmoth brings it back.
Gyruda mills 4 cards and puts another Gyruda into play. Legend rule kills the one with flying counter. (29 cards in library)
Gyruda mills 4 cards and puts Protean Thaumaturge into play. (25 cards in library)
Woe Strider sacrifices Gyruda. Broodmoth brings it back.
Gyruda mills 4 cards and puts another Gyruda into play. Legend rule kills the one with flying counter. (21 cards in library)
Gyruda mills 4 cards and puts Elvish Warmaster into play. 17 cards in library)
Woe Strider sacrifices Gyruda. Broodmoth brings it back.
Gyruda mills 4 cards and puts Sorcerer's Broom into play. (13 cards in library)
Tap Warmaster for mana. (2 black)
Play Hateful Eidolon. Thaumaturge becomes a copy of Broom. (3 cards in hand, 1 black)
Activate Tyvar Kell to create an Elf token. Elvish Warmaster triggers to create an Elf token. Tap both Elf tokens for mana. (5 black, 2 Elf tokens)
Sacrifice the Xorn, it comes back. The Thaumabroom triggers, pay for it. (2 black, 2 untapped Thaumabrooms, 2 Elf tokens)
Play the second Hateful Eidolon. Turn the nontoken Thaumaturge into a Thaumamaster, keep the nontoken Thaumabroom as it is. (2 cards in hand, 1 black)
Sacrifice the original Warmaster. The Thuamabroom triggers. The Warmaster comes back, and the Thaumamaster triggers, creating an Elf token. Tap both Warmasters and the Elf token for mana. Pay for the Thaumabroom trigger. (4 black mana, 1 tapped Thaumamaster, 1 tapped Thaumabroom, 1 untapped Thamabroom, 3 Elf tokens)
Sacrifice the nontoken Thaumamaster. The Thuamabrooms trigger, pay for one. The Thaumamaster comes back as an untapped Thaumaturge. (1 black mana, 1 untapped Thaumaturge, 1 tapped Thaumabroom, 2 untapped Thaumabrooms, 3 Elf tokens)
Play the third Hateful Eidolon. Turn the 3 untapped Thaumaturges into Thaumamasters, keep the tapped one as a Thaumabroom. (1 card in hand, 0 mana, 3 untapped Thaumamasters, 1 tapped Thaumabroom)
Play Skemfar Avenger. The Warmaster and the 3 Thaumamasters trigger, creating 4 Elf tokens. Tap Skemfar Avenger, the 3 Thaumamasters, and the 4 Elf tokens for mana. (16 black mana, 3 tapped Thaumamasters, 1 tapped Thamabroom, 7 Elf tokens)
Sacrifice Warmaster. Avenger triggers, Thaumabroom triggers. (19 life, 1 card in hand, 12 cards in library)
Sacrifice Sorcerer's Broom twice. Pay 15 mana to make 5 copies of Thaumabrooms. (1 black mana, 3 tapped Thaumamasters, 1 tapped Thaumabroom, 5 untapped Thaumabrooms, 7 Elf tokens)
Play the fourth Hateful Eidolon. Turn the 6 Thaumabrooms into Thaumamasters, and the 3 Thaumamasters into Thaumabrooms. (0 mana, 0 cards in hand)
Sacrifice Skemfar Avenger, Thaumabrooms trigger. Avenger comes back, the 6 Thaumamasters trigger, creating 6 Elf tokens. Tap Avenger, the 5 untapped Thaumamasters, and the 6 Elf tokens for mana. (24 black mana, 6 tapped Thaumamasters, 3 tapped Thaumabrooms, 13 Elf tokens)
Sacrifice Kinnan, it comes back. Sacrifice an Elf token. Pay 24 mana to create 8 copies of Thaumabrooms. (0 mana, 6 tapped Thaumamasters, 3 tapped Thuamabrooms, 8 untapped Thaumabrooms, 12 Elf tokens, 1 Thaumabroom trigger left)
Sacrifice the 12 Elf tokens. Each of the 11 Thaumabrooms trigger 12 times, totaling 11*12 + 1 = 133 triggers.
Sacrifice the first Hateful Eidolon. We get 11 more Thaumabroom triggers, for 144 total. Hateful Eidolon comes back. Turn the 8 untapped Thaumabrooms into Thaumamasters, including the Thaumabroom to be copied next. Turn the tapped Thuamabroom to be copied afterwards into a Hateful Eidolon, and the remaining 8 into Thaumabrooms.
We resolve 1 Thaumabroom trigger, creating a Thaumamaster token. The 8 other Thaumamasters trigger, creating 8 Elf tokens. Tap the 9 Thaumamasters and 8 Elf tokens for mana (34 black mana, 9 tapped Thaumamasters, 8 tapped Thaumabrooms, 1 tapped Thaumaeidolon, 8 Elf tokens. 143 triggers left.)
Resolve another Thaumabroom trigger, creating a Thaumaeidolon token. Turn 12 untapped Thaumaturges into Thaumamasters, the next two Thaumaturges to be copied into Thaumamaster and Thaumaeidolon, and the remaining 16 into Thuamabrooms. (1 black mana, 12 untapped Thaumamasters, 1 tapped Thaumamaster, 1 tapped Thaumaeidolon, 16 tapped Thaumabrooms, 6 Elves, 142 triggers)
Resolve another Thuamabroom trigger, creating a Thaumamaster token. The 12 other Thaumamasters trigger, creating 12 Elf tokens. Tap the 13 Thaumamasters and 12 Elf tokens for 50 mana. (51 black mana, 14 tapped Thaumamasters, 1 tapped Thaumaeidolon, 16 tapped Thaumabrooms, 18 Elves, 141 triggers)
Resolve another Thaumabroom trigger, creating a Thaumaeidolon token. Turn 18 untapped Thaumaturges into Thaumamasters, the next two Thaumaturges to be copied into Thaumamaster and Thuamaeidolon, and the remaining 29 into Thaumabrooms. (0 mana, 18 untapped Thaumamasters, 1 tapped Thaumamaster, 1 tapped Thaumaeidolon, 29 tapped Thaumabrooms, 16 Elves, 140 triggers)
Resolve another Thuamabroom trigger, creating a Thaumamaster token. The 18 other Thaumamasters trigger, creating 18 Elf tokens. Tap the 19 Thaumamasters and 18 Elf tokens for 74 mana. (74 black mana, 20 tapped Thaumamasters, 1 tapped Thaumaeidolon, 29 tapped Thaumabrooms, 34 Elves, 139 triggers)
Sacrifice an Elf token. Pay 72 mana to create 24 Thaumabrooms. (2 mana, 20 tapped Thaumamasters, 1 tapped Thaumaeidolon, 29 tapped Thaumabrooms, 24 untapped Thaumabrooms, 33 Elves, 139 triggers)
Resolve another Thaumabroom trigger, creating a Thaumaeidolon token. Turn 25 untapped Thaumaturges into Thaumamasters, the next two Thaumaturges to be copied into Thaumamaster and Thuamaeidolon, and the remaining 48 into Thaumabrooms. (2 mana, 25 untapped Thaumamasters, 1 tapped Thaumamaster, 1 tapped Thaumaeidolon, 48 tapped Thaumabrooms, 33 Elves, 138 triggers)
Resolve another Thuamabroom trigger, creating a Thaumamaster token. The 25 other Thaumamasters trigger, creating 25 Elf tokens. Tap the 26 Thaumamasters and 25 Elf tokens for 102 mana. (104 black mana, 27 tapped Thaumamasters, 1 tapped Thaumaeidolon, 48 tapped Thaumabrooms, 58 Elves, 137 triggers)
Sacrifice an Elf token. Pay 102 mana to create 34 Thaumabrooms. (2 mana, 27 tapped Thaumamasters, 1 tapped Thaumaeidolon, 48 tapped Thaumabrooms, 34 untapped Thaumabrooms, 57 Elves, 137 triggers)
Every cycle of a Thaumaeidolon creation and a Thaumamaster creation multiplies the number of Thaumaturges by more than 4/3. We will use three Thuamabroom triggers near the end to make copies of Gyruda. We use the three ETB triggers to fetch Cogwork Archivist, Spirit of Malevolence, and Skemfar Avenger. We make sure to have some mana available. We use the remaining 134 triggers to for 67 more Eidolon-Warmaster cycles, after which we will have more than 7.12 billion Thaumamasters, 30.85 billion Thaumabrooms, and 28.48 billion Elf tokens.
We sacrifice the first Hateful Eidolon, and it goes to the graveyard. We use a Cogwork Archivist to put Hateful Eidolon into our empty library. Then, we sacrifice our newly acquired Avenger, triggering the other Avenger, and drawing the Hateful Eidolon at the cost of a life (down to 18 life). We play the Hateful Eidolon, getting Constellation triggers; we turn all 37.97 billion Thaumaturges into Thaumabrooms, except three become two Cogwork Archivists and a Gyruda. We sacrifice all of our Elf tokens, getting more than 1.081 * 10^21 triggers.
We can now sacrifice a Hateful Eidolon, do a process similar to the above, except this time we can create a Hateful Eidolon token every time. We start by using a Cogwork Archivist to put a Gyruda, then make a copy of the Gyruda token. This allows to fetch the Gyruda, and respond to its ability by putting Elvish Warmaster into the library, and then fetching it. We can now use every Thaumabroom trigger to create a copy of Hateful Eidolon, put copies of Gyruda and Warmaster into the library (after sacrificing the Warmaster twice), and sacrificing Gyruda to bring it back, and fetch the other Gyruda and Warmaster, triggering our other Warmasters and getting Elves and mana. The end result is that we multiply our Thaumaturges by more than 4/3 each trigger.
