So we have to add Fated Infatuation back? Use Ghitu Encampment as the animatable land and delete World at War, set us back to BB_{w^3+w*3+6}^2(...), but still better than the Archenemy's Charm deck.
I don't think Flayed One or Gisa and Geralf can leak resources. Without Omniscience, playing any colored card is very expansive. To get Omniscience back, we need a mill plus an enchantment-fetching ability. This requires an ETB mill trigger in lower place on the stack (we haven't played the mill card yet), so I would say it is safe.
At Worldfire, Spellweaver Volute is locked at Kaervek's Spite.
No Search for Glory. Legendary creatures should use their Bloodbond March trigger to come back, otherwise we cannot play them cheaply without Omniscience. Especially Anikthea, Hand of Erebos. Riftsweeper can enter many times due to Fated Infatuation, but not above that.
And multiple Archon of Falling Stars die when the higher Volute trigger casting Spite. Get both auras. (3 life)
Resolve down to the TYS/Reality Heist, now we have Soul Foundry and Vedalken Orrery and Mox Ruby.
After that, we rebuild the alternative Ashnod and BM trigger groups of Neurok Replica as usual, and finally push BM triggers for creatures (especially Gandalf and Archon), then flashback Lingering Souls (1 life), which triggers Volute, which cast (Fated Infatuation or Reality Heist, to extract the number remembered by TYS) and Wrong Turn for Foundry and Orrery. Resolve down the new Volute for Spite (3 life), and then resolve down the old lower Volute for Spite (5 life). Finally use Ashnod/Neurok triggers to bounce Foundry and Orrery.
Right, lack of Omniscience makes artifact and legendary mill safe.
There's lots of cards we can add to make this work. For example Clara Oswald could make the single Archon trigger twice to get both auras back. But there's no use for that effect with this version of the layers
We cannot use Pull from Eternity because instants are too expensive during our Foundy stages. We also cannot use Mirror of Fate during Foundry stages because we can only preserve artifacts through the hyperstage transition via donate + bounce. So no token copies to sacrifice during the Foundry stage.
Oh wow, I just discovered this thread coming from a 9 year old summary I found on reddit about v5 which did various recursion loops around casting copy enchantment on Doubling Season. That reddit post was a major motivator for to look at magic back than. Thought I'd revisit the puzzle and came up with using Thousand-Year Storm, Second Harvest and Stormchaser's Talent to upgrade the base loop from tetration to pentation and Insult // Injury for a cleaner finish.
Endurance loops around that base loop was the best I could come up with without cheating an looking at the reference, that was around 2[5]202 for my lower bound. Which is absurdly small even compared to the reference ^^
Had the nagging thought "I wonder whether anyone figured out how to modify the MtG Turing machine to have an upper bound on the number of states it represents and to turn the 1s on the tape into damage". It's really cool that you guys managed to figure that out! Do you have a summary for the current iteration somewhere?
Indeed there is! jfb1337 took on the responsibility of writing up the deck here:
It's not complete yet, and I don't think it has the most current version, but it's a good description of how the most recent decks work. (Hit the "Primer" link for the explanation page)
At the upper limit, we were able to not only implement the Busy Beaver function, we were able to apply multiple levels of recursion on the Busy Beaver function, with the level of recurion signified by the ordinal w^3 + w*3 + 6. Read the primer to understand what that means; for a quick explanation, BB_0(n) is just the Busy Beaver function, and BB_1(n) is BB^n (n), or BB(BB(BB...(n)...)) with n applications of BB. Then BB_2 does the same repeated application but with BB_1, BB_3 does the same but with BB_2, and so on. Then, now that we have defined B_m(n) for all natural numbers m, we can use the infinite ordinal w (that's supposed to be the Greek letter omega, but it's easier to just type w) to create an even faster growing function, by BB_w(n) = BB_n(n). That doesn't sound like a massive improvement, but what it does is that it allows BB_{w+1}(n) to actually iterate over the index, so now the index iteslf will get stupid large instead of just the value. Then BB_{w*2}(n) = BB_{w+n}(n), BB_{w^2}(n) = BB_{w*n}(n), and eventually BB{w^3}(n) = BB{w^2 * n}(n). So yeah that's the state of the art for this challenge.
I'm glad that you found this stuff intersting! Feel free to ask us anything.
EDIT: I'm not seeing the link appear in my post, so I'll just put it in text:
So there was a consideration to cut fated, but didn't work due to the botteneck of getting enough riftsweepers or archons during megastage recovery
There was a concern involving casting Reality heist under a worldfire (TYS-worldfire above volute) to create a self-contained transition by leaking a replica bounce, that was resolved by using Chancelor of the annex over Cephalid shrine, which is not the cose in the current configuration. Is the argument that riftsweeper/archon is a bottleneck requiring an external fated to recover with sufficient to prove that it is safe?
