Gandalf the white is a panharmonicon that affects helix but not a (nonlegendary, nonartifact) lifegain etb.
However, it limits some space by having flash; because if we can have Cowardice in play during a computation (which setups involving Archon of falling stars allows), an opponent's goblin boom keg can die and target to bounce Gandalf, allowing it to be played mid computation.
Interesting; so each damage step does 3^t damage.
A flooding clock has 2 values; its number of creatures X and its minimum remaining toughness Y <= cX+k where c = #coat of arms, k=ambient toughness boost.
It dies at step t' where Y <= sum[t''=t->t']3^t'' = G(t',3)-G(t-1,3) where G(n,r) = sum[k=0->n]r^k = (r^(n+1)-1)/(r-1)
so Y <= (3^(t'+1)-1)/2 - (3^t-1)/2 = (3^(t'+1)-3^t)/2
=> t' >= log_3(2Y+3^t)-1
and when it dies it X*c creatures of various types for various c.
A clock that creates 3 of itself on death is a heartbeat clock.
A clock that creates 9 of itself on death is a heartbeat clock that triggers every 2 steps
A clock that creates 3^n of itself on death is a heartbeat clock that triggers every n steps
the main issue I see is that it's hard to increment an arbitrary clock. A clock that's k steps away from death has about 3^(k+t) toughness; but incrementing that would require tripling the clock; whereas the operations we have access to are *adding* to its toughness; which has an effect closer to setting its death count to the maximum of itself and another value.
Edit:
An abstract model that this is kind of similar to:
A list of values (v_i) for i=1..n, and a matrix (c_ij) for i,j=1..n
At each step, decrement each v_i by 1.
Then, for each i such that v_i=0, and for each j, set v_j := max(v_j,c_ij) [as opposed to TWM where max is +]
Halt if any v_i = 0.
This is *not* TC, because the number of states for each clock v_j is bounded by max(c_ij | i=1..n) or its initial value; thus the total number of states of the system is finite.
So if there's hope of our model being TC, it must be in the more complex behaviour of our death triggers sufficiently distinguishing it from a maximum operation.
Comeuppance is a damage prevention effect, which works like replacement effects and just modifies the original event without a trigger.
Dread slaver is capable of keeping untyped creatures in play indefinitely, including our artifacts and enchantments. Previously we've argued that it's ok for untyped creatures to create computation-breaking choices, since either these choices can only be made before a finite point, or that animating these permanents necessarily also animates key permanents like coat of arms and the dralnus which make a non-halting computation not possible. However, with dread slaver these arguments aren't true; in particular Goblin boom keg can create decisions indefinitely.
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?
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).
Damn; yeah that does work. Dependency checking uses the objects in play rather than "objects that could theoretically exist"; as there are a large number of those. (There are some ambiguities in the dependency rules, but they don't come into play here)
Sanctifer en-vec + Slight of mind looks like it might work? (instants with flashback don't work as they can be cast during a computation; and colour changers that also change basic land types don't work with the stages).
Sanctifier makes it easier to exile some things. But instants, sorceries, and creatures are already easy to exile pre worldfire transition; and it *doesnt* help exile mox ruby so doesn't immediately break the worldfire transition.
Slight of mind also surprisingly looks safe.
Because then it's not accessible for the rest of the combo above it
(it needs to be the same object that was exiled with the imprint ability; moving it causes it to be lost track of; so it's not sufficient to just put the card back into exile when the ability needs to resolve).
I don't think we fully worked out a 2-volute (equivalently, 1-veyran + 1-volute) setup that works with mirrors over riftsweeper. So the multi-veyran + 1-volute setup is much simpler (and more efficient; costing less life for a full transition) + has more startup utility.
Since Harmonic prodigy doesn't effect veyran, I think it needs to be an actual mirror gallery effect; of which I believe the best is Ratadrabik of Urborg. That would improve the above start by the first fated batch (9 copies) making 256 ratadrabiks and 256 veyrans, then the souls creates 256 volute triggers, every 2 of which (switching between other instants) casts fated and exponentiates the number of ratadrabiks and veyrans; ultimately creating somewhere around 2^^128 mind's eyes.
Edit: In fact we get more than that; we can also use up all our life on souls flashbacks; and also use up the tons of helix triggers we get to cast starlight (donating lots of kirks) before using the last one to cast a caress. Somewhere around 2^^^^^(2^^^5) mind's eyes?
