While chaining computations might yield a good result, we can't really tell unless we can implement all machines up to a certain size, so that we know it implements the Busy Beaver up to that size. As FortyTwo noted, we only need one copy of Artificial Evolution or True Polymorph to re-setup the computation, but without it we don't really know what we are getting.
The exception might be for small machines that we can follow explicitly, and see what the output is.
Hmm, that potentially works,though we dont have an extra card in hand to set everything up after the last timetwister and still have an issue with fizzling the output->input zubera trigger.
Edit: Its only one Artificial Evolution or True Polymorph or large Zubera trigger. and we can set up a small one to retrigger computation again
The issue is with targeting as we only have the creatures the opponent has at the time that we sac our board to kaervek's spite as legal targets, and a lot of those die, so we cant target an arbitrary output creature, we have to premake them and target what we want the next input to be in the range of something like BB(x) to BB(x)+10^48 and hope that there's an efficient machine in that range.
hmmm yeah, this is getting complicated to estimate. I don't think there's a good reason to expect that the most productive output from a range of 10^48 inputs should be much larger than BB(10^48).
I got about 3.6*10^70 tokens for the 15-card deck by casting Benevolent Offering about halfway through each Storm King's Thunder stack for most of the Timetwisters (to save the others to copy the next Thunder), although I imagine things don't change much either way.
On the draw, we could add Artificial Evolution to our opening hand to have Bishop gain life from the first Spirits and copy Timetwister 17 times, but that's not ideal.
Yeah - I *think* 10^70 tokens should easily beat 4 stages, but we need to do some Waterfall programming to be sure.
Oh, interesting. What seems to be the threshold?
I redid the math, switching to having Benevolent Offering get 2/3 of the copies - I think about 2/3 is optimal since 2/3 is where the derivative of (1-x)*x^2 is 0. I got 4.5*10^69 tokens this time, think I misplaced a digit last time.
Draw #2: Thunder at X=2. Resolve the two copies, with the original on the stack play Offering, copied 4 times. First resolves (20 mana), play Artificial Evolution to set Bishop to Spirits. Mana goes 19 + 26+12 + 32+12 + 38+12 + 44+12 = 207.
Draw #3: Thunder at X=200. Resolve the two copies, with the original on the stack play Offering, copied 400 times. After the first resolves, play True Polymorph and Artificial Evolution to make a second Bishop set to Spirits. Mana goes 55 + (70+2448)*200 = 503,655.
Draw #4: Thunder at X=503,648. Resolve 134 copies, with the rest on the stack play Offering, copied 67,488,832 times. Mana goes to about 4.55*10^15.
Draw #5: Thunder at X=4.55*10^15, copied 67*503,648 times. Resolve 2/3 of them, play Offering, copied 10^23 times. Mana goes to about 3*10^46.
Draw #6: Thunder at X=3*10^46, copied 5*10^22 times. Resolve all the copies, play Offering, copied 1.5*10^69 times.
Oh, I don't know specifics - but the machines I posted earlier cost like 9 tokens per Knuth arrow. Stages should be more, but not *that* much more. That's all I was thinking.
Oh, I don't know specifics - but the machines I posted earlier cost like 9 tokens per Knuth arrow. Stages should be more, but not *that* much more. That's all I was thinking.
Draw #2: Offering, total 8 times. Mana goes 19+38+44+50+56+62+68+74 = 411. Thunder at X=200.
Draw #3: Thunder at X=201, copied 200 times. Let 134 Thunders resolve, play Offering, copied 26,934 times. Get about 2.17*10^9 mana.
Draw #4: Thunder at X=2.17*10^9, copied 67*201 times. Let 8,978 Thunders resolve, play Offering, copied 1.94*10^13 times. Get about 1.13*10^27 mana.
Draw #5: Thunder at X=1.13*10^27, copied 4489*2.17*10^9 (=9.74*10^12) times. Let 6.49*10^12 Thunders resolve, play Offering, copied 7.33*10^39 times. Get about 1.61*10^80 mana.
Draw #6: Thunder at X=1.61*10^80, copied 3.24*10^13 times. Let all but the original resolve, play Offering, copied 5.22*10^92 times. End up with 1.56*10^93 tokens.
Draw #7: Finish.
Edit: I think we can use a similar approach for the 16-card deck, although in this case the lifegain doesn't scale during the initial rounds.
