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
So at this point we don't really have anything we can easily extrapolate into a small repeated-computation deck. Trying to put one together sounds quite difficult - probably involving something like Worldfire, I guess? At this point, it would really start to resemble a miniature version of the 60-card decks, which would certainly be interesting to explore.
Worldfire, a second Arcbond, either Riftsweeper or Mirror of Fate, a way to get the cards back to hand afterward, a way to maintain the previous computation's output through the Worldfire... Seems like it would probably take around 20 cards, I guess? Given those should include ways to replace some of the cards from the 17-card deck.
Mana Echoes might work well, and could get along with Izzet Guildmage. It's annoying that Twinflame is the only simple copy spell that's cheap enough to work, given that it conflicts with Soulblast, but Double Major could work.
Edit: Mana Echoes + Guildmage + Twinflame would go infinite anyway.
Edit: Wait, we don't need Mana Echoes. Authority of the Consuls can give plenty of life from opponent's creatures entering and Channel can turn it into mana, and both of those fit into existing deck slots.
But the bigger problem is Sanctifier en-Vec making exile easy, I forgot to account for that. Like in the other thread, we need Worldfire to be helping us recur a key colorless card - and it needs to be something we have to do each time we want to replay Arcbond.
Maybe Mirror of Fate? If we can't get usable copies of it, we could force ourselves to exile it with Worldfire every time we want to get Arcbond back into our library. But then that would make getting Mirror out of exile dependent on Karn, the Great Creator, probably.
Trove of Temptation is the top layer, getting the mana for the Djinn of Wishes activations we'll need to replay cards from our deck and to properly interweave Mirror of Fate and Worldfire. Every time we activate Mirror of Fate, we need to play Worldfire in response so Mirror shuffles itself back in, but we can keep other spells on the stack and buffer Djinn activations. Sakashima's Will and Necroduality let us turn the creatures we get from computations into other relevant ones, however we cannot freely make usable copies of treasure tokens, Mirror, or Black Lotus through Astral Dragon due to the lack of haste. Our opening hand should include Necroduality, Artificial Evolution, and Primal Surge, so we can hack Necroduality to copy dragons before dumping our deck onto the field, in order to make enough copies of Trove of Temptation. Mirror of Fate can get back Arcbond once between Worldfire casts, but that's fine since we need to play it twice anyway.
Funny enough, Done for the Day seems roughly equivalent. I don't think a stickerboard really fits the spirit of the challenge, and any stickers powerful enough to go matter would go infinite, but it would be possible to slap down random name/art stickers while doing this.
Edit: Some more notes. We can give the opponent access to mana, which would allow them to activate Djinn, but all they'd be able to do is play a land once and potentially give us one use of it. We don't clear our hand, but we need to play all our instants before we can start a computation, which means we'll only be able to put spells on the stack through Djinn. We can exile any kind of card from our library, but that isn't helpful until we've actually used the card.
Though I'm getting a bit lost on what all needs to happen between computations. We need to turn the output of one computation into the input for the next. I gather along the way we cast at least 2 Worldfires to get the 2 Arcbonds active. I can see ways to keep the output numbers through the the Worldfires, but there's just a lot of cards that need to be accounted for.
Edit: Waaaiit. I think we can get up to 3 arcbonds active at the same time: 1 after Worldfire with buffered Djinn activations to rebuild the computation with a Mirror of Fate activation still on the stack. Another 1 after resolving the mirror activation that puts mirror and arcbond back into the library. And then we can play and sacrifice mirror to get arcbond back into the library and play it 1 more time. (Arcbond gets exiled by sanctifiers)
That makes the mirror unrecoverable, but we don't care because we go infinite with 3 arcbonds and the resulting choice vs. protection.
Though I'm getting a bit lost on what all needs to happen between computations. We need to turn the output of one computation into the input for the next. I gather along the way we cast at least 2 Worldfires to get the 2 Arcbonds active. I can see ways to keep the output numbers through the the Worldfires, but there's just a lot of cards that need to be accounted for.
Edit: Waaaiit. I think we can get up to 3 arcbonds active at the same time: 1 after Worldfire with buffered Djinn activations to rebuild the computation with a Mirror of Fate activation still on the stack. Another 1 after resolving the mirror activation that puts mirror and arcbond back into the library. And then we can play and sacrifice mirror to get arcbond back into the library and play it 1 more time. (Arcbond gets exiled by sanctifiers)
That makes the mirror unrecoverable, but we don't care because we go infinite with 3 arcbonds and the resulting choice vs. protection.