So, after 1.081 * 10^21 triggers, we will have more than (4/3)^(1.081 * 10^21) > 2^(2^68) > 2^^5 Thaumaturges. Each repetition of this process increases the second number by 1. We can drain our life 17 more times, then use Spirit of Malevolence to syphon the opponent's life, allowing for another 19 procedures. Finally, we can sacrifice the other 3 Hateful Eidolons and Purphoros, taking our number of Thaumaturges to more than 2^^45.
We can use Gyruda to fetch Vault Robber from the library after putting it in with Cogwork Assembler, and use the last Constellation trigger to turn all or almost all of our Thaumaturges into Xorns. This allows us to generate more than 2^^45 Treasure tokens from the first use of Vault Robber.
53 creatures, of which we need to keep 3: Sea-Dasher Octopus we need to keep mutating, Kolvari is the front side of The Ringhart Crest, which we need to keep recycling, and we need to keep an enchantment creature around so that we can flash it in. So final damage is currently 3 -> 3 -> 3 -> (3 -> 3 -> 3 -> (3 -> 3 -> 3 -> 50 -> 6) -> 8) -> 8.
Okay, this seems like a pretty good start: (copied some of Iijil's start )
Turn 1:
Tapped Land, go.
Turn 2:
Draw (7 cards in hand, 52 cards in library)
Play Island.
Play Stonecoil Serpent with X=0.
Play Tibalt's Trickery counters Serpent, mills 1 card and casts Genesis Ultimatum. (4 cards in hand, 50 cards in library)
Ultimatum puts Xorn, Purphoros, Bronze-Blooded, Tyvar Kell, Woe Strider and Gyruda, Doom of Depths into play. (45 cards in library)
Gyruda mills 4 cards and puts Luminous Broodmoth into play. (41 cards in library)
Woe Strider sacrifices Gyruda. Broodmoth brings it back.
Gyruda mills 4 cards and puts another Gyruda into play. Legend rule kills the one with flying counter. (37 cards in library)
Gyruda mills 4 cards and puts Kinnan, Bonder Prodigy into play. (33 cards in library)
Woe Strider sacrifices Gyruda. Broodmoth brings it back.
Gyruda mills 4 cards and puts another Gyruda into play. Legend rule kills the one with flying counter. (29 cards in library)
Gyruda mills 4 cards and puts Protean Thaumaturge into play. (25 cards in library)
Woe Strider sacrifices Gyruda. Broodmoth brings it back.
Gyruda mills 4 cards and puts another Gyruda into play. Legend rule kills the one with flying counter. (21 cards in library)
Gyruda mills 4 cards and puts Elvish Warmaster into play. 17 cards in library)
Woe Strider sacrifices Gyruda. Broodmoth brings it back.
Gyruda mills 4 cards and puts Skemfar Avenger into play. (13 cards in library)
Elvish Warmaster triggers to create an Elf token. Tap all 3 Elves for mana. (6 black)
Play Palladium Myr and tap it for mana. (3 cards in hand, 3 black, 3 colorless)
Play Sorcerer's Broom. (2 cards in hand, 3 black, 1 colorless)
Play Hateful Eidolon. Thaumaturge becomes a copy of Broom (1 card in hand, 2 black, 1 colorless)
Sacrifice Warmaster. Avenger triggers. Thaumabroom triggers. Pay for it. Broodmoth brings the Warmaster back. Tap it for mana (19 life, 2 cards in hand, 12 cards in library, 2 black, 2 untapped Thaumabrooms)
Play Duskwielder. Warmaster triggers. Tap the new elves for mana. (1 card in hand, 5 black)
Sacrifice Duskwielder. Broodmoth brings it back. Tap it for mana. Avenger triggers. Thaumabrooms trigger. Pay for them. (18 life, 2 cards in hand, 11 cards in library, 1 black, 4 untapped Thaumabrooms)
Sacrifice Palladium Myr. Broodmoth brings it back. Tap it for mana. Thaumabrooms trigger. Pay for one of them. (1 black, 5 untapped Thaumabrooms)
Play Hateful Eidolon. 4 Thaumabrooms become copies of Warmaster. 1 stays a Thaumabroom (1 card in hand, 4 untapped Thaumamasters, 1 untapped Thaumabroom)
Activate Tyvar Kell to create an Elf token. The Thaumamasters trigger, creating 4 more Elves. Tap all the Elf tokens and one Thaumamaster for mana. (12 black, 7 Elf tokens).
Sacrifice an Elf token. Thaumabroom triggers, pay for it. (18 life, 1 card in hand, 11 cards in library, 9 black, 3 untapped Thuamamasters, 1 tapped Thuamamaster 2 untapped Thaumabrooms)
Sacrifice an Elf token. Thaumabrooms trigger, pay for them. (3 black, 3 untapped Thaumamasters, 1 tapped Thuamamaster, 4 untapped Thaumabrooms, 6 Elf tokens)
Play Hateful Eidolon. 7 Thaumaturges become copies of Palladium Myr, the tapped one becomes a copy of Sorcerer's Broom. Tap the Thaumamyrs for mana. (0 cards in hand, 3 black, 21 colorless, 7 tapped Thaumamyrs, 1 tapped Thaumabroom)
Sacrifice the nontoken Thaumamyr. The Thaumabroom triggers, pay for it. The Protean Thaumaturge comes back. (3, black, 18 colorless, 6 tapped Thaumamyrs, 1 tapped Thaumabroom, 1 untapped Thaumabroom, 1 untapped Thuamaturge)
Sacrifice 2 Elf tokens. Thuamabrooms trigger, pay for them (3 black, 6 tapped Thaumamyrs, 1 tapped Thaumabroom, 7 untapped Thaumabroom, 1 untapped Thaumaturge, 4 Elf tokens)
Play Hateful Eidolon. The 12 Thaumaturges that have not used Warmaster's ability become copies of Warmaster, the remaining 3 become copies of Sorcerer's Broom. (2 black, 8 untapped Thaumamasters, 4 tapped Thaumamasters, 3 tapped Thaumabrooms)
Sacrifice Skemfar Avenger. Luminous Bloodmoth triggers, it comes back. The Thaumamasters trigger, creating 12 Elf tokens. Tap the Avenger, the 8 untapped Thaumamasters, and the 12 Elf tokens for mana (44 black mana, 12 tapped Thaumamasters, 3 tapped Thaumabrooms, 16 Elf tokens)
Sacrifice two Elf tokens. Thaumabrooms trigger, pay for them. (17 black mana, 12 tapped Thaumamasters, 3 tapped Thaumabrooms, 9 untapped Thaumabrooms, 14 Elf tokens)
Sacrifice an Elf token. 12 Thaumabrooms trigger, pay for 5. (2 black mana, 12 tapped Thaumamasters, 3 tapped Thaumabrooms, 14 untapped Thaumabrooms, 13 Elf tokens)
7 Thaumabroom triggers remain on the stack.
Sacrifice Xorn, Purphuros, Kinnan, 1 Goat token, 13 Elf tokens, and 12 tapped Thaumamasters. Luminous Bloodmoth brings Xorn, Purphurous, and Kinnan back.
Sacrifice the first Hateful Eidelon. This triggers Luminous Bloodmoth and all the Thaumabrooms. There are now 30*17 + 7 = 517 Thuamabroom triggers on the stack.
Hateful Eidolon comes back. We have the Thaumabrooms all become copies of Warmaster, except for the second Thaumabroom to be copied (tapped), which becomes a copy of Hateful Eidolon, and one other, which becomes a Thaumbroom. (also tapped)
Resolve the next Thaumabroom trigger. We get a copy of Warmaster. The other 15 Warmasters trigger, and we get 15 Elf tokens.
Tap the 15 Elf tokens and the 15 untapped Warmasters for 60 mana.
Sacrifice 5 Elf tokens, and pay to create 20 new Thaumabrooms (2 black mana, 16 tapped Thaumamasters, 1 tapped Thaumabrooms, 20 untapped Thaumabrooms, 1 tapped Thaumaeidolon, 10 Elf tokens)
Resolve the next Thaumabroom trigger. We get a copy of Hateful Eidolon. The next Thaumaturge to be copied becomes a Hateful Eidolon, the 21 untapped Thaumaturges become Palladium Myrs, and the remaining 17 can become Thaumabrooms.
Tap the Palladium Myrs for mana. (2 black, 63 colorless)
Sacrifice 2 Elf tokens, pay 63 to create 21 copies of Thuamabrooms. (21 tapped Thaumamyrs, 17 tapped Thaumabrooms, 21 untapped Thaumabrooms, 1 tapped Thaumaeidelon)
Resolve the next Thaumabroom trigger. We get a copy of Hateful Eidelon. The next two Thaumaturges to be copied become copies of Warmaster and Hateful Eidelon. We have the Thaumaturges that haven't been used Warmaster's ability become copy of Warmaster (45 total, 21 untapped, 24 tapped). The remaining 14 can become Thaumabrooms.
Resolve the next Thaumabroom trigger. We get a copy of Warmaster.
The other 45 Warmasters trigger, creating 45 Elf tokens.
