Hmm good point about multiple arcbonds. I think that kills any protection short of protection from creatures, which is not easy to grant.
Yeah. Although based on the other thread, it sounds like even a working Rotlung Reanimator strategy wouldn't make Dralnu's Crusade viable anyway.
That said, I feel pretty good about the Sephara, Sky's Blade strategy. If it holds up, I think each layer in the small computation would just take three Xathrid Necromancers, one Bishop of Wings, and a vanilla. To deal with the two toughness of the Necromancer tokens, we could sacrifice a 2/2 to Soulblast, and make a second Coat of Arms to balance out the size of the ticks. Seems like that should get us to about seven layers for the small computation.
In the Rotlung Reanimator computation we need to give the reanimators indestructible because there is no other way for them to survive while the tokens it creates and triggers from keep dying. Sephara doesn't help with that.
Putting it together with Bishop and Necromancers just seems like it is an unnecessary additional card, because we still need Sanctifier en-Vec to get buffer tokens that don't cause triggers when they leave the battlefield. (And then we need the color changer instead of the necromancer to keep the important red cards.)
Edit: Ah I think I understand what you wanted to do. But it doesn't really work.
We do need the buffer-creatures to leave the battlefield so they don't keep buffing the next run of the clock. If they stick around indestructibly they mess up the computation by still providing their coat of arms buff to new non-flying tokens.
Having these buffs stick around is a different computational model, where we can have flooding and self-refilling clocks, but no normal clocks. Great for layers, and maybe it is turing-complete. But I don't see an obvious way to run waterfall programs with it.
In the Rotlung Reanimator computation we need to give the reanimators indestructible because there is no other way for them to survive while the tokens it creates and triggers from keep dying. Sephara doesn't help with that.
Putting it together with Bishop and Necromancers just seems like it is an unnecessary additional card, because we still need Sanctifier en-Vec to get buffer tokens that don't cause triggers when they leave the battlefield. (And then we need the color changer instead of the necromancer to keep the important red cards.)
Edit: Ah I think I understand what you wanted to do. But it doesn't really work.
We do need the buffer-creatures to leave the battlefield so they don't keep buffing the next run of the clock. If they stick around indestructibly they mess up the computation by still providing their coat of arms buff to new non-flying tokens.
Having these buffs stick around is a different computational model, where we can have flooding and self-refilling clocks, but no normal clocks. Great for layers, and maybe it is turing-complete. But I don't see an obvious way to run waterfall programs with it.
Yeah, that was my plan. Ah well.
Next idea: Looking for a way to prove this model to be Turing complete.
We use one creature type per clock, and one bishop that produces a properly dying token per clock, on the diagonal. All other bishops produce the tokens in colors that are getting exiled. And then we just have x bishops that produce type2 whenever type1 dies if the waterfall problem adds x to clock 2 when clock 1 empties.
For example this program for exponentiation:
[[1000,5,5,5,5,5],
[2,2,2,6,0,2],
[4,2,2,0,4,2],
[3,0,4,4,2,2],
[3,4,0,2,4,0],
[15,0,0,0,0,0]]
can be built with 44 bishops. (row 1 is for bookkeeping, column 1 is for the input that translates to vanillas.) Getting the input right might require additional bishops, as only 1 of the vanillas per clock is allowed to die properly with all the others needing to be exiled.
There are optimizations we can do. For example in this case all bishops come in multiples of 2, so we can use 2 white vanillas per clock and use only half of the bishops.
So we get a list, including a startup type to get the equivalent initial input:
1x bishop type1 -> type1 white
1x bishop type1 -> type2 green
3x bishop type1 -> type3 green
1x bishop type1 -> type5 green
1x bishop type2 -> type1 green
1x bishop type2 -> type2 white
2x bishop type2 -> type4 green
1x bishop type2 -> type5 green
2x bishop type3 -> type2 green
1x bishop type3 -> type3 white
1x bishop type3 -> type3 green
1x bishop type3 -> type4 green
1x bishop type3 -> type5 green
2x bishop type4 -> type1 green
1x bishop type4 -> type3 green
1x bishop type4 -> type4 white
1x bishop type4 -> type4 green
2x vanilla type1 white
2x vanilla type2 white
2x vanilla type3 white
2x vanilla type4 white
15x vanilla type5 white, one with arcbond
1x vanilla startType white
2x bishop startType -> type2 green
1x bishop startType -> type3 green
1x bishop startType -> type4 green
(assuming green gets exiled and white dies properly. White vanillas may be colorless)
This exponentiation program produces an output exponential in (#type5/2). It seems to be roughly 6*2^((#type5-1)/2), but that is not exact. Using this might be slightly better than the start without sanctifier, depending on how many type5 vanillas we can actually get. Or rather how much toughness we can give to the type5 vanilla with arcbond.