Hmm. If we let Mirror of Fate get stuck in exile that way, is there a way to actually turn the output of the resulting computation into damage? Seems like even though we could complete an infinite computation, we'd lose access to Soulblast, which is our only way of causing damage.
My thinking is, we'd take back the tokens with Scrambleverse, use Sakashima's Will to turn them into copies of an animated Necroduality, then replay our key creatures for a large number of Necroduality triggers. Then we'd play Worldfire with those triggers on the stack, to construct a correspondingly large board.
Given the number of cards we need to recur and the fact that Mirror of Fate can only pick up seven at a time, with some cards needing to be recurred multiple times per computation (in particular, Mirror itself and Worldfire), I think we'd need about 4 Worldfire casts per computation.
Ah, so to start a computations we need to cast Soulblast, which puts it into graveyard/exile after the computation. To cast it again we need to resolve a Mirror of Fate activation. So we are allowed to get the illegal computation if it makes mirror unavailable. Similar to the illegal combat damage computations in former 60 card decks. That seems to check out.
Go to end step, let the Troves trigger, and resolve the first for 2^^33 treasures, then sacrifice them all for blue mana. At this point we don't have an animated Necroduality and we can't get one with our current board state, so I think the best thing to do is just to just activate Djinn of Wishes a bunch of times in a row, respond by activating Mirror of Fate, and respond with two more consecutive Djinn activations. The first flips Worldfire, exiling everything we've played so far, and the second flips Sanctifier en-Vec, exiling Worldfire.
We now have 12 cards in exile. Mirror of Fate will put seven of them back, but will also exile everything left in our library - that is, everything that wasn't already exiled. We won't need to get back the three from startup, but I think every loop will require spending four slots to put back Mirror of Fate, Worldfire, Djinn of Wishes, and Sanctifier en-Vec in order to properly set up the next loop. That's a lot of wasted mana, but we can afford it.
I guess a place to start would be to also put back Doubling Season, Necroduality, and Artificial Evolution, then recast those alongside the other four? We'll want to leave the enchantments stuck on the stack, but we can have Evolution target the spell form of Necroduality and then resolve so it gets exiled. Then we do the second Mirror+Worldfire and put back Astral Dragon, Sea Gate Stormcaller, and Artificial Evolution, let the enchantments resolve, play Astral Dragon to copy itself and make a bunch of copies of Doubling Season and finish with a batch of Necroduality, play Stormcaller and hack it so it gets a bunch of Necroduality triggers, resolve the first one to buffer a bunch of Stormcaller ETBs triggers...
This is much more inefficient than I thought, and we'll end up needing way more than 4 Worldfire casts per computation. At least at this point we can start getting multiple uses of Artificial Evolution for each time we cast it, and it's convenient that we can use it to hack spells from different iterations of the board.
...Wait, now I'm trying to remember my logic for getting even two Arcbond casts between Worldfires without getting Mirror of Fate stuck in exile. Does that actually work?
Okay, let's go back through this. We activate Mirror of Fate, then respond by activating Djinn of Wishes four times. The first wish to resolve plays Worldfire, exiling Mirror and everything else, then the next two play Sanctifier en-Vec and some other creature (without protection from red), then the fourth plays Arcbond targeting the other creature. Arcbond and Worldfire both end up exiled by Sanctifier, and Mirror puts them back, ready to play properly during this round.
I guess we don't need to manually put back Djinn and Sanctifier each loop, once we start getting to store Necroduality triggers with them.
At this point the problem is Scrambleverse. In the window between resolving Mirror and Worldfire, we're limited to cards we can play from our library by activating Djinn, since we can't resolve down to earlier Necroduality triggers. But that means we can't properly build our board to send it over to them. So that will have to wait until after we resolve the Mirror activation, which means we won't be able to get Scrambleverse back until after the next Worldfire, so we can't use it to set up Sakashima's Will. So we'll need a different way to collect the output.
Worst case scenario we could add a second Scrambleverse, but 21 cards is frustratingly high already.
Edit: Maybe something involving Sky Swallower + Faerie Artisans? Sky Swallower is trickier to work with though, in particular meaning we can't have the original Doubling Season out.
Speaking of complications, getting the opponent to not die at the start of a computation seems annoying with this setup, since Worldfire puts them at 1 life. Authority of the Consuls can help by putting it on their side of the field and then buffering triggers from it - otherwise, we'd need to buffer Bishop of Wings triggers by using Artificial Evolution to kill damaged creatures.