Gisa and Geraf being considered surely doesn't work; Gandalf the white and it are accessible during computations thus allowing for flashing in a zombie legend
What's the startup look like now?
Looks like there are 10 nonlegendary nonartifact creatures to ideally draw before combat.
Usual start is crypt ruby dig experiment tys ii (1 more), from which there are a few choices
- ii with 3 copies for 7 total cards
- - then search for 4 legends (incl veyran), and heist for 22 artifacts (5 other cards)
- search for 3 legends, then ii with 4 copies for 8 other cards
- search for 3 legends incl veyran, and ii for 7 copies for 14 cards
Legends that are useful to start include veyran, ratadrabik, gandalf, anikthea, tyvar, k'irrk, ashnod
gandalf is certainly needed before using helix, and tyvar is needed before making any mana for fundry/replica, casting souls. k'irrk also need to cast souls.
The line that starts with ii for 3 copies could play veyran before search and heist, then we have all the relevant legends and 4 other cards
tyvar mills and returns riftsweeper (1 of the 10 creatures)
play fated (3 other cards) for plenty of copies of relevant legends, milling whatever we need from Flayed one
(or can we avoid fated by bootstrapping into foundry copies of legends? don't see a way of getting in sufficiently many ashnods or bloodbond marches for it. perhaps something could be done with heist copies still on the stack to fetch replica more times..)
after fated we can now scale with replica stage however
punch from hand (2 other cards) makes helix triggers, cast resurgent for volute
with archon (1 other cards left) can do hyperstage stuff (the last card being another creature to be played out before spite) (3 creatures drawn) (with necromancer we technically have computations but can't yet extract the output)
then helix triggers on the stack can resolve more IIs safely with TYS removed from spite; with 3 poison then 6 more can be resoved
first draws worldfire + extra creature (4 drawn), leave one on stack before casting worldfire to extract R from ruby
next draws ssa + ghitu encampment (needs to be drawn once before floating wayfarers can draw it) to convert R to treasures
last 4 IIs, 2 draw 2 extra creatures each (8 drawn) and 2 draw ssa + extra creature
Edit: If we have volute in hand, then instead of drawing worldfire, we can cast it through helix and set up a proper megastage recovery for it. Can't resolve spite prior to doing so, however, (so don't have full hyperstage); otherwise we'd discard the punch in hand needed to start it off.
Edit: Ah, volute also saves having to draw fated; as before needing fated we are able to mill souls and an extra instant and have the mana to flash it back.
Is tyvar untapping foundry a resource leak concern?
Start state: foundry on replica, tyvar untaps to make 2 replicas
Use 1 replica to create ashnod triggers, use some ashnod triggers and a R to setup megastage transition
Resolve the worldfire, exiling tyvar, resolve rest of transition, reclaiming R and unexiling tyvar
Create another megastage transition using more ashnod triggers and R
Resolve the transition, resolving a search under the worldfire to draw tyvar, reclaiming R
Ah, but to fully recover, a spite is required which discards/sacs tyvar, so we can't clear the stack down to empty to use the untap again without giving up life, a more valuable resource than a foundry untap provides.
Tyvar isn't needed during middling stage operations as the only needed tap ability is on foundry, which doesn't need haste if march can be bounced out of the way as needed; and it can be used to accumulate enough colourless mana / Oaken Siren mana as needed at the very top level.
I'm pretty sure Cephalid Shrine instead of Chancellor of the Annex still goes infinite in the latest version. But writing down the infinite with all details filled in is tedious and hyp_cos doesn't seem to like playing it safe
Most lines of play we can do during the regular combo would also enable the infinite unless they specifically require the use of the hyperstage transition floating instant at the bottom of the stack. With Fated Infatuation in the deck it should be possible to get Riftsweeper and Soul Foundry both into the deck for Worldfire. This should avoid the bottleneck in a way usable during the infinite.
But with the starting power we get from fated I expect the difference to be too small to care.
So we have to add Fated Infatuation back? Use Ghitu Encampment as the animatable land and delete World at War, set us back to BB_{w^3+w*3+6}^2(...), but still better than the Archenemy's Charm deck.
I don't think Flayed One or Gisa and Geralf can leak resources. Without Omniscience, playing any colored card is very expansive. To get Omniscience back, we need a mill plus an enchantment-fetching ability. This requires an ETB mill trigger in lower place on the stack (we haven't played the mill card yet), so I would say it is safe.