We tap the 45 Elf tokens and the 22 untapped Warmasters for mana. (136 black mana, 53 Elf tokens)
Sacrifice 3 Elf tokens, pay 135 mana to create 45 more Thaumabrooms. (46 tapped Thaumamasters, 14 tapped Thaumabrooms, 45 untapped Thaumabrooms, 1 tapped Thaumaeidolon. 1 black mana, 50 Elf tokens)
Resolve the next Thaumabroom trigger. We get a copy of Hateful Eidolon. The next Thaumaturge to be copied becomes a Hateful Eidolon, the 46 untapped Thaumaturges become Palladium Myrs, and the remaining 60 can become Thaumabrooms. (1 black, 138 colorless mana)
Sacrifice an Elf token, pay 138 to create 46 copies of Thaumabroom. (46 tapped Thaumamyrs, 60 tapped Thaumabrooms, 46 untapped Thaumabrooms, 1 tapped Thaumaeidolon)
Resolve the next Thaumabroom trigger. We get a copy of Hateful Eidolon. We have the 94 Thuamaturges that have not used Warmaster's ability become copies of Warmaster, as well as the next Thaumaturge to be copied. The Thaumaturge that gets copied next becomes a Hateful Eidolon. The remaining 58 can become Thaumabrooms. (47 untapped Thaumamasters, 48 tapped Thaumamasters, 58 tapped Thaumabrooms, 1 tapped Thaumaeidolon)
Resolve the next Thuamabroom trigger. We get a copy of Warmaster.
The other 94 Warmasters trigger, creating 94 Elf tokens.
We tap the 94 Elf tokens and the 47 untapped Thaumasters for 282 black mana.
Sacrifice 2 Elf tokens, pay for 94 Thamabroom copies. (95 tapped Thaumamasters, 1 untapped Thaumamaster, 58 tapped Thaumabrooms, 94 untapped Thuamabrooms, 1 tapped Thaumaeidolon. 249 Thaumaturges in total.)
For every 3 Thaumabroom triggers, we more than double our count of Thaumaturges. So, after 510 more Thaumabroom triggers, we will have more than 249 * 2^170 > 2^177 Thaumaturges. We will also have more than 2^177 Elf tokens.
We can sacrifice the 2^177 Elf tokens to create more than 2^354 Thuamabroom triggers, and sacrifice the second Hateful Eidolon. This will result in more than 2^2^352 Thaumaturges at the end. Two more Eidolons will get us to more than 2^2^2^2^352 > 2^^7 Thaumaturges by the end.
We can make sure to copy Gyruda 3 times, grabbing a Cogwork Archivist, a Spirit of Malevolence, and a Skemfar Avenger. This will clear our library. We also make sure to make plenty of copies of Cogwork Archivist.
Use Cogwork Archvist to put Hateful Eidolon into the library. Sacrifice a Skemfar Avenger to draw the Hateful Eidolon, dropping to 17 life. Play and sacrifice the Hateful Eidolon to get to 2^^8 Thaumaturges. If one of our Skemfar Avengers is lost to the graveyard, we can use this opportunity to put it into the library, and make a copy of Gyruda to fetch it.
Once we are low on life, we can make copies of Spirit of Malevolence and sacrifice it to syphon life from the enemy. We can use 17 of our life and 19 of the opponent's life to fetch 36 more Hateful Eidolons, increasing the number of Thuamaturges to more than 2^^43.
We can then put Vault Robber into the library, fetch it with a Gyruda, and activate it, after turning all or nearly all Thuamaturges into Xorns, creating more than 2^^43 Treasure tokens.
Edit: So, just to sate my curiosity, I looked at optimizing how we play the enchantment creatures a little more. It looks like we can do better with a 5-cycle: 1 time creating a Thaumawarmaster, 3 times creating a Thaumaeidolon and turning our untapped Thuamaturges into Thaumamyrs, and 1 time creating a Thuamaeidolon and turning our Thaumaturges into Thaumamasters. For this, it is better not to tap our untapped Thaumasters, saving them for when they are Thaumamyrs. The ratio of increased Thuamaturges will converge to 5.28849 per 5-cycle, so after 102 such cycles we will have about 1.5 * 10^76 ~ 2^253 Thaumaturges rather than 2^177. This won't affect the final lower bound of 2^^43, of course.
Whoops, for some reason I thought that Tuktuk Rubblefort had an even mana value. There are other cards that give haste, but none of them seem suitable. With Doomskar Titan for example, we can't get its ETB trigger often enough. So yeah, maybe we just do without Honor Troll, and get a decently high tetration number. It's too bad, since if we can beat 3^^^3, that would increase the 51 in the final expression to a 52.
Edit: I dunno, maybe a Doomskar Titan, followed by a sequence of Crashing Drawbridges and more Doomskar Titans? Seems like it's probably too costly.
Nice! But, we get an extra creature card if we play with Cogwork Archivist (unless you found an infinite?), so I think even mana value enchantment creatures have to be avoided.
I was thinking about using Cogwork Archivist to put cards in the library that we can draw with Skemfar Avenger. We can draw an enchantment creature at the cost of a couple life, allowing us to roughly square our Thaumaturges. Then, we can syphon our opponent's life with the aid of Honor Troll, getting us double exponentiation per opponent life. So we should be able to exceed 2^^40 with that, I think.
Maybe we can do better with Elvish Warmaster, I'll check it out!
Edit: Or, are even mana value enchantment creatures safe with Cogwork Archivist? I haven't investigated it thoroughly.
Hmm, I suppose Blackbloom Rogue and Beledros Witherbloom could save a creature slot, since we could replace both Tyvar Kell and Quandrix Command (theoretically). The problem is getting off the ground; we can use a Witherbloom once, maybe two or three times if we can syphon the opponent's life.
Edit: Oh, perhaps Tyvar Kell + an even mana value Elf goes infinite with Epitaph Golem, but not with Cogwork Archivist. Without being able to fetch enchantment creatures, we can't make copies of Cogwork Archivist. We could try to sacrifice and recycle the Archivist, but we can put two cards in the library with the help of Luminous Moth, and we need to put in at least five to be able to fetch Cogwork Archivist plus another Gyruda. So, I don't think there's an infinite line there.
An even mana value enchantment creature is still probably something to be avoided, as we can do a lot with that.
We can avoid even mana value enchantment creatures, even if it means starting with less; the problem is Tyvar Kell and any even mana value Elf. We would need to replace Skemfar Avenger and Arcane Investigator with two other creatures.
It was actually that Tyvar Kell and Cogwork Archivist went infinite. Unfortunately, I don't see a good replacement for Tyvar Kell; since we need green to be expensive, Skull Prophet is no good, and artifacts are not cheap enough. That leaves a black land, which would probably work for the combo, but wouldn't be good for the start at all.
52 creatures, of which 2 have to be kept around (Sea-Dasher Octopus and one enchantment creature), leading to more than 3 -> 3 -> 3 -> (3 -> 3 -> 3 -> (3 -> 3 -> 3 -> 50 -> 6) -> 8) -> 8 damage.
Okay, I finally figured out a start. I would like to have saved Cogwork Archivist or Epitaph Golem, but I couldn't figure out a strong start using just Palladium Myr. The main problem is not being able to cast enchantment creatures. We could start with something like 4 Xorns, and then Gyruda in Vault Robber, but I didn't see a way to use just a few Treasure tokens and not much else to do better than what I have below.
If we want to cast colored spells, the only thing I really saw was Tyvar Kell, and Cogwork Archivist + Gyruda + Tyvar + Woe Strider + any even mana value Elf like Skemfar Avenger will go infinite I think. I tried to take out one of those pieces to make it work, haven't worked out anything interesting.
So, this is what I have so far. Not being able to copy Kinnan, Bonder Prodigy drops sacrificing an enchantment creature from tetration to squaring, so the final numbers are much less. Only able to fit in 14 enchantment creatures due to available cards and mana; perhaps we could fit a 15th enchantment creature with a little more care taken with our mana, but I don't really feel like doing this again unless I have to.
Name Elf for Realmwalker.
Activate Tyvar to create an Elf token.
Tap Realmwalker and Elf token for 4 mana.
Cast Duskwielder 4 times from the library, and tap them - 8 mana left.
Cast Skemfar Avenger from the library, and tap them - 8 mana left.
Cast Palldium Myr twice from hand, and tap them - 5 black, 3 colorless.
Cast Sorcerer's Broom from hand - 5 black, 1 colorless.
Cast Woe Strider from hand - 3 black.
Sacrifice Gyrudas a bunch of times to fetch Luminous Bloodmoth, Kinnan, Bonder Prodigy, Protean Thaumaturge, and Nyxborn Marauder from the graveyard.
When Nyxborn Marauder comes into play, Protean Thaumaturge becomes a copy of Sorcerer's Broom. (TSB)
Sacrifice a Palladium Myr.
It comes back with a flying counter, tap it for 3 colorless - 3 black, 3 colorless.
Pay 3 colorless to create a copy of the TSB - 3 black left, 2 TSBs.
Sacrifice Realmwalker.
It comes back, name Spirit and tap it for mana - 5 black left.
Draw Palladium Myr, and lose 1 life - 19 life left.
Sacrifice the second Palladium Myr.
It comes back, tap it - 5 black, 3 colorless.
Spend 3 black, 3 colorless to create two copies of TSBs - 2 black left, 4 TSBs.
Sacrifice a Duskwielder.
Draw a fourth Palladium Myr, and lose 1 life - 18 life left.
Duskwielder comes back, tap it - 4 black mana left.
Cast the two Palladium Myrs and tap them - 1 black mana, 3 colorless.
Sacrifice the two Palladium Myrs.
They come back, tap them for 6 colorless mana - 1 black, 9 colorless.
Spend 9 colorless mana to create 3 copies of TSBs - 7 TSBs left.
Cast a Hateful Eidolon from the library- 0 mana left.
Turn the 7 TSBs into Palladium Myrs.
Tap them for 21 colorless - 21 colorless left.
Sacrifice a second Duskwielder.
Draw a Tymaret, Chosen from Death, lose 1 life - 17 life left.