I think we can fix the problem by replacing Sakashima's Will and Necroduality with Mirrorweave and Dual Nature, so we don't need to take the creatures back before profiting from them. I'd been worried about Mirrorweave being an instant, but Worldfire will make sure our hand is empty, and I don't think there's any way to set up a profitable infinite computation without first casting Worldfire.
Oh, hey, Orcish Medicine is a new card that nicely fits this role. Give lifelink to the Arcbond creature, and indestructible to the Rotlung Reanimators. And it wouldn't be relevant to a Reanimator that returns to our own board from Luminous Broodmoth. So I think that would work out to:
20 cards isn't a huge improvement over 21, but at least it's something.
a Rotlung Reanimator on our side of the board easily goes infinite. There's a minor complication of needing the reanimator to stay alive, but that can be worked around:
- Put the Arcbond on a Zombie. The Reanimator stays alive as long as the computation with that arcbond keeps going.
- Let a heartbeat Cleric die every k ticks. The Reanimator sees that accross the board and creates a zombie
- Let other heartbeat clocks create just enough zombies to keep arcbond alive when the reanimator on our side creates the zombie
- To halt just start resolving arcbond before our reanimator trigger.
Oh, hey, Orcish Medicine is a new card that nicely fits this role. Give lifelink to the Arcbond creature, and indestructible to the Rotlung Reanimators. And it wouldn't be relevant to a Reanimator that returns to our own board from Luminous Broodmoth. So I think that would work out to:
20 cards isn't a huge improvement over 21, but at least it's something.
a Rotlung Reanimator on our side of the board easily goes infinite. There's a minor complication of needing the reanimator to stay alive, but that can be worked around:
- Put the Arcbond on a Zombie. The Reanimator stays alive as long as the computation with that arcbond keeps going.
- Let a heartbeat Cleric die every k ticks. The Reanimator sees that accross the board and creates a zombie
- Let other heartbeat clocks create just enough zombies to keep arcbond alive when the reanimator on our side creates the zombie
- To halt just start resolving arcbond before our reanimator trigger.
Oh, Reanimator reacts to creatures on the opponent's side too? So we can't keep the number of Cleric death triggers finite in that case, that's unfortunate.
We can create heartbeat clocks as long as we don't run out of creature types. Since that doesn't require the use of the very limited basic land types I'll assume that we can go infinite if we have a setup where some creature loses toughness when another creature enters the battlefield.
Situation:
"Halter": 1 creature with types A, H with arcbond. (other H creatures to keep it just barely alive.)
"Buffer": 2 creatures, types C, O. (other O creatures keeping them alive, there to provide CoA buffs.)
hacked LaL, in timestamp order:
1. B <-> Forest
2. A <-> Forest
3. B <-> Mountain
4. C <-> Mountain
No other creatures of base type A, B or C.
That initially gives us only 2 dependency:
- 1 depends on 2, since after 2, 1 will apply to Halter.
- 3 depends on 4, since after 4, 3 will apply to Buffer.
No loop, we apply 2. Halter becomes a Forest.
We get the new list of dependencies:
- 3 depends on 1, since after 1, 3 will apply to Halter.
- 3 depends on 4, since after 4, 3 will apply to Buffer.
No loop, apply 1. Halter becomes a B.
New dependencies:
- 3 depends on 4, since after 4, 3 will apply to Buffer.
- 4 depends on 3, since after 3, 4 will apply to Halter.
Loop! Ignore loop dependencies. Apply 3. Halter becomes a Mountain.
Apply 4. Buffer becomes a Mountain and Halter becomes C.
Halter and Buffer share a type, C, and Halter gets +2/+2 from CoA.
Next create 1 token B, "Disrupt", and apply the effects again:
Initial dependency list:
- 1 depends on 2, since after 2, 1 will apply to Halter.
- 2 depends on 1, since after 1, 2 will apply to Disrupt.
- 3 depends on 4, since after 4, 3 will apply to Buffer.
- 4 depends on 3, since after 3, 4 will apply to Disrupt.
Loop! Ignore loop dependencies. Apply 1. Disrupt becomes a Forest.
Next dependency list:
- 3 depends on 4, since after 4, 3 will apply to Buffer.
- 4 depends on 3, since after 3, 4 will apply to Disrupt.
Loop! Ignore loop dependencies. Apply 2. Disrupt becomes A. Halter becomes a Forest.
Next dependency list:
- 3 depends on 4, since after 4, 3 will apply to Buffer.
- 4 depends on 3, since after 3, 4 will apply to Disrupt.
Loop! Ignore loop dependencies. Apply 3. Disrupt becomes a Mountain.