Here's a program I wrote for tetration:
[[10000,8,8,8,8,8,8,8,8],
[2,2,2,2,6,6,0,2,2],
[4,2,2,2,0,0,4,2,2],
[4,2,2,2,0,0,2,4,2],
[3,0,4,2,4,2,2,2,2],
[3,0,2,4,2,4,2,2,2],
[3,4,0,2,2,4,4,0,2],
[5,2,4,0,4,0,2,4,0],
[5,0,0,0,0,0,0,0,0]]
That seems to require too many bishops to be used. But there might be more efficient programs out there.
I can't think of any useful tricks with the sanctifier computation that would set it apart from a waterfall model program, like the part-flooding clocks we had with dralnu.
Edit: Huh, I found a small optimization for the exponentiation program:
[[1000,5,5,5,5,5],
[2,2,2,6,0,2],
[4,2,2,0,6,2],
[3,0,4,4,2,2],
[3,4,0,2,4,0],
[15,0,0,0,0,0]]
Using only 1 additional type2->type4 bishop we improve the output to ~2^#type5. With that improvement this is almost certainly a better start than not using sanctifier.
Awesome! So it sounds like we could build that with something like:
Bishop (Angel>Angel)
Bishop (Angel>Beast)
3x Bishop (Angel>Centaur)
Bishop (Angel>Eldrazi)
Bishop (Beast>Angel)
Bishop (Beast>Beast)
4x Bishop (Beast>Dragon)
Bishop (Beast>Eldrazi)
2x Bishop (Centaur>Beast)
2x Bishop (Centaur>Centaur)
Bishop (Centaur>Dragon)
Bishop (Centaur>Eldrazi)
2x Bishop (Dragon>Angel)
Bishop (Dragon>Centaur)
2x Bishop (Dragon>Dragon)
With one of each diagonal Bishop making white tokens and the others making green ones. That would be a total of 24 Bishops in the main program, plus one sacrificed to start the program - the same numbers as with the previous setup.
We save 16 Swaps from not needing to make four Dralnu's Crusades and not needing to hack those Crusades six times, but we then lose four of those Swaps from needing to play Sanctifier en-Vec and Trait Doctoring, and needing to use Artificial Evolution on our creatures twice rather than just once (since we can't use Crusade to let unhacked Precursors make it target our Humans). So we have twelve extra Swaps for any additional vanillas and Bishops needed...
Wait. We were talking about problems with protection, and Sanctifier has protection. Wouldn't that mean any computation involving Sanctifier has the possibility to run an infinite computation that it terminates by switching from a damage source that wouldn't hit Sanctifier to one that would, to kill it at the right time?
Wait. We were talking about problems with protection, and Sanctifier has protection. Wouldn't that mean any computation involving Sanctifier has the possibility to run an infinite computation that it terminates by switching from a damage source that wouldn't hit Sanctifier to one that would, to kill it at the right time?
So the two ways around the protection problem are to use just one Arcbond, or to drop Comeuppance (and find another way to survive) and use exactly two Arcbonds. I think the small deck really wants to go for the latter, since it opens up the option of using a card like Wildfire Devils to get exactly two uses out of each of our spells - helpful both for building our board and for finishing with a second casting of Soulblast.
Using a bunch of copies of Sea Gate Stormcaller to copy Artificial Evolution without allowing extra Arcbonds seems effective, I haven't come up with a working build yet but 17 cards feels close to working. For finding another way to survive the computation, one card I found very interesting is Endure, since it also keeps any creatures left on our side of the field from taking damage, and I wonder if that could allow some possibilities for strategies that don't wipe our own side of the field. If we were to use Xathrid Necromancer over Bishop of Wings, we'd need to play Endure early in the computation to avoid running out of life, and at that point our creatures won't be able to take any more damage. Could that work to keep our decision points within finite bounds?
