Yeah a specific counterexample is not necessary, It's just a bit trickier than it looks at first glance.
The idea was that Rotlungs can be made indestructible with resolute watchdog before donating them. The watchdog also allows us to make dummy indestructible creatures of the other types to balance out any problems from having the rotlung types.
There were other tricks like additional copies of dralnu's crusade or coat of arms and doubling up on the key creatures. But those were mostly to make the mapping more efficient.
Its a bit less efficient than the necromancer version which is less efficient than bishops, but it should still work.
Edit:
new page here's the deck with the patch: (still should probably prove more rigorously that arbitrary waterfall programs are reachable)
I went back to check, and while post 4018 was written with Necromancers in mind the procedure should work just as well for Reanimators. So we can still implement any waterfall program.
That should work, although the haste from Ignition probably goes infinite by starting an illegal computation from combat. Take Up the Shield seems fine.
Though I can't make any promises about the start being particularly great. The shared creature types between Rotlung Reanimator and the tokens it looks for and creates are really annoying to work with. Particularly when we can't just throw bigger numbers at it.
Edit: Wait, getting lifelink and indestructible from the same effect is no good, because it is the arcbonded creature that needs lifelink to let the opponent survive, but that creature also needs to die for the computation to stop. There might be alternatives, but looking for them should go into the other thread.
This formulation does make setting things up a little more awkward as it is harder to target the opponent's stuff, without martyr of spores, but we don't need to do that a lot.
The main annoyance is probably chancellor of the annex, but we can still bounce it with AE/Arcbond.
So, after thinking about it for a night I've come to the conclusion that Rotlung Reanimator is not enough to prevent dependency loop shenanigans. The reason is that the second creature type on the reanimator can stop it from establishing dependencies that the token it creates then forms.
Concretely:
Lets have the looping dralnus A->B, B->C, C->A. All creatures of those types that are sticking around will have base type C. So none of them can establish that C->A is dependent on B->C, because they are C already so C->A affects them anyway.
In particular there's an A,C reanimator that creates A whenever C dies. So while we have no A token there is no dependency loop because the reanimator is already C. But once the token is created the rules can detect that B->C changes what C->A applies to and see that there's a loop. The switch to timestamp order can then cause the toughness drop in a H,C arcbond creature.
We get into the situation of a C dying by occasionally creating a signalling C token with a S->C reanimator. We also need a C->H reanimator to give the opponent the choice between H,C dying and living.
I think it takes 10 ticks for the C token to die, and then another 10 ticks for the A token to die and reset the situation. So all that remains to get an infinite is add heartbeats that create 1 C (via the S->C reanimator) and 20 H every 21 ticks and synchronize them properly to get the near death event. Using 21 different heartbeat clocks for that makes it easy despite the shared creature types.
I think im missing something from that explanation.
If this is all being kicked off by the C waterclock going to zero, so by definition all of the Cs and C's supported types also die. So I'm not seeing how this construction has the opportunity to not halt the halt clock whenever C zeroes?
Things are kicked off by any type C creature dying. Type C is not used to represent any clock, where all creatures die in a batch. Instead the creature that dies to kick things off is a lonely C token that gets a fixed amount of toughness buffs from a few dralnus and indestructible reanimators, and the arcbond creature, that happen to share a type with it.
The arcbond creature is one of our creatures with 2 creature types, one of which is C. It survives through the accumulated damage by sharing its second type, H, with an increasing amount of tokens. But those H tokens don't share a type with the C token, so they don't buff it, and it can die without also killing the H,C arcbond creature.
Isn't the condition for C->A to be dependant on B->C to have a base B that is not a C; not anything to do with As?
(the A->B effect isn't yet applied while determining whether there's a loop between those 3 effects).
Oh, so the rules can't figure out a dependency on more than one effect together? I should have figured.
Unfortunately the infinite has an easy fix: just replace the C->A reanimator with a C->B reanimator and get the dependency loop by creating a B token. To enable the rules to figure out that B->C is dependent on A->B we can add an A,C indestructible creature.
Though I have to say, the single effect dependency has some strange results. For example with dralnus Y->Z, X->Y and W->X a single W token would not be Z, because the Y->Z dralnu is not dependent on any of the other dralnus alone. I find that very strange in this situation where there's an "obvious" dependency chain.
So, currently it looks like we don't have a way to do computation without any infinites. The Churchill Turing machine setup is maybe something to look at, if we're willing to look at a multiturn version of the challenge. Of course, we should look for the possibility of doing computations first turn - the Waterfall model is still looks like a simple way to achieve Turing completeness, even if we don't have an implementation as of right now.