Apply 4. Disrupt becomes C. Buffer becomes a Mountain.
Halter shares a creature type, A, with Disrupt, so it gets +1/+1 from CoA. Halter doesn't share any creature type with Buffer.
After Disrupt was created Halter went from +2/+2 to +1/+1. That's a loss of toughness, which can lead to dying, which can lead to halting. After an infinitely repeatable choice to create a B or H token first.
So dependency loops only look forward one 'step' of effects at a time?
That's even worse than the way I just thought it worked! (which was look forward through all of them and if a loop is found, break it by going in timestamp order)
I think this means that even a hypothetical DC without the +1/+1 part still has these problems, just from coat of arms!
Edit: and yes any creature decreasing in toughness from another being created is sufficient for there to be an infinite.
So dependency loops only look forward one 'step' of effects at a time?
That's even worse than the way I just thought it worked! (which was look forward through all of them and if a loop is found, break it by going in timestamp order)
Yeah, I'd been imagining that as well, but:
613.8. Within a layer or sublayer, determining which order effects are applied in is sometimes done
using a dependency system. If a dependency exists, it will override the timestamp system.
613.8a An effect is said to “depend on” another if (a) it’s applied in the same layer (and, if
applicable, sublayer) as the other effect; (b) applying the other would change the text or the
existence of the first effect, what it applies to, or what it does to any of the things it applies to;
and (c) neither effect is from a characteristic-defining ability or both effects are from
characteristic-defining abilities. Otherwise, the effect is considered to be independent of the
other effect.
613.8b An effect dependent on one or more other effects waits to apply until just after all of those
effects have been applied. If multiple dependent effects would apply simultaneously in this way,
they’re applied in timestamp order relative to each other. If several dependent effects form a
dependency loop, then this rule is ignored and the effects in the dependency loop are applied in
timestamp order.
613.8c After each effect is applied, the order of remaining effects is reevaluated and may change if
an effect that has not yet been applied becomes dependent on or independent of one or more
other effects that have not yet been applied.
For 8 cards, the latest write-up specifies "stacking the triggers to delay the ones that would turn larger Shapeshifter-Golems into smaller ones", but that doesn't work: pretty soon, one is forced to resolve those triggers in order to get to Inverter of Truth reshuffle triggers deeper in the stack.
The correct approach is the opposite: it is the high-value Shapeshifter triggers that should be left on the stack until they are ready to be used. However, it turns out to be more tricky than I previously imagined it would be.
When having a high-power Shapeshifter-Golem to break down, first cast Saw in Half on a Shapeshifter-Inverter. Place the resulting Inverter reshuffle triggers above the Shapeshifter-changing triggers. Resolve one, getting back the Saw in Half, and cast it on the high-power Shapeshifter-Golem. This produces a bunch more Shapeshifter-changing triggers; let them resolve, turning all the Shapeshifters into the halved-power Shapeshifter-Golem, and then resolve the second Inverter reshuffle trigger to get back the Saw in Half. Now here's the critical part: make sure that the next Shapeshifter-Golem to be Sawed is one of the tokens produced from Sawing that first Shapeshifter-Inverter – there are triggers still on the stack to change Shapeshifters into this creature, and Sawing it locks in its last-known information as the halved-power Shapeshifter-Golem.
(If there is no Shapeshifter-Inverter to begin with, we can get one by Sawing a plain Inverter token, and resolving one Inverter reshuffle trigger and one Shapeshifter-changing trigger; we can afford the extra 3 life at this stage.)
For 8 cards, the latest write-up specifies "stacking the triggers to delay the ones that would turn larger Shapeshifter-Golems into smaller ones", but that doesn't work: pretty soon, one is forced to resolve those triggers in order to get to Inverter of Truth reshuffle triggers deeper in the stack.
The correct approach is the opposite: it is the high-value Shapeshifter triggers that should be left on the stack until they are ready to be used. However, it turns out to be more tricky than I previously imagined it would be.
When having a high-power Shapeshifter-Golem to break down, first cast Saw in Half on a Shapeshifter-Inverter. Place the resulting Inverter reshuffle triggers above the Shapeshifter-changing triggers. Resolve one, getting back the Saw in Half, and cast it on the high-power Shapeshifter-Golem. This produces a bunch more Shapeshifter-changing triggers; let them resolve, turning all the Shapeshifters into the halved-power Shapeshifter-Golem, and then resolve the second Inverter reshuffle trigger to get back the Saw in Half. Now here's the critical part: make sure that the next Shapeshifter-Golem to be Sawed is one of the tokens produced from Sawing that first Shapeshifter-Inverter – there are triggers still on the stack to change Shapeshifters into this creature, and Sawing it locks in its last-known information as the halved-power Shapeshifter-Golem.