Oh, of course Storm God's Thunder can copy itself! I think that lets us be even more efficient than your line, as we can use just two of the copies from each iteration to polymorph and then AE all of the new spirits to bishops that will then gain life for spirits.
Hmm I found a possible infinite....
If after the computation we had a waiting copy of arcbond and below that, a storm god's thunder trigger for Polymorph. we could then set up another arcbond, and then polymorph the spirits we made from saccing our board into bishops. so that when we polymorph to kill an ember fist zubera, we start a computation with bishops on our side, and can potentially mess with computation.
This would require never drawing dralnu's crusade though and just using flooding clocks?
Edit: this can be avoided by a sorcery speed board wipe like Desolation giant, Edit2: hmm no then we keep our hand and can AE computation to mess it up.
Oh, of course Storm God's Thunder can copy itself! I think that lets us be even more efficient than your line, as we can use just two of the copies from each iteration to polymorph and then AE all of the new spirits to bishops that will then gain life for spirits.
Hmm I found a possible infinite....
If after the computation we had a waiting copy of arcbond and below that, a storm god's thunder trigger for Polymorph. we could then set up another arcbond, and then polymorph the spirits we made from saccing our board into bishops. so that when we polymorph to kill an ember fist zubera, we start a computation with bishops on our side, and can potentially mess with computation.
This would require never drawing dralnu's crusade though and just using flooding clocks?
Edit: this can be avoided by a sorcery speed board wipe like Desolation giant, Edit2: hmm no then we keep our hand and can AE computation to mess it up.
Oh, hmm. I think to nest Storm God's Thunder triggers like that, we'd have to first play our permanents, then play True Polymorph to get the copy triggers from the previous draw, then respond by playing Thunder and Arcbond to get a new copy trigger, which we'd then respond to with Kaervek's Spite. That would mean no chance to copy Thunder>Thunder on the last draw and therefore no copy triggers free for Artificial Evolution, so we'd have to set up most of the computation on the previous draw. That would mean having a card slot available for Dralnu's Crusade (and to Polymorph things into more copies of it), but not having the chance to play Evolution on it.
Would we be able to go infinite from there? The Bishops on our side of the field would be copied without text changes, so we'd have limited opportunities to get more tokens and life, and Comeuppance wouldn't protect us from damage from Arcbonds on our own creatures.
Hmm, I imagine just getting life through Angels is enough if we set things up so that they show up a lot. We've been contemplating whether we need Dralnu's Crusade to get Turing-completeness, so while we don't know whether or not we can run an infinite computation with just one version of Dralnu's Crusade, it seems reasonably likely.
Hmm, I imagine just getting life through Angels is enough if we set things up so that they show up a lot. We've been contemplating whether we need Dralnu's Crusade to get Turing-completeness, so while we don't know whether or not we can run an infinite computation with just one version of Dralnu's Crusade, it seems reasonably likely.
How would they show up a lot? We can start with angel tokens, but we wouldn't be able to make more on our own side of the field, so we'd run out eventually. Is there a way to run an infinite computation in this way without doing infinite damage to ourselves in the process?
Oh you're right, with defaults we won't get Angels. I think you're right then, we can't go infinite without Comeuppance preventing damage or Angels coming into play on our side.
why would we need to arcbond our own creature? the opponent still has a ton of stuff.
But yeah needing our bishops to be default I think saves us from problems as our side of the computation is pretty trivial and we can only interfere when our angels die, and we don't have an arbitrary amount of those.
So I guess this means the 14 card version without dralnu's crusade probably wins at that size?
why would we need to arcbond our own creature? the opponent still has a ton of stuff.
But yeah needing our bishops to be default I think saves us from problems as our side of the computation is pretty trivial and we can only interfere when our angels die, and we don't have an arbitrary amount of those.
So I guess this means the 14 card version without dralnu's crusade probably wins at that size?
Ah, I had thought putting Arcbond on our own creatures was the plan for messing with the computation.
What would be different about the non-Dralnu's version?
On a different note, I've been keeping an eye on new Unfinity cards to see if other cards join Saw in Half in being useful here, and one that's caught my attention is Starlight Spectacular. Giving a non-targeted scaling boost at the start of combat is something I'd been looking for while working on some versions of the Saw deck, since it avoids needing to make a bunch of tokens of the highest stage creature ahead of time. Making all the boosts be different amounts is also an interesting detail, although I'm not sure what uses it could have.