Edit: Wait, then we'd need a way to keep the opponent alive.
Edit: I think there's a bunch of inefficient 18-card strategies but there's gotta be a better 17-card one.
But I haven't found a way to make it actually work. Bolas's Citadel seemed like it would have been useful for the start, but it can break computations.
Lotus, Show and Tell, drop One with the Multiverse. Use the free cast to play Astral Dragon and make two new Multiverses.
Use those two to play Vesuvan Duplimancy, then Spiritualize targeting Astral Dragon. Make a second Astral Dragon for two more Multiverses. Use those to play Doubling Season and Arcbond, targeting the original Astral Dragon to make two more. Use the first to make four Doubling Seasons, then the second to make 64 copies of One with the Multiverse so we can play the rest of our cards.
Play Sea Gate Stormcaller, Wondrous Cruible, Coat of Arms, and Bishop of Wings. Play Trait Doctoring, using the initial cast to make 32 Astral Dragons and go to 2^^34 copies of Doubling Season. Then play Artificial Evolution on Astral Dragon as well to go to 2^^2^^34, using the last Dragon to make a bunch of copies of Wondrous Crucible.
One with the Multiverse has been letting us play cards from hand/library interchangeable, but at this point, we should be out of cards in our hand, with our last three unplayed cards being in our library.
Go to end step and let the Crucibles trigger. The first one mills Sanctifier and Scrambleverse and replays Spiritualize, targeting Stormcaller to make 2^^2^^34 Stormcallers and to draw our last card, Soulblast. The second one plays Sanctifier (just one Sanctifier, since Doubling Season doesn't double tokens of permanent spells). The third plays Trait Doctoring targeting Bishop, copying it 2^^2^^34 times and also making 2^^2^^34 more Bishops. We'll first resolve the Duplimancy triggers to create the Bishops, then resolve the Stormcaller triggers to put the Trait Doctoring copies onto the stack, hacking those Bishops and anything else needed, such as Sanctifier (to keep it off red). The fourth plays Arcbond on the original Stormcaller, making another set of copy triggrs (and placing both Arcbonds on creatures with Spiritualize on them). Then replay Artificial Evolution to finish hacking our board, and Scrambleverse to shift whatever we need to the opponent's side.
Play Soulblast from our hand, sacrificing a Bishop keyed to itself to start the computation and make a bunch of tokens of a type that will survive. I assume we'll want to make sure the Doubling Season copies die early enough to avoid causing problems but I think there should be a way to make that work? The opponent survives from Bishop triggers, we survive from Spiritualize triggers. When it finishes, use the next Crucible trigger to replay Soulblast and turn our creatures into damage.
Ooh, Vesuvan Duplimancy would have been a very good card for the deck that no longer exists. Does the job of Mirror Gallery, and also allows the creation of duplicates using spells you already have.
If you want to make sure the Doubling Seasons die, just don't create tokens of their creature type, I guess.
Ooh, Vesuvan Duplimancy would have been a very good card for the deck that no longer exists. Does the job of Mirror Gallery, and also allows the creation of duplicates using spells you already have.
If you want to make sure the Doubling Seasons die, just don't create tokens of their creature type, I guess.
Yeah, the fact that the Doubling Season tokens are significantly smaller in number than the ones we make later means it should be easy enough to prop up the rest of the deck to sufficiently high starting values to avoid conflicts.
That said, replacing Lotus with two separate green mana sources still looks like it should put that deck at just 16 cards, which is an improvement over the previous one (and it's now occurring to me that the line I proposed for the previous deck doesn't work due to playing Sanctifier en-Vec while Scrambleverse is in the graveyard). Depending on the choices for those cards and for the survival card, I wonder if there's any further possible improvements.
Edit: Wait, Precursor Golem can't copy Domineering Will even if it only targets one creature.
No way to profit from a mini-computation here, but I think we can hit decent numbers regardless. Lotus, Show and Tell, Omniscience, TYS, filler spell, Replication Technique to make four more TYS, then Dance with Calamity copied 15 times for a total of 16. I think that's enough to hit decent numbers? For most of them, we can replay Technique and Treason of Isengard, along with other things.