Duskwielder comes back, tap it - 2 black, 21 colorless left.
Cast a 2nd Hateful Eidolon from the library - 1 black, 21 colorless left.
Turn the 7 TSBs into Sorcerer's Brooms.
Sacrifice a third Duskwielder.
Draw a Lampad of Death's Vigil, lose 1 life - 16 life left.
Duskwielder comes back, tap it for 2 black - 3 black, 21 colorless left.
Pay 21 colorless to create 7 copies of TSBs - 14 PTs, 7 tapped, 7 untapped. 3 black left.
Sacrifice the Protean Thaumaturge.
It comes back untapped with a flying counter.
Cast a 3rd Hateful Eidolon from the library- 2 black left.
Turn the 8 untapped PTs into Palladium Myrs, the remaining ones into Sorcerer's Brooms.
Tap the Palladium Myrs for 24 colorless mana - 2 black, 24 colorless left.
Sacrifice the fourth Duskwielder and the Skemfar Avenger.
Draw a Lampad of Death's Vigil, lose 1 life - 15 life left.
The Duskwielder and Skemfar Avenger come back, tap them - 6 black, 24 colorless left.
Pay 24 colorless mana to create 8 TSBs - 22 PTs, 14 tapped, 8 untapped. 6 black left.
Cast a fourth Hateful Eidolon from the library - 5 black left.
Turn the 8 untapped PTs into Palladium Myrs, the rest into Sorcerer's Brooms.
Tap the Palladium Myrs for 24 mana - 5 black, 24 colorless left.
Sacrifice the first Duskwielder.
We draw Lampad of Death's Vigil, lose 1 life - 14 life left.
Pay 24 colorless to create 8 TSBs - 30 PTs, 22 tapped, 8 untapped. 5 black left.
Cast Tymaret, Chosen from Death - 3 black left.
Turn the 8 untapped PTs into Palladium Myrs, the rest into Sorcerer's Brooms.
Tap the Palladium Myrs for 24 mana - 3 black, 24 colorless left.
Sacrifice the second Duskwielder.
We draw Lampad of Death's Vigil, lose 1 life - 13 life left.
Pay 24 colorless to create 8 TSBs - 38 PTs, 30 tapped, 8 untapped. 3 black left.
Cast Lampad of Death's Vigil - 1 black left.
Turn the 8 untapped PTs into Palladium Myrs, the rest into Sorcerer's Brooms.
Tap the Palladium Myrs for 24 colorless - 1 black, 24 colorless colorless left.
Sacrifice the third Duskwielder.
We draw Erebos, Bleak-Hearted, lose 1 life - 12 life left.
Pay 21 colorless to create 7 TSBs - 45 PTs, 38 tapped, 7 untapped. 1 black, 3 colorless left.
Cast the second Lampad of Death's Vigil - 2 colorless left.
Turn one untapped PT into Duskwielder, the remaining 6 untapped PTs into Palladium Myrs, the rest into Sorcerer's Brooms.
Tap the Palladium Myrs for 2 black, 18 colorless - 2 black, 20 colorless left.
Sacrifice the fourth Duskwielder.
We draw Tymaret, Chosen from Death, lose 1 life - 11 life left.
Pay 18 colorless to create 6 TSBs - 51 PTs, 45 tapped, 6 untapped. 2 black, 2 colorless left.
Cast the third Lampad of Death's Vigil - 1 black, 1 colorless left.
Turn the 6 untapped PTs into Palladium Myrs, the rest into Sorcerer's Brooms.
Tap the Palladium Myrs for 18 colorless - 1 black, 19 colorless left.
Sacrifice the Goat token.
Pay 18 colorless to create 6 TSBs - 57 PTs, 51 tapped, 6 untapped. 1 black, 1 colorless left.
Cast the fourth Lampad of Death's Vigil - 0 mana left.
Turn 1 untapped PT into Skemfar Avenger, the remaining 5 untapped PTs into Palladium Myrs, the remaining 51 into TSBs.
Tap the Palladium Myrs for 2 black, 15 colorless mana.
Sacrifice the Elf token.
Pay 12 colorless to create 4 TSBs - 61 PTs, 1 tapped TSA, 5 tapped TPMs, 4 untapped TSBs, 51 tapped TSBs. 2 black, 3 colorless left.
Cast Erebos, Bleack-Hearted - 1 black left.
Turn the 4 untapped PTs into Palladium Myrs, 1 tapped PT into Woe Strider, the remaining 56 into TSBs.
Tap the Palladium Myrs for 12 colorless mana - 1 black, 12 colorless left.
Sacrifice Xorn, it comes back.
Pay 12 colorless to create 4 TSBs - 65 PTs, 1 tapped TWS, 4 tapped TPMs, 4 untapped TSBs, 56 tapped TSBs. 1 black mana left.
52 TSB triggers remain on the stack.
Sacrifice Woe Strider twice, Palladium Myr 4 times, Sorcerer's Broom twice, Kinnan, Bonder Prodigy once, and one Goat token. All but 4 of our 50 tapped TSBs now have 11 triggers on the stack each, with the remaining 6 having 10 each, as well as the untapped TSBs.
Sacrifice 3 tapped TPMs, the 4 tapped TSBs with 11 triggers each, and 18 more tapped TSBs.
This leaves 4 untapped TSBs with 35 triggers each, and 34 TSBs with 36 triggers each. We also have a bunch of triggers from the sacrificed TSBs.
Sacrifice Tymaret, Chosen for Death. It triggers Luminous Moth and our TSBs; the number of triggers per TSB go up to 36 or 37.
Resolve the Luminous Moth trigger first, bringing Tymaret back.
Turn our 4 untapped TSBs into Palladium Myrs, and the TSB with the next trigger on the stack into a Nyxborn Marauder.
Tap the 4 untapped TSBs for 12 colorless - 1 black, 12 colorless left.
Resolve the next TSB trigger, creating a Nyxborn Marauder - 1 black, 9 colorless left
Turn the new untapped Nyxborn Marauder into a Palladium Myr, and the TSB with the next trigger on the stack into a Nyxborn Marauder.
Tap the new untapped Palladium Myr - 1 black, 12 colorless.
Repeat this process for all 1402 TSB triggers for TSBs that still exist, increasing the number of PTs from 40 to 1442.
Spend the 12 colorless to pay for 4 triggers of sacrificed TSBs, increasing to 1446 PTs.
We repeat this procedure for the next enchantment creature - a Hateful Eidolon, say.
We first sacrifice the Tymaret and 721 tapped TSBs, leaving 723 TSBs with 722 triggers each.
We sacrifice Hateful Eidolon, increasing the number of triggers to 723 each.
This results in the creation of another 723^2 TSBs for those triggers, plus 4 for triggers of sacrificed TSBs. We wind up with 725 + 723^2 + 4 = 523458 PTs.
For the next Hateful Eidolon, we sacrifice Hateful Eidolon and 261,727 tapped TSBs, leaving 261,729 TSBs. After the procedure, we go up to 261,731 + 261,729^2 + 4 = 68,502,331,176 PTs.
Each successive iteration of the procedure takes X to more than X^2/4. Near the end, we can create two Skemfar Avenger tokens and sacrifice the original to draw a third Tymaret and Quandrix Command. This allows us to play and sacrifice 14 enchantment creatures, taking the number of Thaumaturges to more than 4*(68,502,331,176/4)^(2^11) > 10^20,959.
Before we finish, we make sure to have a Thaumaturge copy Gyruda, and create a copy, allowing us to fetch Vault Robber from the library. With the last Constellation trigger, we turn all of our Protean Thaumaturges into Xorns (except for three, which we turn into Skemfar Avengers), and activate Vault Robber to create more than 10^20,959 Treasure tokens.
We should probably continue this some more to see that we can do the full combo from here, but I will let you guys check this first.
Turn 1:
Tapped Land, go.
Turn 2:
Draw (7 cards in hand, 52 cards in library)
Play Island.
Play Stonecoil Serpent with X=0.
Play Tibalt's Trickery counters Serpent, mills 1 card and casts Genesis Ultimatum. (4 cards in hand, 50 cards in library)
Ultimatum puts Xorn, Purphoros, Bronze-Blooded, Tyvar Kell, Woe Strider and Gyruda, Doom of Depths into play. (45 cards in library)
Gyruda mills 4 cards and puts Luminous Broodmoth into play. (41 cards in library)
Woe Strider sacrifices Gyruda. Broodmoth brings it back.
Gyruda mills 4 cards and puts another Gyruda into play. Legend rule kills the one with flying counter. (37 cards in library)
Gyruda mills 4 cards and puts Kinnan, Bonder Prodigy into play. (33 cards in library)
Woe Strider sacrifices Gyruda. Broodmoth brings it back.
Gyruda mills 4 cards and puts another Gyruda into play. Legend rule kills the one with flying counter. (29 cards in library)
Gyruda mills 4 cards and puts Protean Thaumaturge into play. (25 cards in library)
Woe Strider sacrifices Gyruda. Broodmoth brings it back.
Gyruda mills 4 cards and puts another Gyruda into play. Legend rule kills the one with flying counter. (21 cards in library)
Gyruda mills 4 cards and puts Elvish Warmaster into play. 17 cards in library)
Woe Strider sacrifices Gyruda. Broodmoth brings it back.