Until we find something, I may look at the traditional megastage version of the deck. We had a deck that was supposed to achieve F_{w^3 + w13 + 4}(X), but of course it had Mimic Vat. I think it had Worldpurge as well, which maybe doesn't work with Soul Foundry? But, I think we should be able to get at least to around that area with our various new ideas.
There's one thing we can still do to get the Sanctifier en-Vec computations to work: limit the deck to only allow one active Arcbond at a time. When we can't choose between different arcbond sources the protection on sanctifier can't create any problems.
So we'd be going back to the techniques we used before Comeuppance, when we had no other way to deal with the asymmetric arcbond damage. Iirc we got our instants stuck in the graveyard, with no way to get them out of there except for Worldfire. So no higher tier stage from Spellweaver Volute.
And the exiling from sanctifier might complicate the "getting stuck" part, as it gets our instants into exile easily. So we'd probably have to get them stuck in graveyard/exile/library.
If we can only get one Arcbond cast between each time we clear the board, what do we do to get enough Artificial Evolutions? Would we need to use something like Sea Gate Stormcaller?
Yes, we have used Sea Gate Stormcaller in the past. I'm also fond of Izzet Guildmage for that task, though I think that never ended up being the best option.
Currently I'm struggling to see how we can get repeated computations. Worldfire doesn't work to get Arcbond unstuck while clearing the board at the same time, because of the Sanctifier en-Vec exile.
The only boardwipe+unstuck combination card I see is Sway of the Stars, which seems sub-optimal. It goes infinite with basically anything that tries to repeat it.
We can't allow Arcbond to get unstuck without wiping the board because we go infinite with multiple arcbond effects. So no amount of resources is high enough to allow the recovery of arcbond, unless the boardwipe is absolutely mandatory.
The other option for repeated computation is not having to recast Arcbond. Then we need the computation to halt without the arcbond creature dying. Something along the lines of a Leonin Relic-Warder dies to end the computation by putting Mark of Asylum back into play.
Leonin Relic-Warder probably goes infinite by smuggling any number of enchantments/artifacts into a computation. I didn't put a lot of effort into finding working cards for this option, because I'm hoping someone has a better idea
A thought that doesn't seem to go anywhere, but I figured I would mention it: We can have one Arcbond, along with Comeuppance, and then the computation will stop when the one Arcbonded creature dies, and to start up again we need to Arcbond another creature. Another way to do it is to have two Arcbonded creatures, and then the Arcbonds will alternate between the two, with no choice ever occurring, until one of them dies. Then again we need another Arcbond to start things up again.
As far as I can tell there's no real advantage to one over the other, other than the latter needing two Arcbonds to start and only one to restart. But, maybe someone will have an idea using this.
Keeping the Arcbond creature around does seem like a promising idea. Leonin Relic-Warder does look like it goes infinite by being able to bring Vedalken Orrery back to the battlefield, allowing us to plop down a creature or whatever. Some cards like Silkwrap are more restrictive on what cards they can exile, but none of the ones I saw had creature types, so they would all die early.
I'm still not completely sure this really sinks our deck like that. Maybe I'm just holding on to vain hope that somehow it can be fixed, but I want to fully understand this before giving it up for lost.
Do the effects look at each other fully before deciding if there is a dependency or not? Does some crusade in a loop have an opportunity to do nothing if it has an early timestamp? or is the C->D crusade forced to apply after the B->C crusade and A->B crusade if there's just an A in play?
Also it seems like that line can only possibly shrink the Cs by one, so we get saved by coat of arms?
I'm not sure about the dependencies on more than a single other effect. But the situation where such dependencies are not detected seems to be the worst for the purpose of going infinite, and the infinite still worked :/
I think we can shrink by an arbitrary amount. Just add N B->B crusades. The type change effect does nothing, so it doesn't matter when it applies and nothing can depend on it. The +1/+1 for B's is applied independently in a later layer. So when our C creature loses the B type it loses N toughness, and only gets 1 back from Coat of Arms
time to figure out a new way to implement noninteractive Turing complete computations! whee! somehow! I did it once i can do it again. (though actually it looks like it never actually worked at all.....)
So, hopefully we can find a new way to do computation - but if not, then I guess it's Sway of the Stars, coupled with a limited way to recycle it? It looks like we can do the normal stuff we do on the ending sequence to get a few layers of top of Busy Beaver, perhaps ending on combat or the opponent's library.
Thinking about how to get a stage going - the creature token stages dependent on Mimic Vat or Soul Foundry depend on bringing stuff back from exile, so maybe those don't work. But, perhaps we can get stages based on color. Sway of the Stars can put cards back in our hand though, so does that mess up our stages?