What arcbond is on doesn't matter as we always control that trigger. However arcbond and Bishop of wings trigger at the same time, but because they are all on the opponent's side APNAP means our arcbond trigger is always below all of their Bishop triggers. If we have a bishop though then we can stack its trigger above arcbond like all of our opponent's or below arcbond where it essentially never happens as arcbond triggers again before it resolves, giving us agency in the computation.
the pure flooding version with 14 cards would use this as a way to set up a flooding waterfall machine, and then run another that we can even interrupt once (all of our angels die at the same time)
I'm not sure how efficient a flooding clock machine can be, but they do seem to grow very quickly.
Remember that, because of how layers interact, it doesn't matter what order we play AE and Polymorph in. We can cast AE on a bunch of spirit tokens, and change "goblin to wizard". Then when that token gets polymorphed later into a Dralnu's Crusade, it will have goblin changed to wizard. So we *can* set up full computations including DC from the previous draw, before having to play DC. And if we can start a computation with (unhacked) bishops on our side in that case, that *does* go infinite; as then there can be a DC saying "all spirits our angels", giving us agency arbitrarily far into the computation.
Remember that, because of how layers interact, it doesn't matter what order we play AE and Polymorph in. We can cast AE on a bunch of spirit tokens, and change "goblin to wizard". Then when that token gets polymorphed later into a Dralnu's Crusade, it will have goblin changed to wizard. So we *can* set up full computations including DC from the previous draw, before having to play DC. And if we can start a computation with (unhacked) bishops on our side in that case, that *does* go infinite; as then there can be a DC saying "all spirits our angels", giving us agency arbitrarily far into the computation.
All of our tokens are fresh from kaervek's spite though, so they cant have AE on them.
We don't need AE on our own tokens - the idea is that we take a token on the opponent's side, hack it to Goblin>Spirit and Zombie>Angel, then turn it into a DC. DC is global, so our unmodified Bishops will make Angel Spirit tokens.
ah I see so the penultimate draw is setup with AE and copied thunders then for the last one we draw:
1 dc
2 zubera
3 coat of arms
4 polymorph
5 thunder
6 arcbond
7 spite
play the permanents, cast polymorph, get a bunch of thunder triggers, use most of them to set up computation. cast a small thunder to copy arcbond
let the first arcbond resolve, and then cast spite to start computation.
after computation the original arcbond resolves, still targeting one of the opponent's creatures.
then we resolve the thunder trigger for polymorph, giving us default bishops and killing a zubera to trigger computation again.
we can now interfere with the computation many times due to the preset DC making spirts angels.
And then in the end the opponent suicides with a zubera trigger.
When the original resolves, play Ember-Fist Zubera and Coat of Arms, then play Fractured Identity. Use the first TYS trigger to pass Bishop/Crusade/Zubera/Coat to the opponent, then the second to take them back as tokens. Before the others resolve, play Second Harvest to scale up our tokens, then let the other Fractured Identity copies resolve to pass as many of those tokens back to the opponent as possible. Then play Artificial Evolution and Arcbond to finish programming the board, and finish with Kaervek's Spite.
Edit: Wait, does this one also let us reconstruct our board afterward by keeping copy triggers waiting to use after the computation? Zubera is such a hassle.
Hmm. Given that this requires using AE on the last round, could we fix the issue by going back to Soulblast? If there's a way to keep it from killing the opponent. (Maybe burning some copies on tokens to trigger their Bishops?)
Edit: With Soulblast + Phthisis, we could use some of our Fractured Identity copies to eliminate most of our TYS clones, so that when we play Second Harvest the final time, the number of Bishop of Wings tokens we end up with is close to the number of Identity copies we have left, to make sure the number of Bishop tokens sacrificed to Soulblast stays reasonable.
This doesn't hit as much damage as its previous version, but here's an alternate take on the 14-card four-stage deck without the Lich's Mirror infinite mana trick.
Astral Dragon making four Purses, Bloodthorn Taunter, Scale the Heights giving two +1/+1 counters to an animated Purse and drawing a card. Tap Taunter to activate the Purse. 12 treasures, 5 colorless.
Play Saw in Half to make four Astral Dragon tokens. The first three target Doubling Season (1>5>69>2^70), the last makes 2^2^70 Mirari Conjectures. Conjectures immediately complete, making that many copy triggers and getting back Scale and Saw. Replay Saw two more times, each time getting copied by the previous Conjectures, which I think gets us to 2^^^^4. Have the last Saw instance target Taunter, use one to activate the Purse boosted last time, and use the resulting Treasures to go to 2^^^^2^^^^4. Then replay Scale to boost another Purse token. Conjecture will copy it, but we can have all the copies target the same purse, then play Saw on it after the first one resolves so we only draw one card.