Gyruda mills 4 cards and puts Sorcerer's Broom into play. (13 cards in library)
Tap Warmaster for mana. (2 black)
Play Hateful Eidolon. Thaumaturge becomes a copy of Broom. (3 cards in hand, 1 black)
Activate Tyvar Kell to create an Elf token. Elvish Warmaster triggers to create an Elf token. Tap both Elf tokens for mana. (5 black, 2 Elf tokens)
Sacrifice the Xorn, it comes back. The Thaumabroom triggers, pay for it. (2 black, 2 untapped Thaumabrooms, 2 Elf tokens)
Play the second Hateful Eidolon. Turn the nontoken Thaumaturge into a Thaumamaster, keep the nontoken Thaumabroom as it is. (2 cards in hand, 1 black)
Sacrifice the original Warmaster. The Thuamabroom triggers. The Warmaster comes back, and the Thaumamaster triggers, creating an Elf token. Tap both Warmasters and the Elf token for mana. Pay for the Thaumabroom trigger. (4 black mana, 1 tapped Thaumamaster, 1 tapped Thaumabroom, 1 untapped Thamabroom, 3 Elf tokens)
Sacrifice the nontoken Thaumamaster. The Thuamabrooms trigger, pay for one. The Thaumamaster comes back as an untapped Thaumaturge. (1 black mana, 1 untapped Thaumaturge, 1 tapped Thaumabroom, 2 untapped Thaumabrooms, 3 Elf tokens)
Play the third Hateful Eidolon. Turn the 3 untapped Thaumaturges into Thaumamasters, keep the tapped one as a Thaumabroom. (1 card in hand, 0 mana, 3 untapped Thaumamasters, 1 tapped Thaumabroom)
Play Skemfar Avenger. The Warmaster and the 3 Thaumamasters trigger, creating 4 Elf tokens. Tap Skemfar Avenger, the 3 Thaumamasters, and the 4 Elf tokens for mana. (16 black mana, 3 tapped Thaumamasters, 1 tapped Thamabroom, 7 Elf tokens)
Sacrifice Warmaster. Avenger triggers, Thaumabroom triggers. (19 life, 1 card in hand, 12 cards in library)
Sacrifice Sorcerer's Broom twice. Pay 15 mana to make 5 copies of Thaumabrooms. (1 black mana, 3 tapped Thaumamasters, 1 tapped Thaumabroom, 5 untapped Thaumabrooms, 7 Elf tokens)
Play the fourth Hateful Eidolon. Turn the 6 Thaumabrooms into Thaumamasters, and the 3 Thaumamasters into Thaumabrooms. (0 mana, 0 cards in hand)
Sacrifice Skemfar Avenger, Thaumabrooms trigger. Avenger comes back, the 6 Thaumamasters trigger, creating 6 Elf tokens. Tap Avenger, the 5 untapped Thaumamasters, and the 6 Elf tokens for mana. (24 black mana, 6 tapped Thaumamasters, 3 tapped Thaumabrooms, 13 Elf tokens)
Sacrifice Kinnan, it comes back. Sacrifice an Elf token. Pay 24 mana to create 8 copies of Thaumabrooms. (0 mana, 6 tapped Thaumamasters, 3 tapped Thuamabrooms, 8 untapped Thaumabrooms, 12 Elf tokens, 1 Thaumabroom trigger left)
Sacrifice the 12 Elf tokens. Each of the 11 Thaumabrooms trigger 12 times, totaling 11*12 + 1 = 133 triggers.
Sacrifice the first Hateful Eidolon. We get 11 more Thaumabroom triggers, for 144 total. Hateful Eidolon comes back. Turn the 8 untapped Thaumabrooms into Thaumamasters, including the Thaumabroom to be copied next. Turn the tapped Thuamabroom to be copied afterwards into a Hateful Eidolon, and the remaining 8 into Thaumabrooms.
We resolve 1 Thaumabroom trigger, creating a Thaumamaster token. The 8 other Thaumamasters trigger, creating 8 Elf tokens. Tap the 9 Thaumamasters and 8 Elf tokens for mana (34 black mana, 9 tapped Thaumamasters, 8 tapped Thaumabrooms, 1 tapped Thaumaeidolon, 8 Elf tokens. 143 triggers left.)
Sacrifice 2 Elf tokens. Pay 33 mana to create 11 Thaumabrooms. (1 black mana, 9 tapped Thaumamasters, 8 tapped Thaumabrooms, 1 tapped Thaumaeidolon, 11 untapped Thaumabrooms, 6 Elf tokens, 143 triggers)
Resolve another Thaumabroom trigger, creating a Thaumaeidolon token. Turn 12 untapped Thaumaturges into Thaumamasters, the next two Thaumaturges to be copied into Thaumamaster and Thaumaeidolon, and the remaining 16 into Thuamabrooms. (1 black mana, 12 untapped Thaumamasters, 1 tapped Thaumamaster, 1 tapped Thaumaeidolon, 16 tapped Thaumabrooms, 6 Elves, 142 triggers)
Resolve another Thuamabroom trigger, creating a Thaumamaster token. The 12 other Thaumamasters trigger, creating 12 Elf tokens. Tap the 13 Thaumamasters and 12 Elf tokens for 50 mana. (51 black mana, 14 tapped Thaumamasters, 1 tapped Thaumaeidolon, 16 tapped Thaumabrooms, 18 Elves, 141 triggers)
Sacrifice 2 Elf tokens. Pay 51 mana to create 17 Thaumabrooms. (0 mana, 14 tapped Thaumamasters, 1 tapped Thaumaeidolon, 16 tapped Thaumabrooms, 17 untapped Thaumabrooms, 16 Elves, 141 triggers)
Resolve another Thaumabroom trigger, creating a Thaumaeidolon token. Turn 18 untapped Thaumaturges into Thaumamasters, the next two Thaumaturges to be copied into Thaumamaster and Thuamaeidolon, and the remaining 29 into Thaumabrooms. (0 mana, 18 untapped Thaumamasters, 1 tapped Thaumamaster, 1 tapped Thaumaeidolon, 29 tapped Thaumabrooms, 16 Elves, 140 triggers)
Resolve another Thuamabroom trigger, creating a Thaumamaster token. The 18 other Thaumamasters trigger, creating 18 Elf tokens. Tap the 19 Thaumamasters and 18 Elf tokens for 74 mana. (74 black mana, 20 tapped Thaumamasters, 1 tapped Thaumaeidolon, 29 tapped Thaumabrooms, 34 Elves, 139 triggers)
Sacrifice an Elf token. Pay 72 mana to create 24 Thaumabrooms. (2 mana, 20 tapped Thaumamasters, 1 tapped Thaumaeidolon, 29 tapped Thaumabrooms, 24 untapped Thaumabrooms, 33 Elves, 139 triggers)
Resolve another Thaumabroom trigger, creating a Thaumaeidolon token. Turn 25 untapped Thaumaturges into Thaumamasters, the next two Thaumaturges to be copied into Thaumamaster and Thuamaeidolon, and the remaining 48 into Thaumabrooms. (2 mana, 25 untapped Thaumamasters, 1 tapped Thaumamaster, 1 tapped Thaumaeidolon, 48 tapped Thaumabrooms, 33 Elves, 138 triggers)
Resolve another Thuamabroom trigger, creating a Thaumamaster token. The 25 other Thaumamasters trigger, creating 25 Elf tokens. Tap the 26 Thaumamasters and 25 Elf tokens for 102 mana. (104 black mana, 27 tapped Thaumamasters, 1 tapped Thaumaeidolon, 48 tapped Thaumabrooms, 58 Elves, 137 triggers)
Sacrifice an Elf token. Pay 102 mana to create 34 Thaumabrooms. (2 mana, 27 tapped Thaumamasters, 1 tapped Thaumaeidolon, 48 tapped Thaumabrooms, 34 untapped Thaumabrooms, 57 Elves, 137 triggers)
Every cycle of a Thaumaeidolon creation and a Thaumamaster creation multiplies the number of Thaumaturges by more than 4/3. We will use three Thuamabroom triggers near the end to make copies of Gyruda. We use the three ETB triggers to fetch Cogwork Archivist, Spirit of Malevolence, and Skemfar Avenger. We make sure to have some mana available. We use the remaining 134 triggers to for 67 more Eidolon-Warmaster cycles, after which we will have more than 7.12 billion Thaumamasters, 30.85 billion Thaumabrooms, and 28.48 billion Elf tokens.
We sacrifice the first Hateful Eidolon, and it goes to the graveyard. We use a Cogwork Archivist to put Hateful Eidolon into our empty library. Then, we sacrifice our newly acquired Avenger, triggering the other Avenger, and drawing the Hateful Eidolon at the cost of a life (down to 18 life). We play the Hateful Eidolon, getting Constellation triggers; we turn all 37.97 billion Thaumaturges into Thaumabrooms, except three become two Cogwork Archivists and a Gyruda. We sacrifice all of our Elf tokens, getting more than 1.081 * 10^21 triggers.
We can now sacrifice a Hateful Eidolon, do a process similar to the above, except this time we can create a Hateful Eidolon token every time. We start by using a Cogwork Archivist to put a Gyruda, then make a copy of the Gyruda token. This allows to fetch the Gyruda, and respond to its ability by putting Elvish Warmaster into the library, and then fetching it. We can now use every Thaumabroom trigger to create a copy of Hateful Eidolon, put copies of Gyruda and Warmaster into the library (after sacrificing the Warmaster twice), and sacrificing Gyruda to bring it back, and fetch the other Gyruda and Warmaster, triggering our other Warmasters and getting Elves and mana. The end result is that we multiply our Thaumaturges by more than 4/3 each trigger.
So, after 1.081 * 10^21 triggers, we will have more than (4/3)^(1.081 * 10^21) > 2^(2^68) > 2^^5 Thaumaturges. Each repetition of this process increases the second number by 1. We can drain our life 17 more times, then use Spirit of Malevolence to syphon the opponent's life, allowing for another 19 procedures. Finally, we can sacrifice the other 3 Hateful Eidolons and Purphoros, taking our number of Thaumaturges to more than 2^^45.