Is there a possibility of getting computations with Last Laugh rather than Arcbond?
It would place a lot of limits - no animating enchantments, no donating enchantments, no letting any type of permanent go from the battlefield to the graveyard before clearing our board (which can't be with Kaervek's Spite since we need to keep it on our side of the field) but at this point, could it be worth it anyway?
We've considered Last laugh as well as Massacre girl before, but yeah they're hugely restricting
(technically though last laugh *does* work with kaervek's spite through Archon of falling stars returning it however)
So the main issue with Sanctifier en-vec is that protection allows different arcbond sources to be distinguished. Is there some way to force a "Damage can't be prevented" effect to be active? The trouble is is that this stops Comeuppence from working too.
Or more unlikely is there any way to force a Thran lens or Mycrosynth Lattice to be in play, forcing the protection to do nothing?
We've considered Last laugh as well as Massacre girl before, but yeah they're hugely restricting
(technically though last laugh *does* work with kaervek's spite through Archon of falling stars returning it however)
So the main issue with Sanctifier en-vec is that protection allows different arcbond sources to be distinguished. Is there some way to force a "Damage can't be prevented" effect to be active? The trouble is is that this stops Comeuppence from working too.
Or more unlikely is there any way to force a Thran lens or Mycrosynth Lattice to be in play, forcing the protection to do nothing?
Wouldn't making all permanents colorless keep the exile effect from happening as well?
Looking through the anti-damage prevention effects, most of them have a variety of problems, but Flaring Pain looks like it could be relevant if we can make it so that computations would require first getting a trigger from casting it.
Making Flaring Pain mandatory would be nice, but I'm not sure how to go about doing so - having it deal damage without a sweep effect is no good, for example.
How does Last Laugh work as a replacement for Arcbond? Arcbond allows the computation to halt when the Arcbond creature dies, but it seems like Last Laugh would either die early if Opalescence was in play, or never die if it wasn't. I suppose the computation can halt when Last Laugh runs out of triggers with a long enough stretch with nothing being put into the graveyard - do we have a way to control that?
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The idea was that Rotlungs can be made indestructible with resolute watchdog before donating them. The watchdog also allows us to make dummy indestructible creatures of the other types to balance out any problems from having the rotlung types.
There were other tricks like additional copies of dralnu's crusade or coat of arms and doubling up on the key creatures. But those were mostly to make the mapping more efficient.
Its a bit less efficient than the necromancer version which is less efficient than bishops, but it should still work.
Edit:
new page here's the deck with the patch: (still should probably prove more rigorously that arbitrary waterfall programs are reachable)
1 Coat of Arms
2 Rotlung Reanimator
3 Artificial Evolution
4 Arcbond
5 Comeuppance
6 Dralnu's Crusade
Starting a Computation
7 Opalescence
8 Wrong Turn
9 Kaervek's Spite
10 Goblin Boom Keg
11 March of the Machines
Utility
12 Vedalken Orrery
13 Metalworker
14 Twinning Glass
15 Thousand-Year Storm
16 Bloodbond March
17 Chancellor of the Annex
Foundry Stage
18 Resolute Watchdog
19 Soul Foundry
20 Phabine, Boss's Confidant
21 Cowardice
22 Mirror of Fate
23 Chromescale Drake
24 Ashnod the Uncaring
25 Ratadrabik of Urborg
26 Spellweaver Volute
27 Veyran, Voice of Duality
28 Fated Infatuation
29 Lingering Souls
30 K'rrik, Son of Yawgmoth
31 Archon of Falling Stars
32 Pious Interdiction
Helix Megastage
33 Spellweaver Helix
34 Worldfire
35 Starlight
36 Abandon the Post
37 Abandon the Post
38 Mox Ruby
39 Yarok, the Desecrated
Blue Mana Stage
40 Master Transmuter
41 Floodchaser
42 Great Furnace
43 Brutal Suppression
44 Search for Glory
45 Snow-Covered Island
46 Arboreal Grazer
47 Firebrand Ranger
48 Groundskeeper
49 Forest
White Mana Stage
50 Ruin Ghost
51 Weathered Wayfarer
52 Archaeological Dig
53 Ghitu Encampment
Start
54 Mana Crypt
55 Epic Experiment
56 Resurgent Belief
57 Omniscience
58 Infectious Inquiry
End Layers
59 Mind's Eye
60 Smoke Spirits' Aid
The main advantage of the resolute/reanimator fix over Slight/Sanctifier is that it doesn't cost a deck slot. (unless I'm missing something there?)