Play Hornbash Mentor, then run a single stage using the Purse tokens to get to F{w}(2^^^^2^^^^4). Replay Scale, boosting Hornbash this time, again making sure it only happens once.
Play Scattershot Archer and run a double stage using Hornbash Mentor. Then draw and play Rite of Passage, boosting Hornbash again, but this time using it for a triple stage. Draw and play Frillscare Mentor, run another triple stage, then draw and play Might Weaver to run a single instance of a quadruple stage.
I think this gets us to F{w4}(F{w3}(F{w3}(F{w2}(F{w}(2^^^^2^^^^4))))). Not sure if there's a better way to write that.
As for the other multistage decks, 11-card and 13-card have less need for Lich's Mirror since they can use Fight Rigging and Finest Hour to still hit two layers on top of their stage count. 10-card can enter combat with five Fight Riggings and one Wingspan Mentor to run a single instance of a double stage. 12-card would probably just want to copy this up to the first instance of the triple stage.
Speaking of versions with and without infinite mana, I think the 9-card deck could get slightly higher numbers with Lich's Mirror, since that would mean not having to spend Temur Ascendancy triggers on getting to its last two cards.
12-card: Start with the Lotus/Channel/Mirror loop, then play Doubling Season, Codex Shredder, Astral Dragon making four Seasons, Saw in Half making 64 dragons for a bunch of Doubling Seasons and Codex Shredders, Hornbash Mentor, Rite of Passage, and then Winter Sky to put +1/+1 counters on everything. Sacrifice the original Shredder to get back Winter Sky and use it to draw Bloodthorn Taunter, use it to give haste to another Shredder to get back Saw for more Taunters. Play through the Shredder stage, then use Winter Sky to draw Scattershot Archer (and cast Saw on it) before activating Hornbash Mentor.
Once that all finishes, use Winter Sky for damage 18 more times, since that's the most the life totals will allow. Each time, get Rite of Passage triggers for all the creatures. 13-card version adds Bellowing Aegisaur for an additional layer.
Saw in Half on Astral Dragon. First three dragons make Doubling Seasons, fourth makes Conjectures, get back Wisps and Saw. Replay Saw, initially targeting dragons but using the last on Hornbash Mentor, placing trample counters as necessary. Play Wisps on three Mentors to draw the remaining cards, giving them haste and turning them red. Point the extra copies at an Astral Dragon, replay Saw on the dragon in response to counter the extras. 8 treasures.
At this point we can activate one of the hasted Hornbash Mentors to give +1/+1 counters to a wave of Purse tokens. Play Bloodthorn Taunter, give the Purse haste, and activate it to get enough mana to play our remaining cards. Before activating the other two hasted Hornbash Mentors, use Might Weaver to give trample to all three of them, since they're red. Run the lower stages, accumulating counters on the three red Hornbash Mentors, then use them as the top layer to run all four stages.
With 14 cards, the same thing except we can make five red Hornbash Mentors instead of three.
Go to combat. Have four Sunrise draw, six give +1/+1, three gain life. 10 colorless, 3 treasures.
Play The Mirari Conjecture, getting back Saw. Make four dragons, three copy Doubling Season, one copies Conjecture. Play Bloodthorn Taunter, give haste to a Purse, activate it. Use the treasures to loop Saw, splitting Taunter and other Purses as needed.
Play Hornbash Mentor, eventually play World at War and copy it for every Conjecture. Go to additional combats for F{w2+3}.
For non-Mirror 13, do the same thing but copy Sunrise a fourth time for the additional two draws. The Mirror deck doesn't have a good way to get multiple castings of World at War since it exiles, so I think this puts non-Mirror in the lead for 13-card.
Hmm, the lich's mirror loops seem like they could be used better because channel can trigger the mirror at instant speed. But I don't think there's an exploitable infinite as the only instant is saw in half which will not have targets.
At the very least we can have doubling season on the stack when we die, so the combo is a bit better, though still limited by the opponent's life.
Edit: also, other interesting unfinity cards: Exchange of words knockoff true polymorph only changing text, does silly things with multiples and opalescence. Magar of the magic strings not sure exactly how this could be useful, but it is certainly a powerful effect.
The exception might be for small machines that we can follow explicitly, and see what the output is.