We can use Gyruda to fetch Vault Robber from the library after putting it in with Cogwork Assembler, and use the last Constellation trigger to turn all or almost all of our Thaumaturges into Xorns. This allows us to generate more than 2^^45 Treasure tokens from the first use of Vault Robber.
Current deck:
1 Akoum Warrior
2 Island
3 Stonecoil Serpent
4 Tibalt's Trickery
5 Genesis Ultimatum
6 Vault Robber
Engine/utility:
7 Sorcerer's Broom
8 Protean Thaumaturge
9 Scaled Herbalist
10 Purphoros, Bronze-Blooded
11 Volo, Guide to Monsters
12 Sea Gate Stormcaller
13 Sea-Dasher Octopus
14 Tyvar Kell
15 Vadrok, Apex of Thunder
16 Arcane Investigator
17 Farideh, Devil's Chosen
18 Rolling Regrowth
19 Cogwork Archivist
Second Stage:
20 Skemfar Avenger
21 Toralf, God of Fury
22 Duskfang Mentor
23 Clackbridge Troll
Layers:
24 Palukranos, Unchained
25 The Ringhart Crest
26 Heliod's Intervention
27 Dual Strike
28 Kinnan, Bonder Prodigy
29 Kargan Intimidator
31 Hama Pashar, Ruin Seeker
32 Planar Ally
33 Moraug, Fury of Akoum
More setup:
33 Woe Strider
34 Luminous Bloodmoth
35 Spirit of Malevolence
36 Elvish Warmaster
4 Gyruda, Doom of Depths
4 Hateful Eidolon
1 Palladium Myr
1 Duskwielder
1 Skemfar Avenger
13 more cards
I forgot that I took off Dual Strike when we switched to Orvar; with Orvar gone, we need it back for Heliod's Intervention.
53 creatures, of which we need to keep 3: Sea-Dasher Octopus we need to keep mutating, Kolvari is the front side of The Ringhart Crest, which we need to keep recycling, and we need to keep an enchantment creature around so that we can flash it in. So final damage is currently 3 -> 3 -> 3 -> (3 -> 3 -> 3 -> (3 -> 3 -> 3 -> 50 -> 6) -> 8) -> 8.
Turn 1:
Tapped Land, go.
Turn 2:
Draw (7 cards in hand, 52 cards in library)
Play Island.
Play Stonecoil Serpent with X=0.
Play Tibalt's Trickery counters Serpent, mills 1 card and casts Genesis Ultimatum. (4 cards in hand, 50 cards in library)
Ultimatum puts Xorn, Purphoros, Bronze-Blooded, Tyvar Kell, Woe Strider and Gyruda, Doom of Depths into play. (45 cards in library)
Gyruda mills 4 cards and puts Luminous Broodmoth into play. (41 cards in library)
Woe Strider sacrifices Gyruda. Broodmoth brings it back.
Gyruda mills 4 cards and puts another Gyruda into play. Legend rule kills the one with flying counter. (37 cards in library)
Gyruda mills 4 cards and puts Kinnan, Bonder Prodigy into play. (33 cards in library)
Woe Strider sacrifices Gyruda. Broodmoth brings it back.
Gyruda mills 4 cards and puts another Gyruda into play. Legend rule kills the one with flying counter. (29 cards in library)
Gyruda mills 4 cards and puts Protean Thaumaturge into play. (25 cards in library)
Woe Strider sacrifices Gyruda. Broodmoth brings it back.
Gyruda mills 4 cards and puts another Gyruda into play. Legend rule kills the one with flying counter. (21 cards in library)
Gyruda mills 4 cards and puts Elvish Warmaster into play. 17 cards in library)
Woe Strider sacrifices Gyruda. Broodmoth brings it back.
Gyruda mills 4 cards and puts Skemfar Avenger into play. (13 cards in library)
Elvish Warmaster triggers to create an Elf token. Tap all 3 Elves for mana. (6 black)
Play Palladium Myr and tap it for mana. (3 cards in hand, 3 black, 3 colorless)
Play Sorcerer's Broom. (2 cards in hand, 3 black, 1 colorless)
Play Hateful Eidolon. Thaumaturge becomes a copy of Broom (1 card in hand, 2 black, 1 colorless)
Sacrifice Warmaster. Avenger triggers. Thaumabroom triggers. Pay for it. Broodmoth brings the Warmaster back. Tap it for mana (19 life, 2 cards in hand, 12 cards in library, 2 black, 2 untapped Thaumabrooms)
Play Duskwielder. Warmaster triggers. Tap the new elves for mana. (1 card in hand, 5 black)
Sacrifice Duskwielder. Broodmoth brings it back. Tap it for mana. Avenger triggers. Thaumabrooms trigger. Pay for them. (18 life, 2 cards in hand, 11 cards in library, 1 black, 4 untapped Thaumabrooms)
Sacrifice Palladium Myr. Broodmoth brings it back. Tap it for mana. Thaumabrooms trigger. Pay for one of them. (1 black, 5 untapped Thaumabrooms)
Play Hateful Eidolon. 4 Thaumabrooms become copies of Warmaster. 1 stays a Thaumabroom (1 card in hand, 4 untapped Thaumamasters, 1 untapped Thaumabroom)
Activate Tyvar Kell to create an Elf token. The Thaumamasters trigger, creating 4 more Elves. Tap all the Elf tokens and one Thaumamaster for mana. (12 black, 7 Elf tokens).
Sacrifice an Elf token. Thaumabroom triggers, pay for it. (18 life, 1 card in hand, 11 cards in library, 9 black, 3 untapped Thuamamasters, 1 tapped Thuamamaster 2 untapped Thaumabrooms)
Sacrifice an Elf token. Thaumabrooms trigger, pay for them. (3 black, 3 untapped Thaumamasters, 1 tapped Thuamamaster, 4 untapped Thaumabrooms, 6 Elf tokens)
Play Hateful Eidolon. 7 Thaumaturges become copies of Palladium Myr, the tapped one becomes a copy of Sorcerer's Broom. Tap the Thaumamyrs for mana. (0 cards in hand, 3 black, 21 colorless, 7 tapped Thaumamyrs, 1 tapped Thaumabroom)
Sacrifice the nontoken Thaumamyr. The Thaumabroom triggers, pay for it. The Protean Thaumaturge comes back. (3, black, 18 colorless, 6 tapped Thaumamyrs, 1 tapped Thaumabroom, 1 untapped Thaumabroom, 1 untapped Thuamaturge)
Sacrifice 2 Elf tokens. Thuamabrooms trigger, pay for them (3 black, 6 tapped Thaumamyrs, 1 tapped Thaumabroom, 7 untapped Thaumabroom, 1 untapped Thaumaturge, 4 Elf tokens)
Play Hateful Eidolon. The 12 Thaumaturges that have not used Warmaster's ability become copies of Warmaster, the remaining 3 become copies of Sorcerer's Broom. (2 black, 8 untapped Thaumamasters, 4 tapped Thaumamasters, 3 tapped Thaumabrooms)
Sacrifice Skemfar Avenger. Luminous Bloodmoth triggers, it comes back. The Thaumamasters trigger, creating 12 Elf tokens. Tap the Avenger, the 8 untapped Thaumamasters, and the 12 Elf tokens for mana (44 black mana, 12 tapped Thaumamasters, 3 tapped Thaumabrooms, 16 Elf tokens)
Sacrifice two Elf tokens. Thaumabrooms trigger, pay for them. (17 black mana, 12 tapped Thaumamasters, 3 tapped Thaumabrooms, 9 untapped Thaumabrooms, 14 Elf tokens)
Sacrifice an Elf token. 12 Thaumabrooms trigger, pay for 5. (2 black mana, 12 tapped Thaumamasters, 3 tapped Thaumabrooms, 14 untapped Thaumabrooms, 13 Elf tokens)
7 Thaumabroom triggers remain on the stack.
Sacrifice Xorn, Purphuros, Kinnan, 1 Goat token, 13 Elf tokens, and 12 tapped Thaumamasters. Luminous Bloodmoth brings Xorn, Purphurous, and Kinnan back.
Sacrifice the first Hateful Eidelon. This triggers Luminous Bloodmoth and all the Thaumabrooms. There are now 30*17 + 7 = 517 Thuamabroom triggers on the stack.
Hateful Eidolon comes back. We have the Thaumabrooms all become copies of Warmaster, except for the second Thaumabroom to be copied (tapped), which becomes a copy of Hateful Eidolon, and one other, which becomes a Thaumbroom. (also tapped)
Resolve the next Thaumabroom trigger. We get a copy of Warmaster. The other 15 Warmasters trigger, and we get 15 Elf tokens.
Tap the 15 Elf tokens and the 15 untapped Warmasters for 60 mana.
Sacrifice 5 Elf tokens, and pay to create 20 new Thaumabrooms (2 black mana, 16 tapped Thaumamasters, 1 tapped Thaumabrooms, 20 untapped Thaumabrooms, 1 tapped Thaumaeidolon, 10 Elf tokens)
Resolve the next Thaumabroom trigger. We get a copy of Hateful Eidolon. The next Thaumaturge to be copied becomes a Hateful Eidolon, the 21 untapped Thaumaturges become Palladium Myrs, and the remaining 17 can become Thaumabrooms.