That should work, although the haste from Ignition probably goes infinite by starting an illegal computation from combat. Take Up the Shield seems fine.
Though I can't make any promises about the start being particularly great. The shared creature types between Rotlung Reanimator and the tokens it looks for and creates are really annoying to work with. Particularly when we can't just throw bigger numbers at it.
Edit: Wait, getting lifelink and indestructible from the same effect is no good, because it is the arcbonded creature that needs lifelink to let the opponent survive, but that creature also needs to die for the computation to stop. There might be alternatives, but looking for them should go into the other thread.
This formulation does make setting things up a little more awkward as it is harder to target the opponent's stuff, without martyr of spores, but we don't need to do that a lot.
The main annoyance is probably chancellor of the annex, but we can still bounce it with AE/Arcbond.
Concretely:
Lets have the looping dralnus A->B, B->C, C->A. All creatures of those types that are sticking around will have base type C. So none of them can establish that C->A is dependent on B->C, because they are C already so C->A affects them anyway.
In particular there's an A,C reanimator that creates A whenever C dies. So while we have no A token there is no dependency loop because the reanimator is already C. But once the token is created the rules can detect that B->C changes what C->A applies to and see that there's a loop. The switch to timestamp order can then cause the toughness drop in a H,C arcbond creature.
We get into the situation of a C dying by occasionally creating a signalling C token with a S->C reanimator. We also need a C->H reanimator to give the opponent the choice between H,C dying and living.
I think it takes 10 ticks for the C token to die, and then another 10 ticks for the A token to die and reset the situation. So all that remains to get an infinite is add heartbeats that create 1 C (via the S->C reanimator) and 20 H every 21 ticks and synchronize them properly to get the near death event. Using 21 different heartbeat clocks for that makes it easy despite the shared creature types.
1 Coat of Arms
2 Rotlung Reanimator
3 Artificial Evolution
4 Arcbond
5 Comeuppance
6 Sanctifier en-Vec
7 Sleight of Mind
Starting a Computation
8 Opalescence
9 Wrong Turn
10 Kaervek's Spite
11 Goblin Boom Keg
12 March of the Machines
Utility
13 Vedalken Orrery
14 Metalworker
15 Twinning Glass
16 Thousand-Year Storm
17 Bloodbond March
18 Chancellor of the Annex
Foundry Stage
19 Resolute Watchdog
20 Soul Foundry
21 Phabine, Boss's Confidant
22 Cowardice
23 Mirror of Fate
24 Chromescale Drake
25 Ashnod the Uncaring
26 Ratadrabik of Urborg
27 Spellweaver Volute
28 Veyran, Voice of Duality
29 Fated Infatuation
30 Lingering Souls
31 K'rrik, Son of Yawgmoth
32 Archon of Falling Stars
33 Pious Interdiction
Helix Megastage
34 Spellweaver Helix
35 Worldfire
36 Starlight
37 Abandon the Post
38 Abandon the Post
39 Mox Ruby
40 Yarok, the Desecrated
Blue Mana Stage
41 Master Transmuter
42 Floodchaser
43 Great Furnace
44 Brutal Suppression
45 Search for Glory
46 Snow-Covered Island
47 Arboreal Grazer
48 Firebrand Ranger
49 Groundskeeper
50 Forest
White Mana Stage
51 Ruin Ghost
52 Weathered Wayfarer
53 Archaeological Dig
54 Ghitu Encampment
Start
55 Mana Crypt
56 Epic Experiment
57 Resurgent Belief
58 Omniscience
59 Infectious Inquiry
End Layers
60 Smoke Spirits' Aid
The loss of Mind's Eye drops us to around BB_{w^3 + w3 + 1}(55).
I think im missing something from that explanation.
If this is all being kicked off by the C waterclock going to zero, so by definition all of the Cs and C's supported types also die. So I'm not seeing how this construction has the opportunity to not halt the halt clock whenever C zeroes?
The arcbond creature is one of our creatures with 2 creature types, one of which is C. It survives through the accumulated damage by sharing its second type, H, with an increasing amount of tokens. But those H tokens don't share a type with the C token, so they don't buff it, and it can die without also killing the H,C arcbond creature.
(the A->B effect isn't yet applied while determining whether there's a loop between those 3 effects).
Unfortunately the infinite has an easy fix: just replace the C->A reanimator with a C->B reanimator and get the dependency loop by creating a B token. To enable the rules to figure out that B->C is dependent on A->B we can add an A,C indestructible creature.
Though I have to say, the single effect dependency has some strange results. For example with dralnus Y->Z, X->Y and W->X a single W token would not be Z, because the Y->Z dralnu is not dependent on any of the other dralnus alone. I find that very strange in this situation where there's an "obvious" dependency chain.