1 Coat of Arms
2 Xathrid Necromancer
3 Artificial Evolution
4 Arcbond
5 Comeuppance
6 Wrong Turn
7 March of the Machines
8 Kaervek's Spite
9 Goblin Boom Keg
Utility
10 Vedalken Orrery
11 Omniscience
12 Metalworker
13 Tyvar, Jubilant Brawler
14 Thousand-Year Storm
15 Anikthea, Hand of Erebos
16 Ratadrabik of Urborg
Foundry Stage
17 Neurok Replica
18 Oaken Siren
19 Ashnod the Uncaring
20 Soul Foundry
21 Flayed One
22 Riftsweeper
23 Bloodbond March
24 Cephalid Shrine
25 Spellweaver Volute
26 Veyran, Voice of Duality
27 Fated Infatuation
28 Lingering Souls
29 K'rrik, Son of Yawgmoth
30 Archon of Falling Stars
31 Pious Interdiction
Megastage
32 Spellweaver Helix
33 Gandalf the White
34 Gravitic Punch
35 Gravitic Punch
36 Mox Ruby
37 Worldfire
38 Search for Glory
39 Reality Heist
Blue Mana Stage
40 Great Furnace
41 Muzzio, Visionary Architect
42 Floodchaser
43 Brutal Suppression
44 Arboreal Grazer
45 Snow-Covered Island
46 Firebrand Ranger
47 Groundskeeper
48 Forest
White Mana Stage
49 Ruin Ghost
50 Weathered Wayfarer
51 Archaeological Dig
52 Ghitu Encampment
End Layers
53 Jolene, Plunder Queen
54 Smoke Spirits' Aid
55 Evidence Examiner
56 Full Throttle
Start
57 Mana Crypt
58 Epic Experiment
59 Resurgent Belief
60 Infectious Inquiry
A megastage recovery stack should look like this:
- TYS/Worldfire
- ETB mill triggers
- BM/creatures
- Ashnod/Neurok
- TYS/Fated Infatuation
- one Volute trigger
- BM/creatures
- Ashnod/Neurok
- TYS/Reality Heist
- one Volute trigger
- BM/creatures
- Ashnod/Neurok
At Worldfire, Spellweaver Volute is locked at Kaervek's Spite.No Search for Glory. Legendary creatures should use their Bloodbond March trigger to come back, otherwise we cannot play them cheaply without Omniscience. Especially Anikthea, Hand of Erebos.
Riftsweeper can enter many times due to Fated Infatuation, but not above that.
And multiple Archon of Falling Stars die when the higher Volute trigger casting Spite. Get both auras. (3 life)
Resolve down to the TYS/Reality Heist, now we have Soul Foundry and Vedalken Orrery and Mox Ruby.
After that, we rebuild the alternative Ashnod and BM trigger groups of Neurok Replica as usual, and finally push BM triggers for creatures (especially Gandalf and Archon), then flashback Lingering Souls (1 life), which triggers Volute, which cast (Fated Infatuation or Reality Heist, to extract the number remembered by TYS) and Wrong Turn for Foundry and Orrery. Resolve down the new Volute for Spite (3 life), and then resolve down the old lower Volute for Spite (5 life). Finally use Ashnod/Neurok triggers to bounce Foundry and Orrery.
There's lots of cards we can add to make this work. For example Clara Oswald could make the single Archon trigger twice to get both auras back. But there's no use for that effect with this version of the layers
Cutting World at War for Fated Infatuation looks simplest to me. Hurray for two main phases with Full Throttle!
We cannot use Pull from Eternity because instants are too expensive during our Foundy stages. We also cannot use Mirror of Fate during Foundry stages because we can only preserve artifacts through the hyperstage transition via donate + bounce. So no token copies to sacrifice during the Foundry stage.
Endurance loops around that base loop was the best I could come up with without cheating an looking at the reference, that was around 2[5]202 for my lower bound. Which is absurdly small even compared to the reference ^^
Had the nagging thought "I wonder whether anyone figured out how to modify the MtG Turing machine to have an upper bound on the number of states it represents and to turn the 1s on the tape into damage". It's really cool that you guys managed to figure that out! Do you have a summary for the current iteration somewhere?
It's not complete yet, and I don't think it has the most current version, but it's a good description of how the most recent decks work. (Hit the "Primer" link for the explanation page)
At the upper limit, we were able to not only implement the Busy Beaver function, we were able to apply multiple levels of recursion on the Busy Beaver function, with the level of recurion signified by the ordinal w^3 + w*3 + 6. Read the primer to understand what that means; for a quick explanation, BB_0(n) is just the Busy Beaver function, and BB_1(n) is BB^n (n), or BB(BB(BB...(n)...)) with n applications of BB. Then BB_2 does the same repeated application but with BB_1, BB_3 does the same but with BB_2, and so on. Then, now that we have defined B_m(n) for all natural numbers m, we can use the infinite ordinal w (that's supposed to be the Greek letter omega, but it's easier to just type w) to create an even faster growing function, by BB_w(n) = BB_n(n). That doesn't sound like a massive improvement, but what it does is that it allows BB_{w+1}(n) to actually iterate over the index, so now the index iteslf will get stupid large instead of just the value. Then BB_{w*2}(n) = BB_{w+n}(n), BB_{w^2}(n) = BB_{w*n}(n), and eventually BB{w^3}(n) = BB{w^2 * n}(n). So yeah that's the state of the art for this challenge.