Edit: Its only one Artificial Evolution or True Polymorph or large Zubera trigger. and we can set up a small one to retrigger computation again
The issue is with targeting as we only have the creatures the opponent has at the time that we sac our board to kaervek's spite as legal targets, and a lot of those die, so we cant target an arbitrary output creature, we have to premake them and target what we want the next input to be in the range of something like BB(x) to BB(x)+10^48 and hope that there's an efficient machine in that range.
On the draw, we could add Artificial Evolution to our opening hand to have Bishop gain life from the first Spirits and copy Timetwister 17 times, but that's not ideal.
I redid the math, switching to having Benevolent Offering get 2/3 of the copies - I think about 2/3 is optimal since 2/3 is where the derivative of (1-x)*x^2 is 0. I got 4.5*10^69 tokens this time, think I misplaced a digit last time.
Bishop of Wings, Benevolent Offering (16 mana). Storm King's Thunder at X=6, Timetwister (4 mana).
Draw #1: Benevolent Offering (14 mana). Storm King's Thunder at X=2.
Draw #2: Thunder at X=2. Resolve the two copies, with the original on the stack play Offering, copied 4 times. First resolves (20 mana), play Artificial Evolution to set Bishop to Spirits. Mana goes 19 + 26+12 + 32+12 + 38+12 + 44+12 = 207.
Draw #3: Thunder at X=200. Resolve the two copies, with the original on the stack play Offering, copied 400 times. After the first resolves, play True Polymorph and Artificial Evolution to make a second Bishop set to Spirits. Mana goes 55 + (70+2448)*200 = 503,655.
Draw #4: Thunder at X=503,648. Resolve 134 copies, with the rest on the stack play Offering, copied 67,488,832 times. Mana goes to about 4.55*10^15.
Draw #5: Thunder at X=4.55*10^15, copied 67*503,648 times. Resolve 2/3 of them, play Offering, copied 10^23 times. Mana goes to about 3*10^46.
Draw #6: Thunder at X=3*10^46, copied 5*10^22 times. Resolve all the copies, play Offering, copied 1.5*10^69 times.
Draw #7: Coat of Arms, Dralnu's Crusade, Ember-Fist Zubera, Storm King's Thunder, True Polymorph + Artificial Evolution, Kaervek's Spite.
Better version of the Timetwister sequence:
Draw #1: Offering, 14 mana. Thunder at X=7.
Draw #2: Offering, total 8 times. Mana goes 19+38+44+50+56+62+68+74 = 411. Thunder at X=200.
Draw #3: Thunder at X=201, copied 200 times. Let 134 Thunders resolve, play Offering, copied 26,934 times. Get about 2.17*10^9 mana.
Draw #4: Thunder at X=2.17*10^9, copied 67*201 times. Let 8,978 Thunders resolve, play Offering, copied 1.94*10^13 times. Get about 1.13*10^27 mana.
Draw #5: Thunder at X=1.13*10^27, copied 4489*2.17*10^9 (=9.74*10^12) times. Let 6.49*10^12 Thunders resolve, play Offering, copied 7.33*10^39 times. Get about 1.61*10^80 mana.
Draw #6: Thunder at X=1.61*10^80, copied 3.24*10^13 times. Let all but the original resolve, play Offering, copied 5.22*10^92 times. End up with 1.56*10^93 tokens.
Draw #7: Finish.
Edit: I think we can use a similar approach for the 16-card deck, although in this case the lifegain doesn't scale during the initial rounds.
2 Channel
3 Mycosynth Lattice
4 Storm King's Thunder
5 War Report
6 Echo of Eons
7 Eiganjo Uprising
8 True Polymorph
10 Kaervek's Spite
11 Coat of Arms
12 Bishop of Wings
13 Artificial Evolution
14 Arcbond
15 Comeuppance
16 Dralnu's Crusade
Black Lotus, Channel, Mycosynth Lattice. 14 mana.
Eiganjo Uprising at X=8. War Report, gain 15+16 life. Storm King's Thunder at X=18, Echo of Eons.
First draw, War Report for 31 life, Storm King's Thunder at X=10. Second draw, Storm King's Thunder at X=11, resolve 6 copies of it, War Report copied 66 times, etc.
Hmm I found a possible infinite....
If after the computation we had a waiting copy of arcbond and below that, a storm god's thunder trigger for Polymorph. we could then set up another arcbond, and then polymorph the spirits we made from saccing our board into bishops. so that when we polymorph to kill an ember fist zubera, we start a computation with bishops on our side, and can potentially mess with computation.