How does Treason of Isengard ever get replayed? The original is still on the stack when it resolves. All of its copies have to resolve before it. So it can't tuck itself back into the library?
How does Treason of Isengard ever get replayed? The original is still on the stack when it resolves. All of its copies have to resolve before it. So it can't tuck itself back into the library?
Good point. In that case we'll need something like Meldweb Curator instead.
That deck definitely ends up in an interesting range for the input. Somewhere between 10^10 and 10^100 I think?
With only one computation of that size it is tough to establish a lower bound. We'll probably want to emulate an universal turing machine. But the most important stat for our UTM choice is not the number of states, but the length of the encoding that the UTM uses, as the encoded tape will be the main bottleneck. I'm not sure how to look for UTMs that optimize for that.
Maybe there are UTMs with encoding linear in the number of states of the simulated TM. But the TM emulation in the waterfall model then reads that input tape as a binary number and requires its own input in unary. So we end up with a waterfall encoded input of length exponential in the states of the target TM.
That leaves the input range 10^10 - 10^100 in an awkward spot. While quite big it is not big enough to ignore logarithms, so we might not end up with a too impressive result.
Buuuut we can use creature types that are not required to run the UTM to build another layer of input encoding. We could then get an input of 187 by creating say 1 cat, 8 rats and 7 bats. This shrinks the cost of creating big inputs logarithmically. So we end up with mtg input sizes ~ linear to target tm states.
But then the input size to the UTM is limited by the number of creature types we have left. Choosing a different base for the encoding increases the limit, but also the cost of representing a specific number.
Looks like we are very much in the range where things get messy and interesting.
TLDR: Please find a setup that gets an additional layer of input, so we can ignore all this
(Actually it would be fun to think about more. But I'll wait to see if the additional input layer is found first)
Hmm, I think it would be possible to start an illegal computation with the -1/-1 from Massacre Girl entering. None of the creature cards die to it, but we can prepare a 1/1 spirit token by spending a few of the Audacious Swap copies to cast Bishop of Wings -> Artificial Evolution -> Scrambleverse -> Soulblast, sacrificing only a hacked bishop that replaces itself with a 1/1. Nothing but a few audacious swap copies is lost for that and we can continue to set up the computation as normal, but with bishops on our side. Then start it by casting Massacre Girl instead of Soulblast.
Hmm, I think it would be possible to start an illegal computation with the -1/-1 from Massacre Girl entering. None of the creature cards die to it, but we can prepare a 1/1 spirit token by spending a few of the Audacious Swap copies to cast Bishop of Wings -> Artificial Evolution -> Scrambleverse -> Soulblast, sacrificing only a hacked bishop that replaces itself with a 1/1. Nothing but a few audacious swap copies is lost for that and we can continue to set up the computation as normal, but with bishops on our side. Then start it by casting Massacre Girl instead of Soulblast.
That particular line, yes. But there is a more devestating version of the infinite.
Start a normal computation with a bunch of audacious swaps still on the stack. After it halts there are a bunch of damaged output creatures around, keeping each other alive with Coat of Arms. We can then use the remaining audacious swap copies to build another computation with bishops on our side of the board. Then start that computation with Artificial Evolution, taking the shared type away from one of the damaged output creatures.
That sort of infinite might also apply to the Last Laugh version. We only need to be able to rebuild bishops and start another computation after going through a short computation early. That early computation can actually just be the Soulblast damaging a single creature once, so that it is only kept alive by Coat of Arms.
So with Massacre Girl or Last Laugh it is pretty easy to start illegal computations.
That particular line, yes. But there is a more devestating version of the infinite.
Start a normal computation with a bunch of audacious swaps still on the stack. After it halts there are a bunch of damaged output creatures around, keeping each other alive with Coat of Arms. We can then use the remaining audacious swap copies to build another computation with bishops on our side of the board. Then start that computation with Artificial Evolution, taking the shared type away from one of the damaged output creatures.
That sort of infinite might also apply to the Last Laugh version. We only need to be able to rebuild bishops and start another computation after going through a short computation early. That early computation can actually just be the Soulblast damaging a single creature once, so that it is only kept alive by Coat of Arms.
So with Massacre Girl or Last Laugh it is pretty easy to start illegal computations.
Ugh, that's a problem. Maybe if there's a way to ensure that after casting Soulblast (or some other sacrifice card), there's no way to go back to having Bishops on our side of the field? But that seems quite difficult.