Tap the Palladium Myrs for mana. (2 black, 63 colorless)
Sacrifice 2 Elf tokens, pay 63 to create 21 copies of Thuamabrooms. (21 tapped Thaumamyrs, 17 tapped Thaumabrooms, 21 untapped Thaumabrooms, 1 tapped Thaumaeidelon)
Resolve the next Thaumabroom trigger. We get a copy of Hateful Eidelon. The next two Thaumaturges to be copied become copies of Warmaster and Hateful Eidelon. We have the Thaumaturges that haven't been used Warmaster's ability become copy of Warmaster (45 total, 21 untapped, 24 tapped). The remaining 14 can become Thaumabrooms.
Resolve the next Thaumabroom trigger. We get a copy of Warmaster.
The other 45 Warmasters trigger, creating 45 Elf tokens.
We tap the 45 Elf tokens and the 22 untapped Warmasters for mana. (136 black mana, 53 Elf tokens)
Sacrifice 3 Elf tokens, pay 135 mana to create 45 more Thaumabrooms. (46 tapped Thaumamasters, 14 tapped Thaumabrooms, 45 untapped Thaumabrooms, 1 tapped Thaumaeidolon. 1 black mana, 50 Elf tokens)
Resolve the next Thaumabroom trigger. We get a copy of Hateful Eidolon. The next Thaumaturge to be copied becomes a Hateful Eidolon, the 46 untapped Thaumaturges become Palladium Myrs, and the remaining 60 can become Thaumabrooms. (1 black, 138 colorless mana)
Sacrifice an Elf token, pay 138 to create 46 copies of Thaumabroom. (46 tapped Thaumamyrs, 60 tapped Thaumabrooms, 46 untapped Thaumabrooms, 1 tapped Thaumaeidolon)
Resolve the next Thaumabroom trigger. We get a copy of Hateful Eidolon. We have the 94 Thuamaturges that have not used Warmaster's ability become copies of Warmaster, as well as the next Thaumaturge to be copied. The Thaumaturge that gets copied next becomes a Hateful Eidolon. The remaining 58 can become Thaumabrooms. (47 untapped Thaumamasters, 48 tapped Thaumamasters, 58 tapped Thaumabrooms, 1 tapped Thaumaeidolon)
Resolve the next Thuamabroom trigger. We get a copy of Warmaster.
The other 94 Warmasters trigger, creating 94 Elf tokens.
We tap the 94 Elf tokens and the 47 untapped Thaumasters for 282 black mana.
Sacrifice 2 Elf tokens, pay for 94 Thamabroom copies. (95 tapped Thaumamasters, 1 untapped Thaumamaster, 58 tapped Thaumabrooms, 94 untapped Thuamabrooms, 1 tapped Thaumaeidolon. 249 Thaumaturges in total.)
For every 3 Thaumabroom triggers, we more than double our count of Thaumaturges. So, after 510 more Thaumabroom triggers, we will have more than 249 * 2^170 > 2^177 Thaumaturges. We will also have more than 2^177 Elf tokens.
We can sacrifice the 2^177 Elf tokens to create more than 2^354 Thuamabroom triggers, and sacrifice the second Hateful Eidolon. This will result in more than 2^2^352 Thaumaturges at the end. Two more Eidolons will get us to more than 2^2^2^2^352 > 2^^7 Thaumaturges by the end.
We can make sure to copy Gyruda 3 times, grabbing a Cogwork Archivist, a Spirit of Malevolence, and a Skemfar Avenger. This will clear our library. We also make sure to make plenty of copies of Cogwork Archivist.
Use Cogwork Archvist to put Hateful Eidolon into the library. Sacrifice a Skemfar Avenger to draw the Hateful Eidolon, dropping to 17 life. Play and sacrifice the Hateful Eidolon to get to 2^^8 Thaumaturges. If one of our Skemfar Avengers is lost to the graveyard, we can use this opportunity to put it into the library, and make a copy of Gyruda to fetch it.
Once we are low on life, we can make copies of Spirit of Malevolence and sacrifice it to syphon life from the enemy. We can use 17 of our life and 19 of the opponent's life to fetch 36 more Hateful Eidolons, increasing the number of Thuamaturges to more than 2^^43.
We can then put Vault Robber into the library, fetch it with a Gyruda, and activate it, after turning all or nearly all Thuamaturges into Xorns, creating more than 2^^43 Treasure tokens.
Edit: So, just to sate my curiosity, I looked at optimizing how we play the enchantment creatures a little more. It looks like we can do better with a 5-cycle: 1 time creating a Thaumawarmaster, 3 times creating a Thaumaeidolon and turning our untapped Thuamaturges into Thaumamyrs, and 1 time creating a Thuamaeidolon and turning our Thaumaturges into Thaumamasters. For this, it is better not to tap our untapped Thaumasters, saving them for when they are Thaumamyrs. The ratio of increased Thuamaturges will converge to 5.28849 per 5-cycle, so after 102 such cycles we will have about 1.5 * 10^76 ~ 2^253 Thaumaturges rather than 2^177. This won't affect the final lower bound of 2^^43, of course.
Edit: I dunno, maybe a Doomskar Titan, followed by a sequence of Crashing Drawbridges and more Doomskar Titans? Seems like it's probably too costly.
I was thinking about using Cogwork Archivist to put cards in the library that we can draw with Skemfar Avenger. We can draw an enchantment creature at the cost of a couple life, allowing us to roughly square our Thaumaturges. Then, we can syphon our opponent's life with the aid of Honor Troll, getting us double exponentiation per opponent life. So we should be able to exceed 2^^40 with that, I think.
Maybe we can do better with Elvish Warmaster, I'll check it out!
Edit: Or, are even mana value enchantment creatures safe with Cogwork Archivist? I haven't investigated it thoroughly.
Edit: Oh, perhaps Tyvar Kell + an even mana value Elf goes infinite with Epitaph Golem, but not with Cogwork Archivist. Without being able to fetch enchantment creatures, we can't make copies of Cogwork Archivist. We could try to sacrifice and recycle the Archivist, but we can put two cards in the library with the help of Luminous Moth, and we need to put in at least five to be able to fetch Cogwork Archivist plus another Gyruda. So, I don't think there's an infinite line there.
An even mana value enchantment creature is still probably something to be avoided, as we can do a lot with that.
1 Akoum Warrior
2 Island
3 Stonecoil Serpent
4 Tibalt's Trickery
5 Genesis Ultimatum
6 Vault Robber
Engine/utility:
7 Sorcerer's Broom
8 Protean Thaumaturge
9 Scaled Herbalist
10 Purphoros, Bronze-Blooded
11 Volo, Guide to Monsters
12 Sea Gate Stormcaller
13 Sea-Dasher Octopus
14 Tyvar Kell
15 Vadrok, Apex of Thunder
16 Arcane Investigator
17 Farideh, Devil's Chosen
18 Rolling Regrowth
19 Quandrix Command
Second Stage:
20 Skemfar Avenger
21 Toralf, God of Fury
22 Duskfang Mentor
23 Clackbridge Troll
Layers:
24 Palukranos, Unchained
25 The Ringhart Crest
26 Heliod's Intervention
27 Kinnan, Bonder Prodigy
28 Kargan Intimidator
30 Hama Pashar, Ruin Seeker
31 Planar Ally
32 Moraug, Fury of Akoum
More setup:
33 Woe Strider
34 Realmwalker
35 Luminous Bloodmoth
3 Gyruda, Doom of Depths
4 Palladium Myr
4 Duskwielder
4 Hateful Eidolon
4 Lampad of Death's Vigil
3 Tymaret, Chosen for Death
1 Erebos, Black-Hearted
1 Nyxborn Marauder
52 creatures, of which 2 have to be kept around (Sea-Dasher Octopus and one enchantment creature), leading to more than 3 -> 3 -> 3 -> (3 -> 3 -> 3 -> (3 -> 3 -> 3 -> 50 -> 6) -> 8) -> 8 damage.
If we want to cast colored spells, the only thing I really saw was Tyvar Kell, and Cogwork Archivist + Gyruda + Tyvar + Woe Strider + any even mana value Elf like Skemfar Avenger will go infinite I think. I tried to take out one of those pieces to make it work, haven't worked out anything interesting.
So, this is what I have so far. Not being able to copy Kinnan, Bonder Prodigy drops sacrificing an enchantment creature from tetration to squaring, so the final numbers are much less. Only able to fit in 14 enchantment creatures due to available cards and mana; perhaps we could fit a 15th enchantment creature with a little more care taken with our mana, but I don't really feel like doing this again unless I have to.
Hand:
Woe Strider
Palladium Myr
Palladium Myr
Sorcerer's Broom
Genesis Ultimatum puts into play:
Xorn
Realmwalker
Purphoros, Bronze-Blooded
Tyvar Kell
Gyruda, Doom of Depths
Gyruda fetches:
Luminous Bloodmoth
Kinnan, Bonder Prodigy
Protean Thaumaturge
Nyxborn Marauder
Name Elf for Realmwalker.
Activate Tyvar to create an Elf token.
Tap Realmwalker and Elf token for 4 mana.
Cast Duskwielder 4 times from the library, and tap them - 8 mana left.
Cast Skemfar Avenger from the library, and tap them - 8 mana left.
Cast Palldium Myr twice from hand, and tap them - 5 black, 3 colorless.
Cast Sorcerer's Broom from hand - 5 black, 1 colorless.
Cast Woe Strider from hand - 3 black.
Sacrifice Gyrudas a bunch of times to fetch Luminous Bloodmoth, Kinnan, Bonder Prodigy, Protean Thaumaturge, and Nyxborn Marauder from the graveyard.
When Nyxborn Marauder comes into play, Protean Thaumaturge becomes a copy of Sorcerer's Broom. (TSB)
Sacrifice a Palladium Myr.