Until we find something, I may look at the traditional megastage version of the deck. We had a deck that was supposed to achieve F_{w^3 + w13 + 4}(X), but of course it had Mimic Vat. I think it had Worldpurge as well, which maybe doesn't work with Soul Foundry? But, I think we should be able to get at least to around that area with our various new ideas.
So we'd be going back to the techniques we used before Comeuppance, when we had no other way to deal with the asymmetric arcbond damage. Iirc we got our instants stuck in the graveyard, with no way to get them out of there except for Worldfire. So no higher tier stage from Spellweaver Volute.
And the exiling from sanctifier might complicate the "getting stuck" part, as it gets our instants into exile easily. So we'd probably have to get them stuck in graveyard/exile/library.
Then we have to figure out how to get back our stuff with Pull from Eternity after a Worldfire.
Currently I'm struggling to see how we can get repeated computations. Worldfire doesn't work to get Arcbond unstuck while clearing the board at the same time, because of the Sanctifier en-Vec exile.
The only boardwipe+unstuck combination card I see is Sway of the Stars, which seems sub-optimal. It goes infinite with basically anything that tries to repeat it.
We can't allow Arcbond to get unstuck without wiping the board because we go infinite with multiple arcbond effects. So no amount of resources is high enough to allow the recovery of arcbond, unless the boardwipe is absolutely mandatory.
The other option for repeated computation is not having to recast Arcbond. Then we need the computation to halt without the arcbond creature dying. Something along the lines of a Leonin Relic-Warder dies to end the computation by putting Mark of Asylum back into play.
Leonin Relic-Warder probably goes infinite by smuggling any number of enchantments/artifacts into a computation. I didn't put a lot of effort into finding working cards for this option, because I'm hoping someone has a better idea
As far as I can tell there's no real advantage to one over the other, other than the latter needing two Arcbonds to start and only one to restart. But, maybe someone will have an idea using this.
Keeping the Arcbond creature around does seem like a promising idea. Leonin Relic-Warder does look like it goes infinite by being able to bring Vedalken Orrery back to the battlefield, allowing us to plop down a creature or whatever. Some cards like Silkwrap are more restrictive on what cards they can exile, but none of the ones I saw had creature types, so they would all die early.
Do the effects look at each other fully before deciding if there is a dependency or not? Does some crusade in a loop have an opportunity to do nothing if it has an early timestamp? or is the C->D crusade forced to apply after the B->C crusade and A->B crusade if there's just an A in play?
Also it seems like that line can only possibly shrink the Cs by one, so we get saved by coat of arms?
I think we can shrink by an arbitrary amount. Just add N B->B crusades. The type change effect does nothing, so it doesn't matter when it applies and nothing can depend on it. The +1/+1 for B's is applied independently in a later layer. So when our C creature loses the B type it loses N toughness, and only gets 1 back from Coat of Arms
That really sucks.
time to figure out a new way to implement noninteractive Turing complete computations! whee! somehow! I did it once i can do it again. (though actually it looks like it never actually worked at all.....)
Thinking about how to get a stage going - the creature token stages dependent on Mimic Vat or Soul Foundry depend on bringing stuff back from exile, so maybe those don't work. But, perhaps we can get stages based on color. Sway of the Stars can put cards back in our hand though, so does that mess up our stages?
It would place a lot of limits - no animating enchantments, no donating enchantments, no letting any type of permanent go from the battlefield to the graveyard before clearing our board (which can't be with Kaervek's Spite since we need to keep it on our side of the field) but at this point, could it be worth it anyway?
(technically though last laugh *does* work with kaervek's spite through Archon of falling stars returning it however)
So the main issue with Sanctifier en-vec is that protection allows different arcbond sources to be distinguished. Is there some way to force a "Damage can't be prevented" effect to be active? The trouble is is that this stops Comeuppence from working too.
Or more unlikely is there any way to force a Thran lens or Mycrosynth Lattice to be in play, forcing the protection to do nothing?
Looking through the anti-damage prevention effects, most of them have a variety of problems, but Flaring Pain looks like it could be relevant if we can make it so that computations would require first getting a trigger from casting it.
For the Archon of Falling Stars method, would the timing work out to actually get Last Laugh to trigger?
How does Last Laugh work as a replacement for Arcbond? Arcbond allows the computation to halt when the Arcbond creature dies, but it seems like Last Laugh would either die early if Opalescence was in play, or never die if it wasn't. I suppose the computation can halt when Last Laugh runs out of triggers with a long enough stretch with nothing being put into the graveyard - do we have a way to control that?