I'm glad that you found this stuff intersting! Feel free to ask us anything.
EDIT: I'm not seeing the link appear in my post, so I'll just put it in text:
https://moxfield.com/decks/ywOD31s8eES4kqGdv6b9tQ
So there was a consideration to cut fated, but didn't work due to the botteneck of getting enough riftsweepers or archons during megastage recovery
There was a concern involving casting Reality heist under a worldfire (TYS-worldfire above volute) to create a self-contained transition by leaking a replica bounce, that was resolved by using Chancelor of the annex over Cephalid shrine, which is not the cose in the current configuration. Is the argument that riftsweeper/archon is a bottleneck requiring an external fated to recover with sufficient to prove that it is safe?
Gisa and Geraf being considered surely doesn't work; Gandalf the white and it are accessible during computations thus allowing for flashing in a zombie legend
What's the startup look like now?
Looks like there are 10 nonlegendary nonartifact creatures to ideally draw before combat.
Usual start is crypt ruby dig experiment tys ii (1 more), from which there are a few choices
- ii with 3 copies for 7 total cards
- - then search for 4 legends (incl veyran), and heist for 22 artifacts (5 other cards)
- search for 3 legends, then ii with 4 copies for 8 other cards
- search for 3 legends incl veyran, and ii for 7 copies for 14 cards
Legends that are useful to start include veyran, ratadrabik, gandalf, anikthea, tyvar, k'irrk, ashnod
gandalf is certainly needed before using helix, and tyvar is needed before making any mana for fundry/replica, casting souls. k'irrk also need to cast souls.
The line that starts with ii for 3 copies could play veyran before search and heist, then we have all the relevant legends and 4 other cards
tyvar mills and returns riftsweeper (1 of the 10 creatures)
play fated (3 other cards) for plenty of copies of relevant legends, milling whatever we need from Flayed one
(or can we avoid fated by bootstrapping into foundry copies of legends? don't see a way of getting in sufficiently many ashnods or bloodbond marches for it. perhaps something could be done with heist copies still on the stack to fetch replica more times..)
after fated we can now scale with replica stage however
punch from hand (2 other cards) makes helix triggers, cast resurgent for volute
with archon (1 other cards left) can do hyperstage stuff (the last card being another creature to be played out before spite) (3 creatures drawn) (with necromancer we technically have computations but can't yet extract the output)
then helix triggers on the stack can resolve more IIs safely with TYS removed from spite; with 3 poison then 6 more can be resoved
first draws worldfire + extra creature (4 drawn), leave one on stack before casting worldfire to extract R from ruby
next draws ssa + ghitu encampment (needs to be drawn once before floating wayfarers can draw it) to convert R to treasures
last 4 IIs, 2 draw 2 extra creatures each (8 drawn) and 2 draw ssa + extra creature
Edit: If we have volute in hand, then instead of drawing worldfire, we can cast it through helix and set up a proper megastage recovery for it. Can't resolve spite prior to doing so, however, (so don't have full hyperstage); otherwise we'd discard the punch in hand needed to start it off.
Edit: Ah, volute also saves having to draw fated; as before needing fated we are able to mill souls and an extra instant and have the mana to flash it back.
Is tyvar untapping foundry a resource leak concern?
Start state: foundry on replica, tyvar untaps to make 2 replicas
Use 1 replica to create ashnod triggers, use some ashnod triggers and a R to setup megastage transition
Resolve the worldfire, exiling tyvar, resolve rest of transition, reclaiming R and unexiling tyvar
Create another megastage transition using more ashnod triggers and R
Resolve the transition, resolving a search under the worldfire to draw tyvar, reclaiming R
Ah, but to fully recover, a spite is required which discards/sacs tyvar, so we can't clear the stack down to empty to use the untap again without giving up life, a more valuable resource than a foundry untap provides.
Tyvar isn't needed during middling stage operations as the only needed tap ability is on foundry, which doesn't need haste if march can be bounced out of the way as needed; and it can be used to accumulate enough colourless mana / Oaken Siren mana as needed at the very top level.
Most lines of play we can do during the regular combo would also enable the infinite unless they specifically require the use of the hyperstage transition floating instant at the bottom of the stack. With Fated Infatuation in the deck it should be possible to get Riftsweeper and Soul Foundry both into the deck for Worldfire. This should avoid the bottleneck in a way usable during the infinite.
But with the starting power we get from fated I expect the difference to be too small to care.