It comes back with a flying counter, tap it for 3 colorless - 3 black, 3 colorless.
Pay 3 colorless to create a copy of the TSB - 3 black left, 2 TSBs.
Sacrifice Realmwalker.
It comes back, name Spirit and tap it for mana - 5 black left.
Draw Palladium Myr, and lose 1 life - 19 life left.
Sacrifice the second Palladium Myr.
It comes back, tap it - 5 black, 3 colorless.
Spend 3 black, 3 colorless to create two copies of TSBs - 2 black left, 4 TSBs.
Sacrifice a Duskwielder.
Draw a fourth Palladium Myr, and lose 1 life - 18 life left.
Duskwielder comes back, tap it - 4 black mana left.
Cast the two Palladium Myrs and tap them - 1 black mana, 3 colorless.
Sacrifice the two Palladium Myrs.
They come back, tap them for 6 colorless mana - 1 black, 9 colorless.
Spend 9 colorless mana to create 3 copies of TSBs - 7 TSBs left.
Cast a Hateful Eidolon from the library- 0 mana left.
Turn the 7 TSBs into Palladium Myrs.
Tap them for 21 colorless - 21 colorless left.
Sacrifice a second Duskwielder.
Draw a Tymaret, Chosen from Death, lose 1 life - 17 life left.
Duskwielder comes back, tap it - 2 black, 21 colorless left.
Cast a 2nd Hateful Eidolon from the library - 1 black, 21 colorless left.
Turn the 7 TSBs into Sorcerer's Brooms.
Sacrifice a third Duskwielder.
Draw a Lampad of Death's Vigil, lose 1 life - 16 life left.
Duskwielder comes back, tap it for 2 black - 3 black, 21 colorless left.
Pay 21 colorless to create 7 copies of TSBs - 14 PTs, 7 tapped, 7 untapped. 3 black left.
Sacrifice the Protean Thaumaturge.
It comes back untapped with a flying counter.
Cast a 3rd Hateful Eidolon from the library- 2 black left.
Turn the 8 untapped PTs into Palladium Myrs, the remaining ones into Sorcerer's Brooms.
Tap the Palladium Myrs for 24 colorless mana - 2 black, 24 colorless left.
Sacrifice the fourth Duskwielder and the Skemfar Avenger.
Draw a Lampad of Death's Vigil, lose 1 life - 15 life left.
The Duskwielder and Skemfar Avenger come back, tap them - 6 black, 24 colorless left.
Pay 24 colorless mana to create 8 TSBs - 22 PTs, 14 tapped, 8 untapped. 6 black left.
Cast a fourth Hateful Eidolon from the library - 5 black left.
Turn the 8 untapped PTs into Palladium Myrs, the rest into Sorcerer's Brooms.
Tap the Palladium Myrs for 24 mana - 5 black, 24 colorless left.
Sacrifice the first Duskwielder.
We draw Lampad of Death's Vigil, lose 1 life - 14 life left.
Pay 24 colorless to create 8 TSBs - 30 PTs, 22 tapped, 8 untapped. 5 black left.
Cast Tymaret, Chosen from Death - 3 black left.
Turn the 8 untapped PTs into Palladium Myrs, the rest into Sorcerer's Brooms.
Tap the Palladium Myrs for 24 mana - 3 black, 24 colorless left.
Sacrifice the second Duskwielder.
We draw Lampad of Death's Vigil, lose 1 life - 13 life left.
Pay 24 colorless to create 8 TSBs - 38 PTs, 30 tapped, 8 untapped. 3 black left.
Cast Lampad of Death's Vigil - 1 black left.
Turn the 8 untapped PTs into Palladium Myrs, the rest into Sorcerer's Brooms.
Tap the Palladium Myrs for 24 colorless - 1 black, 24 colorless colorless left.
Sacrifice the third Duskwielder.
We draw Erebos, Bleak-Hearted, lose 1 life - 12 life left.
Pay 21 colorless to create 7 TSBs - 45 PTs, 38 tapped, 7 untapped. 1 black, 3 colorless left.
Cast the second Lampad of Death's Vigil - 2 colorless left.
Turn one untapped PT into Duskwielder, the remaining 6 untapped PTs into Palladium Myrs, the rest into Sorcerer's Brooms.
Tap the Palladium Myrs for 2 black, 18 colorless - 2 black, 20 colorless left.
Sacrifice the fourth Duskwielder.
We draw Tymaret, Chosen from Death, lose 1 life - 11 life left.
Pay 18 colorless to create 6 TSBs - 51 PTs, 45 tapped, 6 untapped. 2 black, 2 colorless left.
Cast the third Lampad of Death's Vigil - 1 black, 1 colorless left.
Turn the 6 untapped PTs into Palladium Myrs, the rest into Sorcerer's Brooms.
Tap the Palladium Myrs for 18 colorless - 1 black, 19 colorless left.
Sacrifice the Goat token.
Pay 18 colorless to create 6 TSBs - 57 PTs, 51 tapped, 6 untapped. 1 black, 1 colorless left.
Cast the fourth Lampad of Death's Vigil - 0 mana left.
Turn 1 untapped PT into Skemfar Avenger, the remaining 5 untapped PTs into Palladium Myrs, the remaining 51 into TSBs.
Tap the Palladium Myrs for 2 black, 15 colorless mana.
Sacrifice the Elf token.
Pay 12 colorless to create 4 TSBs - 61 PTs, 1 tapped TSA, 5 tapped TPMs, 4 untapped TSBs, 51 tapped TSBs. 2 black, 3 colorless left.
Cast Erebos, Bleack-Hearted - 1 black left.
Turn the 4 untapped PTs into Palladium Myrs, 1 tapped PT into Woe Strider, the remaining 56 into TSBs.
Tap the Palladium Myrs for 12 colorless mana - 1 black, 12 colorless left.
Sacrifice Xorn, it comes back.
Pay 12 colorless to create 4 TSBs - 65 PTs, 1 tapped TWS, 4 tapped TPMs, 4 untapped TSBs, 56 tapped TSBs. 1 black mana left.
52 TSB triggers remain on the stack.
Sacrifice Woe Strider twice, Palladium Myr 4 times, Sorcerer's Broom twice, Kinnan, Bonder Prodigy once, and one Goat token. All but 4 of our 50 tapped TSBs now have 11 triggers on the stack each, with the remaining 6 having 10 each, as well as the untapped TSBs.
Sacrifice 3 tapped TPMs, the 4 tapped TSBs with 11 triggers each, and 18 more tapped TSBs.
This leaves 4 untapped TSBs with 35 triggers each, and 34 TSBs with 36 triggers each. We also have a bunch of triggers from the sacrificed TSBs.
Sacrifice Tymaret, Chosen for Death. It triggers Luminous Moth and our TSBs; the number of triggers per TSB go up to 36 or 37.
Resolve the Luminous Moth trigger first, bringing Tymaret back.
Turn our 4 untapped TSBs into Palladium Myrs, and the TSB with the next trigger on the stack into a Nyxborn Marauder.
Tap the 4 untapped TSBs for 12 colorless - 1 black, 12 colorless left.
Resolve the next TSB trigger, creating a Nyxborn Marauder - 1 black, 9 colorless left
Turn the new untapped Nyxborn Marauder into a Palladium Myr, and the TSB with the next trigger on the stack into a Nyxborn Marauder.
Tap the new untapped Palladium Myr - 1 black, 12 colorless.
Repeat this process for all 1402 TSB triggers for TSBs that still exist, increasing the number of PTs from 40 to 1442.
Spend the 12 colorless to pay for 4 triggers of sacrificed TSBs, increasing to 1446 PTs.
We repeat this procedure for the next enchantment creature - a Hateful Eidolon, say.
We first sacrifice the Tymaret and 721 tapped TSBs, leaving 723 TSBs with 722 triggers each.
We sacrifice Hateful Eidolon, increasing the number of triggers to 723 each.
This results in the creation of another 723^2 TSBs for those triggers, plus 4 for triggers of sacrificed TSBs. We wind up with 725 + 723^2 + 4 = 523458 PTs.
For the next Hateful Eidolon, we sacrifice Hateful Eidolon and 261,727 tapped TSBs, leaving 261,729 TSBs. After the procedure, we go up to 261,731 + 261,729^2 + 4 = 68,502,331,176 PTs.
Each successive iteration of the procedure takes X to more than X^2/4. Near the end, we can create two Skemfar Avenger tokens and sacrifice the original to draw a third Tymaret and Quandrix Command. This allows us to play and sacrifice 14 enchantment creatures, taking the number of Thaumaturges to more than 4*(68,502,331,176/4)^(2^11) > 10^20,959.
Before we finish, we make sure to have a Thaumaturge copy Gyruda, and create a copy, allowing us to fetch Vault Robber from the library. With the last Constellation trigger, we turn all of our Protean Thaumaturges into Xorns (except for three, which we turn into Skemfar Avengers), and activate Vault Robber to create more than 10^20,959 Treasure tokens.
We should probably continue this some more to see that we can do the full combo from here, but I will let you guys check this first.
The only recent thing I was looking at was to maybe fit in Epitaph Golem to add one more creature, by avoiding any loops with Gyruda.
Edit: Question - if I add a nonflash mutate creature in a cheap color (specifically, Regal Leosaur with cheap red), will it go infinite?
It would certainly help to be able to mutate onto Kinnan, Bonder Prodigy in the opening without blue mana, otherwise it is very slow going.
Edit: I think Volo, Guide to Monsters should be able to replace both copies of Reflections of Littjara, as Sea-Dasher Octopus is the only Octopus, and we have the Warlord if necessary.