This would require never drawing dralnu's crusade though and just using flooding clocks?
Edit: this can be avoided by a sorcery speed board wipe like Desolation giant, Edit2: hmm no then we keep our hand and can AE computation to mess it up.
Would we be able to go infinite from there? The Bishops on our side of the field would be copied without text changes, so we'd have limited opportunities to get more tokens and life, and Comeuppance wouldn't protect us from damage from Arcbonds on our own creatures.
But yeah needing our bishops to be default I think saves us from problems as our side of the computation is pretty trivial and we can only interfere when our angels die, and we don't have an arbitrary amount of those.
So I guess this means the 14 card version without dralnu's crusade probably wins at that size?
What would be different about the non-Dralnu's version?
On a different note, I've been keeping an eye on new Unfinity cards to see if other cards join Saw in Half in being useful here, and one that's caught my attention is Starlight Spectacular. Giving a non-targeted scaling boost at the start of combat is something I'd been looking for while working on some versions of the Saw deck, since it avoids needing to make a bunch of tokens of the highest stage creature ahead of time. Making all the boosts be different amounts is also an interesting detail, although I'm not sure what uses it could have.
the pure flooding version with 14 cards would use this as a way to set up a flooding waterfall machine, and then run another that we can even interrupt once (all of our angels die at the same time)
I'm not sure how efficient a flooding clock machine can be, but they do seem to grow very quickly.
1 dc
2 zubera
3 coat of arms
4 polymorph
5 thunder
6 arcbond
7 spite
play the permanents, cast polymorph, get a bunch of thunder triggers, use most of them to set up computation. cast a small thunder to copy arcbond
let the first arcbond resolve, and then cast spite to start computation.
after computation the original arcbond resolves, still targeting one of the opponent's creatures.
then we resolve the thunder trigger for polymorph, giving us default bishops and killing a zubera to trigger computation again.
we can now interfere with the computation many times due to the preset DC making spirts angels.
And then in the end the opponent suicides with a zubera trigger.
2 Show and Tell
3 Omniscience
4 Thousand-Year Storm
5 Fractured Identity
6 Second Harvest
7 Echo of Eons
9 Kaervek's Spite
10 Coat of Arms
11 Bishop of Wings
12 Artificial Evolution
13 Arcbond
14 Comeuppance
15 Dralnu's Crusade
Black Lotus, Show and Tell, Omniscience, Thousand-Year Storm, Fractured Identity giving TYS to the opponent. (The original fizzles.) Play Comeuppance, followed by Echo of Eons.
Redraw Fractured Identity and use it to get TYS back as a token. Play Bishop of Wings and Dralnu's Crusade, then Artificial Evolution and Arcbond, followed by Second Harvest at storm count 7. Double our token count 8 times, ending with 256 TYS. Then play Black Lotus to flashback Echo of Eons, which gets copied 2048 times.
Each Echo, play Artificial Evolution, Arcbond, and Comeuppance to raise storm count, followed by Second Harvest. Repeat for all 2048 copies.
When the original resolves, play Ember-Fist Zubera and Coat of Arms, then play Fractured Identity. Use the first TYS trigger to pass Bishop/Crusade/Zubera/Coat to the opponent, then the second to take them back as tokens. Before the others resolve, play Second Harvest to scale up our tokens, then let the other Fractured Identity copies resolve to pass as many of those tokens back to the opponent as possible. Then play Artificial Evolution and Arcbond to finish programming the board, and finish with Kaervek's Spite.
Edit: Wait, does this one also let us reconstruct our board afterward by keeping copy triggers waiting to use after the computation? Zubera is such a hassle.
Hmm. Given that this requires using AE on the last round, could we fix the issue by going back to Soulblast? If there's a way to keep it from killing the opponent. (Maybe burning some copies on tokens to trigger their Bishops?)
Edit: With Soulblast + Phthisis, we could use some of our Fractured Identity copies to eliminate most of our TYS clones, so that when we play Second Harvest the final time, the number of Bishop of Wings tokens we end up with is close to the number of Identity copies we have left, to make sure the number of Bishop tokens sacrificed to Soulblast stays reasonable.