(If there is no Shapeshifter-Inverter to begin with, we can get one by Sawing a plain Inverter token, and resolving one Inverter reshuffle trigger and one Shapeshifter-changing trigger; we can afford the extra 3 life at this stage.)
Thanks for the catch!
I haven't been working on these writeups as much lately, it's felt weird having the Busy Beaver decks now so much further from the really small ones. Maybe I'll do a writeup focused specifically on up to like 8 cards for now, then do small Busy Beaver as a separate thing. (Doesn't help that the main place I was planning on posting it was Reddit, which is currently exploding.)
Could also go up to 10 cards to demonstrate multiple stages, although that would make me want to go back to trying to find a way to improve the 9-card record to F{w+2}.
Just popping in to point out that since flooding clocks are turing complete now, we can go back to the old small BB decks and make them actually work by removing Dralnu's crusade.
Just popping in to point out that since flooding clocks are turing complete now, we can go back to the old small BB decks and make them actually work by removing Dralnu's crusade.
To elaborate, my concern with the current 13-card proposal is that for 14-card, we were using Iijil's method here to run a mini-computation that outputs 2^^^^24, getting us to BB^(2^^^^24)(15) damage. But that method used four copies of Dralnu's Crusade, so now the question becomes how high we can get that number without it, and if that number is high enough to constitute a proper UTM. The four Dralnu's Crusades together cost 16 Swaps, so we can spend those on Bishops instead for a total of about 41 Bishops, but how much can we do with that?
Yeah getting a good estimate of that deck is difficult.
The general conversion from waterfall to flooding waterfall is notably worse than say squaring, so we aren't anywhere close to converting even a small waterfall program into flooding for the first computation. For that we'd need to find a halting flooding program using those audacious swaps as efficiently as possible, however, even fairly small flooding programs tend to explode. I think there was a simple pattern of n clocks that computed 2^n? so we can at least escape into proper BB numbers once we get going. We can definitely do better than that though.
I tried shoving the 15 state, 2 symbol universal turing machine by T. Neary and D. Woods into my TM to Waterfall compiler and the resulting waterfall program into Ais523s compiler to get a universal flooding program. The result ends up using 296 clocks and about 14 million bishops.
We need 1 creature type per clock, so this construction barely doesn't fit. We currently have 287 types. So close!
Further, if I remember the start correctly, we were only able to get to ~1.6 million bishops without using Dralnu for the bootstrap program. Although it's quite possible that this is improvable that currently also leaves us short of the 14 million bishops we need.
That leaves us in an uncomfortable position. The universal program mentioned above is certainly not optimal. I'd say it is virtually certain that there is some more efficient universal program within the reach of the 13 card deck. But we don't quite know that. We need to improve one of the compilation steps or find some other way to get a universal flooding waterfall computation.
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Worldfire, a second Arcbond, either Riftsweeper or Mirror of Fate, a way to get the cards back to hand afterward, a way to maintain the previous computation's output through the Worldfire... Seems like it would probably take around 20 cards, I guess? Given those should include ways to replace some of the cards from the 17-card deck.
Mana Echoes might work well, and could get along with Izzet Guildmage. It's annoying that Twinflame is the only simple copy spell that's cheap enough to work, given that it conflicts with Soulblast, but Double Major could work.
Edit: Mana Echoes + Guildmage + Twinflame would go infinite anyway.
Edit: Same problem with Double Major.
For a top layer, Fight Rigging might be helpful.
Edit: Wait, we don't need Mana Echoes. Authority of the Consuls can give plenty of life from opponent's creatures entering and Channel can turn it into mana, and both of those fit into existing deck slots.
But the bigger problem is Sanctifier en-Vec making exile easy, I forgot to account for that. Like in the other thread, we need Worldfire to be helping us recur a key colorless card - and it needs to be something we have to do each time we want to replay Arcbond.
Maybe Mirror of Fate? If we can't get usable copies of it, we could force ourselves to exile it with Worldfire every time we want to get Arcbond back into our library. But then that would make getting Mirror out of exile dependent on Karn, the Great Creator, probably.