Firewake sliver's targetting and haste being limited to slivers makes it difficult to use it to use on other things as often as we need; as we only cast AE at hyperstage transitions; and it also can't bounce untyped creatures (artifacts and enchantments) at all.
But along the same lines Martyr of spores is a possible pathmage alternative that frees up other haste enablers. (Phabine, Boss's Confidant is also a useful combat trigger; however it doesn't help produce mana to create the first metalworker token).
I'm not sure how useful Sliver grandmother is; it's encore ability for haste and reanimation is too slow for general use (assuming it's safe in the first place); and it's utility for startup is limited too (it can get some milled creatures into play, but that doesn't help get them to hand).
Well the above line doesn't quite reach 21 (or 11) sams; it only can cast search once (for krirk; otherwise we can't trigger volute) and gets stuck with not enough cards milled early enough to continue.
Other possible lines I've considered:
search->yarok, drake, abandon - like above but it ends up with fewer total mills
search->veyran, drake->[panharmonicon,helix,abandon], abandon - the idea is to get 2 helix triggers; but we're so low on mills that we accomplish nothing with them
cowardice,drake,abandon - abandon helps bounce drake an extra time to mill some more; but it still seems like fewer total mills than the above line
anything without abandon or drake in it seems like it makes no progress at all (no mills and/or no enchantments). Best I can find is TYS,search,fated - search finds a few legends including veyran and Ratadrabik of urborg (replacing mirror gallery); fated copies them. but that does nothing; copying sam is only useful with academy manufactor in play, which we don't get without drake.
Edit: TYS,search,fated is actually really close with search fetching ratadrabik,veyran,Leinore, autumn sovreign; it makes a bunch of leinores before combat; however it doesn't get orrery so we can't do anything with the draws.
I was thinking about replacing the Drownyard temple slot; which would require having one of the other lands in the deck be easily fetchable after the megastage transition (we don't actually need it before then). An extra land with a fetchable type (an artifact land or Urza's saga) is equivalent to temple.
But Search for glory is interesting; one of our basics or the manland could be snow, and searching for other things could help setup. In particular, it reduces the number of creatures that Infectious inquiry needs to draw and thus increases the number of SSAs we can cast before combat.
Could it replace II? Here's my best attempt at a start involving it:
- Put omni into play with 4 cards (2 storm). Remaining cards are drake, fated, abandon.
- Drake finds panharmonicon. Fated drake (3 storm); have 8 total remaining artifacts/mills.
- Helix for abandon,epic experiment,resurgent,search for glory (5 artifacts/mills)
- Abandon (6 storm) casting the other spells (9 storm). search gets krirk, resurgent gets volute->fated, embelem, TYS
- Metalworker, flashback souls (10 storm), cast fated. 11 drakes? But then we're stuck.
Gets further than previous no-support starts as it can get krirk into play enable a souls flashback; but it doesn't mill enough relevant enchantments/spells. With more cards seen from drakes early, we may be able to cast souls into fated a few more times, to eventually make some sunrises before combat (on the order of ~100), to draw the rest of the deck and feed a 2-card layer sequence.
However, it limits some space by having flash; because if we can have Cowardice in play during a computation (which setups involving Archon of falling stars allows), an opponent's goblin boom keg can die and target to bounce Gandalf, allowing it to be played mid computation.
Alternatively you could use 2 legendary panharmonicons (Elesh norn, mother of machines + Nabahn, dean of iteration) and no mirror galleries, to allow a 1-life etb to gain exactly 3 life
A flooding clock has 2 values; its number of creatures X and its minimum remaining toughness Y <= cX+k where c = #coat of arms, k=ambient toughness boost.
It dies at step t' where Y <= sum[t''=t->t']3^t'' = G(t',3)-G(t-1,3) where G(n,r) = sum[k=0->n]r^k = (r^(n+1)-1)/(r-1)
so Y <= (3^(t'+1)-1)/2 - (3^t-1)/2 = (3^(t'+1)-3^t)/2
=> t' >= log_3(2Y+3^t)-1
and when it dies it X*c creatures of various types for various c.
A clock that creates 3 of itself on death is a heartbeat clock.
A clock that creates 9 of itself on death is a heartbeat clock that triggers every 2 steps
A clock that creates 3^n of itself on death is a heartbeat clock that triggers every n steps
the main issue I see is that it's hard to increment an arbitrary clock. A clock that's k steps away from death has about 3^(k+t) toughness; but incrementing that would require tripling the clock; whereas the operations we have access to are *adding* to its toughness; which has an effect closer to setting its death count to the maximum of itself and another value.