Oh, I thought the 17-card deck still needed to be replaced, but we can prevent the original Doubling Season from being an issue by keeping it under our own control so it won't affect the opponent. The sequence I described doesn't quite work, but I think we can fix it by swapping the first cast of Arcbond with Artificial Evolution and Sanctifier with Coat of Arms, to make it so we hack Sanctifier with the Trait Doctoring copy before playing any red spells. So I think that's still in the lead for small decks, at 2^^2^^34.
In that case I should mention that the input can be increased to >2^^^2^^^7 by creating more Vesuvan Duplimancy instead of focusing on Doubling Seasons immediately.
Instead of creating 4 doubling seasons and 64 One with the Multiverse create 4 Duplimancies and 4 OwtM.
Then the trait doctoring gets 5 duplimancy triggers on Astral Dragon.
Trigger 1: 2 Dragons gives 1->5->69 doubling seasons
Trigger 2: 2^70 Dragons gives >2^^2^70 doubling seasons.
2^70 > 2^16 = 2^2^2^2 = 2^^4 = 2^^^3, so 2^^2^70>2^^^4.
The remaining 3 triggers then get us to 2^^^7, with the last 2 dragons topping of Duplimancy and OwtM.
Then the Duplimancy triggers from Arcbond get us to 2^^^2^^^7.
That is a really cool combination of cards you found there
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That said, I feel pretty good about the Sephara, Sky's Blade strategy. If it holds up, I think each layer in the small computation would just take three Xathrid Necromancers, one Bishop of Wings, and a vanilla. To deal with the two toughness of the Necromancer tokens, we could sacrifice a 2/2 to Soulblast, and make a second Coat of Arms to balance out the size of the ticks. Seems like that should get us to about seven layers for the small computation.
Does that all sound like it works?
In the Rotlung Reanimator computation we need to give the reanimators indestructible because there is no other way for them to survive while the tokens it creates and triggers from keep dying. Sephara doesn't help with that.
Putting it together with Bishop and Necromancers just seems like it is an unnecessary additional card, because we still need Sanctifier en-Vec to get buffer tokens that don't cause triggers when they leave the battlefield. (And then we need the color changer instead of the necromancer to keep the important red cards.)
Edit: Ah I think I understand what you wanted to do. But it doesn't really work.
We do need the buffer-creatures to leave the battlefield so they don't keep buffing the next run of the clock. If they stick around indestructibly they mess up the computation by still providing their coat of arms buff to new non-flying tokens.
Having these buffs stick around is a different computational model, where we can have flooding and self-refilling clocks, but no normal clocks. Great for layers, and maybe it is turing-complete. But I don't see an obvious way to run waterfall programs with it.
Next idea: Looking for a way to prove this model to be Turing complete.We use one creature type per clock, and one bishop that produces a properly dying token per clock, on the diagonal. All other bishops produce the tokens in colors that are getting exiled. And then we just have x bishops that produce type2 whenever type1 dies if the waterfall problem adds x to clock 2 when clock 1 empties.
For example this program for exponentiation:
[[1000,5,5,5,5,5],
[2,2,2,6,0,2],
[4,2,2,0,4,2],
[3,0,4,4,2,2],
[3,4,0,2,4,0],
[15,0,0,0,0,0]]
can be built with 44 bishops. (row 1 is for bookkeeping, column 1 is for the input that translates to vanillas.) Getting the input right might require additional bishops, as only 1 of the vanillas per clock is allowed to die properly with all the others needing to be exiled.
There are optimizations we can do. For example in this case all bishops come in multiples of 2, so we can use 2 white vanillas per clock and use only half of the bishops.