2 Show and Tell
3 Omniscience
4 Primal Surge
5 Djinn of Wishes
6 Doubling Season
7 Astral Dragon
8 Sea Gate Stormcaller
9 Sakashima's Will
10 Necroduality
11 Mirror of Fate
12 Worldfire
13 Trove of Temptation
14 Bishop of Wings
15 Artificial Evolution
16 Sanctifier en-Vec
17 Trait Doctoring
18 Arcbond
19 Authority of the Consuls
20 Scrambleverse
21 Soulblast
Trove of Temptation is the top layer, getting the mana for the Djinn of Wishes activations we'll need to replay cards from our deck and to properly interweave Mirror of Fate and Worldfire. Every time we activate Mirror of Fate, we need to play Worldfire in response so Mirror shuffles itself back in, but we can keep other spells on the stack and buffer Djinn activations. Sakashima's Will and Necroduality let us turn the creatures we get from computations into other relevant ones, however we cannot freely make usable copies of treasure tokens, Mirror, or Black Lotus through Astral Dragon due to the lack of haste. Our opening hand should include Necroduality, Artificial Evolution, and Primal Surge, so we can hack Necroduality to copy dragons before dumping our deck onto the field, in order to make enough copies of Trove of Temptation. Mirror of Fate can get back Arcbond once between Worldfire casts, but that's fine since we need to play it twice anyway.
Funny enough, Done for the Day seems roughly equivalent. I don't think a stickerboard really fits the spirit of the challenge, and any stickers powerful enough to go matter would go infinite, but it would be possible to slap down random name/art stickers while doing this.
Edit: Some more notes. We can give the opponent access to mana, which would allow them to activate Djinn, but all they'd be able to do is play a land once and potentially give us one use of it. We don't clear our hand, but we need to play all our instants before we can start a computation, which means we'll only be able to put spells on the stack through Djinn. We can exile any kind of card from our library, but that isn't helpful until we've actually used the card.
Though I'm getting a bit lost on what all needs to happen between computations. We need to turn the output of one computation into the input for the next. I gather along the way we cast at least 2 Worldfires to get the 2 Arcbonds active. I can see ways to keep the output numbers through the the Worldfires, but there's just a lot of cards that need to be accounted for.
Edit: Waaaiit. I think we can get up to 3 arcbonds active at the same time: 1 after Worldfire with buffered Djinn activations to rebuild the computation with a Mirror of Fate activation still on the stack. Another 1 after resolving the mirror activation that puts mirror and arcbond back into the library. And then we can play and sacrifice mirror to get arcbond back into the library and play it 1 more time. (Arcbond gets exiled by sanctifiers)
That makes the mirror unrecoverable, but we don't care because we go infinite with 3 arcbonds and the resulting choice vs. protection.
My thinking is, we'd take back the tokens with Scrambleverse, use Sakashima's Will to turn them into copies of an animated Necroduality, then replay our key creatures for a large number of Necroduality triggers. Then we'd play Worldfire with those triggers on the stack, to construct a correspondingly large board.
Given the number of cards we need to recur and the fact that Mirror of Fate can only pick up seven at a time, with some cards needing to be recurred multiple times per computation (in particular, Mirror itself and Worldfire), I think we'd need about 4 Worldfire casts per computation.
Play Black Lotus, Show and Tell, Omniscience, Necroduality, Artificial Evolution hacking Zombie>Dragon, and Primal Surge. Flip Doubling Season, Trove of Temptation, Mirror of Fate, and Astral Dragon, then exile something else and leave it in exile. Get a Necroduality trigger and an Astral Dragon trigger targeting Doubling Season, and resolve the latter first to make four more copies of Doubling Season, then make 32 Astral Dragons. Have the first 31 target Doubling Season, reaching 2^^33, and use the last to make 2^^33 copies of Trove. Then play Djinn of Wishes as the last card from our hand so it enters with 2^^33 wish counters.
Go to end step, let the Troves trigger, and resolve the first for 2^^33 treasures, then sacrifice them all for blue mana. At this point we don't have an animated Necroduality and we can't get one with our current board state, so I think the best thing to do is just to just activate Djinn of Wishes a bunch of times in a row, respond by activating Mirror of Fate, and respond with two more consecutive Djinn activations. The first flips Worldfire, exiling everything we've played so far, and the second flips Sanctifier en-Vec, exiling Worldfire.
We now have 12 cards in exile. Mirror of Fate will put seven of them back, but will also exile everything left in our library - that is, everything that wasn't already exiled. We won't need to get back the three from startup, but I think every loop will require spending four slots to put back Mirror of Fate, Worldfire, Djinn of Wishes, and Sanctifier en-Vec in order to properly set up the next loop. That's a lot of wasted mana, but we can afford it.