Edit:
An abstract model that this is kind of similar to:
A list of values (v_i) for i=1..n, and a matrix (c_ij) for i,j=1..n
At each step, decrement each v_i by 1.
Then, for each i such that v_i=0, and for each j, set v_j := max(v_j,c_ij) [as opposed to TWM where max is +]
Halt if any v_i = 0.
This is *not* TC, because the number of states for each clock v_j is bounded by max(c_ij | i=1..n) or its initial value; thus the total number of states of the system is finite.
So if there's hope of our model being TC, it must be in the more complex behaviour of our death triggers sufficiently distinguishing it from a maximum operation.
Dread slaver is capable of keeping untyped creatures in play indefinitely, including our artifacts and enchantments. Previously we've argued that it's ok for untyped creatures to create computation-breaking choices, since either these choices can only be made before a finite point, or that animating these permanents necessarily also animates key permanents like coat of arms and the dralnus which make a non-halting computation not possible. However, with dread slaver these arguments aren't true; in particular Goblin boom keg can create decisions indefinitely.
(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?
(the A->B effect isn't yet applied while determining whether there's a loop between those 3 effects).
Sanctifer en-vec + Slight of mind looks like it might work? (instants with flashback don't work as they can be cast during a computation; and colour changers that also change basic land types don't work with the stages).
Sanctifier makes it easier to exile some things. But instants, sorceries, and creatures are already easy to exile pre worldfire transition; and it *doesnt* help exile mox ruby so doesn't immediately break the worldfire transition.
Slight of mind also surprisingly looks safe.
(it needs to be the same object that was exiled with the imprint ability; moving it causes it to be lost track of; so it's not sufficient to just put the card back into exile when the ability needs to resolve).
2-volute doesn't seem to save a card slot, right?
Edit: In fact we get more than that; we can also use up all our life on souls flashbacks; and also use up the tons of helix triggers we get to cast starlight (donating lots of kirks) before using the last one to cast a caress. Somewhere around 2^^^^^(2^^^5) mind's eyes?
But along the same lines Martyr of spores is a possible pathmage alternative that frees up other haste enablers. (Phabine, Boss's Confidant is also a useful combat trigger; however it doesn't help produce mana to create the first metalworker token).
I'm not sure how useful Sliver grandmother is; it's encore ability for haste and reanimation is too slow for general use (assuming it's safe in the first place); and it's utility for startup is limited too (it can get some milled creatures into play, but that doesn't help get them to hand).
Other possible lines I've considered:
search->yarok, drake, abandon - like above but it ends up with fewer total mills
search->veyran, drake->[panharmonicon,helix,abandon], abandon - the idea is to get 2 helix triggers; but we're so low on mills that we accomplish nothing with them
cowardice,drake,abandon - abandon helps bounce drake an extra time to mill some more; but it still seems like fewer total mills than the above line
anything without abandon or drake in it seems like it makes no progress at all (no mills and/or no enchantments). Best I can find is TYS,search,fated - search finds a few legends including veyran and Ratadrabik of urborg (replacing mirror gallery); fated copies them. but that does nothing; copying sam is only useful with academy manufactor in play, which we don't get without drake.
Edit: TYS,search,fated is actually really close with search fetching ratadrabik,veyran,Leinore, autumn sovreign; it makes a bunch of leinores before combat; however it doesn't get orrery so we can't do anything with the draws.
But Search for glory is interesting; one of our basics or the manland could be snow, and searching for other things could help setup. In particular, it reduces the number of creatures that Infectious inquiry needs to draw and thus increases the number of SSAs we can cast before combat.
Could it replace II? Here's my best attempt at a start involving it:
- Put omni into play with 4 cards (2 storm). Remaining cards are drake, fated, abandon.
- Drake finds panharmonicon. Fated drake (3 storm); have 8 total remaining artifacts/mills.
- Helix for abandon,epic experiment,resurgent,search for glory (5 artifacts/mills)
- Abandon (6 storm) casting the other spells (9 storm). search gets krirk, resurgent gets volute->fated, embelem, TYS
- Metalworker, flashback souls (10 storm), cast fated. 11 drakes? But then we're stuck.
Gets further than previous no-support starts as it can get krirk into play enable a souls flashback; but it doesn't mill enough relevant enchantments/spells. With more cards seen from drakes early, we may be able to cast souls into fated a few more times, to eventually make some sunrises before combat (on the order of ~100), to draw the rest of the deck and feed a 2-card layer sequence.