2 Show and Tell
3 Omniscience
4 Thousand-Year Storm
5 Fractured Identity
6 Second Harvest
7 Echo of Eons
9 Phthisis
10 Coat of Arms
11 Bishop of Wings
12 Artificial Evolution
13 Arcbond
14 Comeuppance
15 Dralnu's Crusade
2 Channel
3 Doubling Season
4 Bucknard's Everfull Purse
5 Astral Dragon
6 Scale the Heights
7 The Mirari Conjecture
8 Saw in Half
9 Bloodthorn Taunter
10 Hornbash Mentor
11 Might Weaver
12 Frillscare Mentor
13 Scattershot Archer
14 Rite of Passage
Black Lotus, Channel, Doubling Season, Bucknard's Everfull Purse, activate Purse. 8 treasures, 12 colorless.
Astral Dragon making four Purses, Bloodthorn Taunter, Scale the Heights giving two +1/+1 counters to an animated Purse and drawing a card. Tap Taunter to activate the Purse. 12 treasures, 5 colorless.
Play The Mirari Conjecture, which goes to two lore counters. Get back Scale the Heights and play it on another Purse. 9 treasures, 2 colorless.
Play Saw in Half to make four Astral Dragon tokens. The first three target Doubling Season (1>5>69>2^70), the last makes 2^2^70 Mirari Conjectures. Conjectures immediately complete, making that many copy triggers and getting back Scale and Saw. Replay Saw two more times, each time getting copied by the previous Conjectures, which I think gets us to 2^^^^4. Have the last Saw instance target Taunter, use one to activate the Purse boosted last time, and use the resulting Treasures to go to 2^^^^2^^^^4. Then replay Scale to boost another Purse token. Conjecture will copy it, but we can have all the copies target the same purse, then play Saw on it after the first one resolves so we only draw one card.
Play Hornbash Mentor, then run a single stage using the Purse tokens to get to F{w}(2^^^^2^^^^4). Replay Scale, boosting Hornbash this time, again making sure it only happens once.
Play Scattershot Archer and run a double stage using Hornbash Mentor. Then draw and play Rite of Passage, boosting Hornbash again, but this time using it for a triple stage. Draw and play Frillscare Mentor, run another triple stage, then draw and play Might Weaver to run a single instance of a quadruple stage.
I think this gets us to F{w4}(F{w3}(F{w3}(F{w2}(F{w}(2^^^^2^^^^4))))). Not sure if there's a better way to write that.
As for the other multistage decks, 11-card and 13-card have less need for Lich's Mirror since they can use Fight Rigging and Finest Hour to still hit two layers on top of their stage count. 10-card can enter combat with five Fight Riggings and one Wingspan Mentor to run a single instance of a double stage. 12-card would probably just want to copy this up to the first instance of the triple stage.
Speaking of versions with and without infinite mana, I think the 9-card deck could get slightly higher numbers with Lich's Mirror, since that would mean not having to spend Temur Ascendancy triggers on getting to its last two cards.
Mirror:
2 Channel
3 Lich's Mirror
4 Doubling Season
5 Astral Dragon
6 Codex Shredder
7 Saw in Half
8 Bloodthorn Taunter
9 Hornbash Mentor
10 Frillscare Mentor
11 Might Weaver
12 Scattershot Archer
13 Rite of Passage
14 Winter Sky
2 Channel
3 Lich's Mirror
4 Doubling Season
5 Astral Dragon
6 Codex Shredder
7 Saw in Half
8 Bloodthorn Taunter
9 Hornbash Mentor
10 Scattershot Archer
11 Rite of Passage
12 Winter Sky
13 Bellowing Aegisaur
2 Channel
3 Lich's Mirror
4 Doubling Season
5 Astral Dragon
6 Codex Shredder
7 Saw in Half
8 Bloodthorn Taunter
9 Hornbash Mentor
10 Scattershot Archer
11 Rite of Passage
12 Winter Sky
12-card: Start with the Lotus/Channel/Mirror loop, then play Doubling Season, Codex Shredder, Astral Dragon making four Seasons, Saw in Half making 64 dragons for a bunch of Doubling Seasons and Codex Shredders, Hornbash Mentor, Rite of Passage, and then Winter Sky to put +1/+1 counters on everything. Sacrifice the original Shredder to get back Winter Sky and use it to draw Bloodthorn Taunter, use it to give haste to another Shredder to get back Saw for more Taunters. Play through the Shredder stage, then use Winter Sky to draw Scattershot Archer (and cast Saw on it) before activating Hornbash Mentor.
Once that all finishes, use Winter Sky for damage 18 more times, since that's the most the life totals will allow. Each time, get Rite of Passage triggers for all the creatures. 13-card version adds Bellowing Aegisaur for an additional layer.