I guess a place to start would be to also put back Doubling Season, Necroduality, and Artificial Evolution, then recast those alongside the other four? We'll want to leave the enchantments stuck on the stack, but we can have Evolution target the spell form of Necroduality and then resolve so it gets exiled. Then we do the second Mirror+Worldfire and put back Astral Dragon, Sea Gate Stormcaller, and Artificial Evolution, let the enchantments resolve, play Astral Dragon to copy itself and make a bunch of copies of Doubling Season and finish with a batch of Necroduality, play Stormcaller and hack it so it gets a bunch of Necroduality triggers, resolve the first one to buffer a bunch of Stormcaller ETBs triggers...
This is much more inefficient than I thought, and we'll end up needing way more than 4 Worldfire casts per computation. At least at this point we can start getting multiple uses of Artificial Evolution for each time we cast it, and it's convenient that we can use it to hack spells from different iterations of the board.
...Wait, now I'm trying to remember my logic for getting even two Arcbond casts between Worldfires without getting Mirror of Fate stuck in exile. Does that actually work?
I guess we don't need to manually put back Djinn and Sanctifier each loop, once we start getting to store Necroduality triggers with them.
At this point the problem is Scrambleverse. In the window between resolving Mirror and Worldfire, we're limited to cards we can play from our library by activating Djinn, since we can't resolve down to earlier Necroduality triggers. But that means we can't properly build our board to send it over to them. So that will have to wait until after we resolve the Mirror activation, which means we won't be able to get Scrambleverse back until after the next Worldfire, so we can't use it to set up Sakashima's Will. So we'll need a different way to collect the output.
Worst case scenario we could add a second Scrambleverse, but 21 cards is frustratingly high already.
Edit: Maybe something involving Sky Swallower + Faerie Artisans? Sky Swallower is trickier to work with though, in particular meaning we can't have the original Doubling Season out.
Speaking of complications, getting the opponent to not die at the start of a computation seems annoying with this setup, since Worldfire puts them at 1 life. Authority of the Consuls can help by putting it on their side of the field and then buffering triggers from it - otherwise, we'd need to buffer Bishop of Wings triggers by using Artificial Evolution to kill damaged creatures.
Thinking more about Necroduality, Dual Nature might just be better.
- Put the Arcbond on a Zombie. The Reanimator stays alive as long as the computation with that arcbond keeps going.
- Let a heartbeat Cleric die every k ticks. The Reanimator sees that accross the board and creates a zombie
- Let other heartbeat clocks create just enough zombies to keep arcbond alive when the reanimator on our side creates the zombie
- To halt just start resolving arcbond before our reanimator trigger.
2 Channel
3 Vessel of Endless Rest
4 Precursor Golem
5 Replication Technique
6 Audacious Swap
7 Possibility Storm
8 Coat of Arms
9 Bishop of Wings
10 Artificial Evolution
11 Life and Limb
12 Trait Doctoring
13 Treacherous Pit-Dweller
14 Solemnity
15 Golgari Germination
16 Arcbond
17 Comeuppance
18 Scrambleverse
19 Soulblast
Life and Limb provides five clocks, Treacherous Pit-Dweller + Golgari Germination provides the sixth.
We can create heartbeat clocks as long as we don't run out of creature types. Since that doesn't require the use of the very limited basic land types I'll assume that we can go infinite if we have a setup where some creature loses toughness when another creature enters the battlefield.
Situation:
"Halter": 1 creature with types A, H with arcbond. (other H creatures to keep it just barely alive.)
"Buffer": 2 creatures, types C, O. (other O creatures keeping them alive, there to provide CoA buffs.)
hacked LaL, in timestamp order:
1. B <-> Forest
2. A <-> Forest
3. B <-> Mountain
4. C <-> Mountain
No other creatures of base type A, B or C.
That initially gives us only 2 dependency:
- 1 depends on 2, since after 2, 1 will apply to Halter.
- 3 depends on 4, since after 4, 3 will apply to Buffer.
No loop, we apply 2. Halter becomes a Forest.
We get the new list of dependencies:
- 3 depends on 1, since after 1, 3 will apply to Halter.
- 3 depends on 4, since after 4, 3 will apply to Buffer.
No loop, apply 1. Halter becomes a B.
New dependencies:
- 3 depends on 4, since after 4, 3 will apply to Buffer.
- 4 depends on 3, since after 3, 4 will apply to Halter.
Loop! Ignore loop dependencies. Apply 3. Halter becomes a Mountain.
Apply 4. Buffer becomes a Mountain and Halter becomes C.
Halter and Buffer share a type, C, and Halter gets +2/+2 from CoA.