So we get a list, including a startup type to get the equivalent initial input:
1x bishop type1 -> type1 white
1x bishop type1 -> type2 green
3x bishop type1 -> type3 green
1x bishop type1 -> type5 green
1x bishop type2 -> type1 green
1x bishop type2 -> type2 white
2x bishop type2 -> type4 green
1x bishop type2 -> type5 green
2x bishop type3 -> type2 green
1x bishop type3 -> type3 white
1x bishop type3 -> type3 green
1x bishop type3 -> type4 green
1x bishop type3 -> type5 green
2x bishop type4 -> type1 green
1x bishop type4 -> type3 green
1x bishop type4 -> type4 white
1x bishop type4 -> type4 green
2x vanilla type1 white
2x vanilla type2 white
2x vanilla type3 white
2x vanilla type4 white
15x vanilla type5 white, one with arcbond
1x vanilla startType white
2x bishop startType -> type2 green
1x bishop startType -> type3 green
1x bishop startType -> type4 green
(assuming green gets exiled and white dies properly. White vanillas may be colorless)
This exponentiation program produces an output exponential in (#type5/2). It seems to be roughly 6*2^((#type5-1)/2), but that is not exact. Using this might be slightly better than the start without sanctifier, depending on how many type5 vanillas we can actually get. Or rather how much toughness we can give to the type5 vanilla with arcbond.
Here's a program I wrote for tetration:
[[10000,8,8,8,8,8,8,8,8],
[2,2,2,2,6,6,0,2,2],
[4,2,2,2,0,0,4,2,2],
[4,2,2,2,0,0,2,4,2],
[3,0,4,2,4,2,2,2,2],
[3,0,2,4,2,4,2,2,2],
[3,4,0,2,2,4,4,0,2],
[5,2,4,0,4,0,2,4,0],
[5,0,0,0,0,0,0,0,0]]
That seems to require too many bishops to be used. But there might be more efficient programs out there.
I can't think of any useful tricks with the sanctifier computation that would set it apart from a waterfall model program, like the part-flooding clocks we had with dralnu.
Edit: Huh, I found a small optimization for the exponentiation program:
[[1000,5,5,5,5,5],
[2,2,2,6,0,2],
[4,2,2,0,6,2],
[3,0,4,4,2,2],
[3,4,0,2,4,0],
[15,0,0,0,0,0]]
Using only 1 additional type2->type4 bishop we improve the output to ~2^#type5. With that improvement this is almost certainly a better start than not using sanctifier.
- Bishop (Angel>Angel)
- Bishop (Angel>Beast)
- 3x Bishop (Angel>Centaur)
- Bishop (Angel>Eldrazi)
- Bishop (Beast>Angel)
- Bishop (Beast>Beast)
- 4x Bishop (Beast>Dragon)
- Bishop (Beast>Eldrazi)
- 2x Bishop (Centaur>Beast)
- 2x Bishop (Centaur>Centaur)
- Bishop (Centaur>Dragon)
- Bishop (Centaur>Eldrazi)
- 2x Bishop (Dragon>Angel)
- Bishop (Dragon>Centaur)
- 2x Bishop (Dragon>Dragon)
With one of each diagonal Bishop making white tokens and the others making green ones. That would be a total of 24 Bishops in the main program, plus one sacrificed to start the program - the same numbers as with the previous setup.We save 16 Swaps from not needing to make four Dralnu's Crusades and not needing to hack those Crusades six times, but we then lose four of those Swaps from needing to play Sanctifier en-Vec and Trait Doctoring, and needing to use Artificial Evolution on our creatures twice rather than just once (since we can't use Crusade to let unhacked Precursors make it target our Humans). So we have twelve extra Swaps for any additional vanillas and Bishops needed...
Wait. We were talking about problems with protection, and Sanctifier has protection. Wouldn't that mean any computation involving Sanctifier has the possibility to run an infinite computation that it terminates by switching from a damage source that wouldn't hit Sanctifier to one that would, to kill it at the right time?
I don't think any way we know to do turing complete computations is left
Using a bunch of copies of Sea Gate Stormcaller to copy Artificial Evolution without allowing extra Arcbonds seems effective, I haven't come up with a working build yet but 17 cards feels close to working. For finding another way to survive the computation, one card I found very interesting is Endure, since it also keeps any creatures left on our side of the field from taking damage, and I wonder if that could allow some possibilities for strategies that don't wipe our own side of the field. If we were to use Xathrid Necromancer over Bishop of Wings, we'd need to play Endure early in the computation to avoid running out of life, and at that point our creatures won't be able to take any more damage. Could that work to keep our decision points within finite bounds?
Edit: Wait, then we'd need a way to keep the opponent alive.
Edit: I think there's a bunch of inefficient 18-card strategies but there's gotta be a better 17-card one.