Next create 1 token B, "Disrupt", and apply the effects again:
Initial dependency list:
- 1 depends on 2, since after 2, 1 will apply to Halter.
- 2 depends on 1, since after 1, 2 will apply to Disrupt.
- 3 depends on 4, since after 4, 3 will apply to Buffer.
- 4 depends on 3, since after 3, 4 will apply to Disrupt.
Loop! Ignore loop dependencies. Apply 1. Disrupt becomes a Forest.
Next dependency list:
- 3 depends on 4, since after 4, 3 will apply to Buffer.
- 4 depends on 3, since after 3, 4 will apply to Disrupt.
Loop! Ignore loop dependencies. Apply 2. Disrupt becomes A. Halter becomes a Forest.
Next dependency list:
- 3 depends on 4, since after 4, 3 will apply to Buffer.
- 4 depends on 3, since after 3, 4 will apply to Disrupt.
Loop! Ignore loop dependencies. Apply 3. Disrupt becomes a Mountain.
Apply 4. Disrupt becomes C. Buffer becomes a Mountain.
Halter shares a creature type, A, with Disrupt, so it gets +1/+1 from CoA. Halter doesn't share any creature type with Buffer.
After Disrupt was created Halter went from +2/+2 to +1/+1. That's a loss of toughness, which can lead to dying, which can lead to halting. After an infinitely repeatable choice to create a B or H token first.
That's even worse than the way I just thought it worked! (which was look forward through all of them and if a loop is found, break it by going in timestamp order)
I think this means that even a hypothetical DC without the +1/+1 part still has these problems, just from coat of arms!
Edit: and yes any creature decreasing in toughness from another being created is sufficient for there to be an infinite.
The correct approach is the opposite: it is the high-value Shapeshifter triggers that should be left on the stack until they are ready to be used. However, it turns out to be more tricky than I previously imagined it would be.
When having a high-power Shapeshifter-Golem to break down, first cast Saw in Half on a Shapeshifter-Inverter. Place the resulting Inverter reshuffle triggers above the Shapeshifter-changing triggers. Resolve one, getting back the Saw in Half, and cast it on the high-power Shapeshifter-Golem. This produces a bunch more Shapeshifter-changing triggers; let them resolve, turning all the Shapeshifters into the halved-power Shapeshifter-Golem, and then resolve the second Inverter reshuffle trigger to get back the Saw in Half. Now here's the critical part: make sure that the next Shapeshifter-Golem to be Sawed is one of the tokens produced from Sawing that first Shapeshifter-Inverter – there are triggers still on the stack to change Shapeshifters into this creature, and Sawing it locks in its last-known information as the halved-power Shapeshifter-Golem.
(If there is no Shapeshifter-Inverter to begin with, we can get one by Sawing a plain Inverter token, and resolving one Inverter reshuffle trigger and one Shapeshifter-changing trigger; we can afford the extra 3 life at this stage.)
I haven't been working on these writeups as much lately, it's felt weird having the Busy Beaver decks now so much further from the really small ones. Maybe I'll do a writeup focused specifically on up to like 8 cards for now, then do small Busy Beaver as a separate thing. (Doesn't help that the main place I was planning on posting it was Reddit, which is currently exploding.)
Could also go up to 10 cards to demonstrate multiple stages, although that would make me want to go back to trying to find a way to improve the 9-card record to F{w+2}.
So we have something like this for 13 cards:
2 Channel
3 Vessel of Endless Rest
4 Precursor Golem
5 Replication Technique
6 Audacious Swap
7 Scrambleverse
9 Bishop of Wings
10 Artificial Evolution
11 Arcbond
12 Comeuppance
13 Soulblast
The general conversion from waterfall to flooding waterfall is notably worse than say squaring, so we aren't anywhere close to converting even a small waterfall program into flooding for the first computation. For that we'd need to find a halting flooding program using those audacious swaps as efficiently as possible, however, even fairly small flooding programs tend to explode. I think there was a simple pattern of n clocks that computed 2^n? so we can at least escape into proper BB numbers once we get going. We can definitely do better than that though.
We need 1 creature type per clock, so this construction barely doesn't fit. We currently have 287 types. So close!
Further, if I remember the start correctly, we were only able to get to ~1.6 million bishops without using Dralnu for the bootstrap program. Although it's quite possible that this is improvable that currently also leaves us short of the 14 million bishops we need.
That leaves us in an uncomfortable position. The universal program mentioned above is certainly not optimal. I'd say it is virtually certain that there is some more efficient universal program within the reach of the 13 card deck. But we don't quite know that.