- Black Lotus
- Accelerator (Channel or Show and Tell)
- Mana/library support (ex. Chromatic Orrery or One with the Multiverse)
- Token multiplier (ex. Doubling Season or Adrix and Nev, Twincasters)
- Token generator #1 (ex. Astral Dragon or Ratadrabik of Urborg)
- Token generator #2 (ex. Replication Technique or Clone Legion)
- Spell copier (Sea Gate Stormcaller or Izzet Guildmage)
- Flashback effect (ex. Scholar of the Lost Trove or Wondrous Crucible)
- Coat of Arms
- Bishop of Wings
- Artificial Evolution
- Trait Doctoring
- Sanctifier en-Vec
- Arcbond
- Survival support (ex. Authority of the Consuls or Endure)
- Scrambleverse
- Soulblast
But I haven't found a way to make it actually work. Bolas's Citadel seemed like it would have been useful for the start, but it can break computations.2 Show and Tell
3 One with the Multiverse
4 Astral Dragon
5 Doubling Season
6 Vesuvan Duplimancy
7 Sea Gate Stormcaller
8 Wondrous Crucible
9 Coat of Arms
10 Bishop of Wings
11 Artificial Evolution
12 Trait Doctoring
13 Sanctifier en-Vec
14 Arcbond
15 Spiritualize
16 Scrambleverse
17 Soulblast
Lotus, Show and Tell, drop One with the Multiverse. Use the free cast to play Astral Dragon and make two new Multiverses.
Use those two to play Vesuvan Duplimancy, then Spiritualize targeting Astral Dragon. Make a second Astral Dragon for two more Multiverses. Use those to play Doubling Season and Arcbond, targeting the original Astral Dragon to make two more. Use the first to make four Doubling Seasons, then the second to make 64 copies of One with the Multiverse so we can play the rest of our cards.
Play Sea Gate Stormcaller, Wondrous Cruible, Coat of Arms, and Bishop of Wings. Play Trait Doctoring, using the initial cast to make 32 Astral Dragons and go to 2^^34 copies of Doubling Season. Then play Artificial Evolution on Astral Dragon as well to go to 2^^2^^34, using the last Dragon to make a bunch of copies of Wondrous Crucible.
One with the Multiverse has been letting us play cards from hand/library interchangeable, but at this point, we should be out of cards in our hand, with our last three unplayed cards being in our library.
Go to end step and let the Crucibles trigger. The first one mills Sanctifier and Scrambleverse and replays Spiritualize, targeting Stormcaller to make 2^^2^^34 Stormcallers and to draw our last card, Soulblast. The second one plays Sanctifier (just one Sanctifier, since Doubling Season doesn't double tokens of permanent spells). The third plays Trait Doctoring targeting Bishop, copying it 2^^2^^34 times and also making 2^^2^^34 more Bishops. We'll first resolve the Duplimancy triggers to create the Bishops, then resolve the Stormcaller triggers to put the Trait Doctoring copies onto the stack, hacking those Bishops and anything else needed, such as Sanctifier (to keep it off red). The fourth plays Arcbond on the original Stormcaller, making another set of copy triggrs (and placing both Arcbonds on creatures with Spiritualize on them). Then replay Artificial Evolution to finish hacking our board, and Scrambleverse to shift whatever we need to the opponent's side.
Play Soulblast from our hand, sacrificing a Bishop keyed to itself to start the computation and make a bunch of tokens of a type that will survive. I assume we'll want to make sure the Doubling Season copies die early enough to avoid causing problems but I think there should be a way to make that work? The opponent survives from Bishop triggers, we survive from Spiritualize triggers. When it finishes, use the next Crucible trigger to replay Soulblast and turn our creatures into damage.
If you want to make sure the Doubling Seasons die, just don't create tokens of their creature type, I guess.
That said, replacing Lotus with two separate green mana sources still looks like it should put that deck at just 16 cards, which is an improvement over the previous one (and it's now occurring to me that the line I proposed for the previous deck doesn't work due to playing Sanctifier en-Vec while Scrambleverse is in the graveyard). Depending on the choices for those cards and for the survival card, I wonder if there's any further possible improvements.
Edit: Wait, Precursor Golem can't copy Domineering Will even if it only targets one creature.
But fortunately, I think we have a better alternative.
2 Show and Tell
3 Omniscience
4 Thousand-Year Storm
5 Replication Technique
6 Dance with Calamity
7 Treason of Isengard
8 Coat of Arms
9 Bishop of Wings
10 Artificial Evolution
11 Trait Doctoring
12 Sanctifier en-Vec
13 Last Laugh
14 Safe Passage
15 Domineering Will
16 Soulblast
No way to profit from a mini-computation here, but I think we can hit decent numbers regardless. Lotus, Show and Tell, Omniscience, TYS, filler spell, Replication Technique to make four more TYS, then Dance with Calamity copied 15 times for a total of 16. I think that's enough to hit decent numbers? For most of them, we can replay Technique and Treason of Isengard, along with other things.
Either way, the numbers might be a bit low here.
That deck definitely ends up in an interesting range for the input. Somewhere between 10^10 and 10^100 I think?
With only one computation of that size it is tough to establish a lower bound. We'll probably want to emulate an universal turing machine. But the most important stat for our UTM choice is not the number of states, but the length of the encoding that the UTM uses, as the encoded tape will be the main bottleneck. I'm not sure how to look for UTMs that optimize for that.
Maybe there are UTMs with encoding linear in the number of states of the simulated TM. But the TM emulation in the waterfall model then reads that input tape as a binary number and requires its own input in unary. So we end up with a waterfall encoded input of length exponential in the states of the target TM.
That leaves the input range 10^10 - 10^100 in an awkward spot. While quite big it is not big enough to ignore logarithms, so we might not end up with a too impressive result.
Buuuut we can use creature types that are not required to run the UTM to build another layer of input encoding. We could then get an input of 187 by creating say 1 cat, 8 rats and 7 bats. This shrinks the cost of creating big inputs logarithmically. So we end up with mtg input sizes ~ linear to target tm states.
But then the input size to the UTM is limited by the number of creature types we have left. Choosing a different base for the encoding increases the limit, but also the cost of representing a specific number.
Looks like we are very much in the range where things get messy and interesting.
TLDR: Please find a setup that gets an additional layer of input, so we can ignore all this
(Actually it would be fun to think about more. But I'll wait to see if the additional input layer is found first)
Fortunately, I think Massacre Girl lets us go back to the Precursor-Swap strategy, as long as we're careful to avoid having a way to copy her:
2 Channel
3 Chromatic Orrery
4 Precursor Golem
5 March of Progress
6 Audacious Swap
7 Elixir of Immortality
8 Cytoshape
9 Coat of Arms
10 Bishop of Wings
11 Artificial Evolution
12 Sanctifier en-Vec
13 Trait Doctoring
14 Massacre Girl
15 Scrambleverse
16 Soulblast
Edit: Wait, Soulblast can set an opposing creature to 1 HP. Argh.
Start a normal computation with a bunch of audacious swaps still on the stack. After it halts there are a bunch of damaged output creatures around, keeping each other alive with Coat of Arms. We can then use the remaining audacious swap copies to build another computation with bishops on our side of the board. Then start that computation with Artificial Evolution, taking the shared type away from one of the damaged output creatures.
That sort of infinite might also apply to the Last Laugh version. We only need to be able to rebuild bishops and start another computation after going through a short computation early. That early computation can actually just be the Soulblast damaging a single creature once, so that it is only kept alive by Coat of Arms.
So with Massacre Girl or Last Laugh it is pretty easy to start illegal computations.
In that case I should mention that the input can be increased to >2^^^2^^^7 by creating more Vesuvan Duplimancy instead of focusing on Doubling Seasons immediately.
Instead of creating 4 doubling seasons and 64 One with the Multiverse create 4 Duplimancies and 4 OwtM.
Then the trait doctoring gets 5 duplimancy triggers on Astral Dragon.
Trigger 1: 2 Dragons gives 1->5->69 doubling seasons
Trigger 2: 2^70 Dragons gives >2^^2^70 doubling seasons.
2^70 > 2^16 = 2^2^2^2 = 2^^4 = 2^^^3, so 2^^2^70>2^^^4.
The remaining 3 triggers then get us to 2^^^7, with the last 2 dragons topping of Duplimancy and OwtM.
Then the Duplimancy triggers from Arcbond get us to 2^^^2^^^7.
That is a really cool combination of cards you found there