12 cards: F{w3+2}(18)
13 cards: F{w3+3}(18)
14 cards: F{w4+2}(18)
2 Channel
3 Doubling Season
4 Bucknard's Everfull Purse
5 Astral Dragon
6 Crimson Wisps
7 The Mirari Conjecture
8 Saw in Half
9 Bloodthorn Taunter
10 Hornbash Mentor
11 Might Weaver
12 Frillscare Mentor
2 Channel
3 Doubling Season
4 Bucknard's Everfull Purse
5 Astral Dragon
6 Crimson Wisps
7 The Mirari Conjecture
8 Saw in Half
9 Bloodthorn Taunter
10 Hornbash Mentor
11 Might Weaver
12 Frillscare Mentor
13 Scattershot Archer
14 Rite of Passage
With 12 cards:
Black Lotus, Channel, Doubling Season, Bucknard's Everfull Purse. 12 colorless, 8 treasures.
Astral Dragon copying Purse, Crimson Wisps targeting Purse, activate Purse. 5 colorless, 13 treasures.
Hornbash Mentor, The Mirari Conjecture getting back Wisps, replay Wisps on a Purse, activate it. 18 treasures.
Saw in Half on Astral Dragon. First three dragons make Doubling Seasons, fourth makes Conjectures, get back Wisps and Saw. Replay Saw, initially targeting dragons but using the last on Hornbash Mentor, placing trample counters as necessary. Play Wisps on three Mentors to draw the remaining cards, giving them haste and turning them red. Point the extra copies at an Astral Dragon, replay Saw on the dragon in response to counter the extras. 8 treasures.
At this point we can activate one of the hasted Hornbash Mentors to give +1/+1 counters to a wave of Purse tokens. Play Bloodthorn Taunter, give the Purse haste, and activate it to get enough mana to play our remaining cards. Before activating the other two hasted Hornbash Mentors, use Might Weaver to give trample to all three of them, since they're red. Run the lower stages, accumulating counters on the three red Hornbash Mentors, then use them as the top layer to run all four stages.
With 14 cards, the same thing except we can make five red Hornbash Mentors instead of three.
I think this works out to:
12 cards: F{w3+1}(3)
14 cards: F{w4+1}(5)
Edit: Glorious Sunrise ports cleanly over Citadel Siege in Mirror 10/11 since those don't need to worry about drawing. For non-Mirror:
2 Channel
3 Doubling Season
4 Bucknard's Everfull Purse
5 Astral Dragon
6 Saw in Half
7 Glorious Sunrise
8 The Mirari Conjecture
9 Bloodthorn Taunter
10 Hornbash Mentor
11 World at War
12 Scattershot Archer
13 Rite of Passage
2 Channel
3 Doubling Season
4 Bucknard's Everfull Purse
5 Astral Dragon
6 Saw in Half
7 Glorious Sunrise
8 The Mirari Conjecture
9 Bloodthorn Taunter
10 Hornbash Mentor
11 World at War
11-card: Black Lotus, Channel, Doubling Season, Bucknard's Everfull Purse. 12 colorless, 8 treasures.
Glorious Sunrise, Astral Dragon, Saw in Half. Copy Purse twice (8x Purse) and Sunrise three times (13x Sunrise). 1 colorless, 3 treasures.
Go to combat. Have four Sunrise draw, six give +1/+1, three gain life. 10 colorless, 3 treasures.
Play The Mirari Conjecture, getting back Saw. Make four dragons, three copy Doubling Season, one copies Conjecture. Play Bloodthorn Taunter, give haste to a Purse, activate it. Use the treasures to loop Saw, splitting Taunter and other Purses as needed.
Play Hornbash Mentor, eventually play World at War and copy it for every Conjecture. Go to additional combats for F{w2+3}.
For non-Mirror 13, do the same thing but copy Sunrise a fourth time for the additional two draws. The Mirror deck doesn't have a good way to get multiple castings of World at War since it exiles, so I think this puts non-Mirror in the lead for 13-card.
Edit: Winter Sky doesn't work in 12-card because it'll kill all our Bloodthorn Taunters, but I think we can swap in Chandra's Ignition. (In 14-card, it can get +1/+1 counters from Hornbash Mentor because of Might Weaver.)
At the very least we can have doubling season on the stack when we die, so the combo is a bit better, though still limited by the opponent's life.
Edit: also, other interesting unfinity cards:
Exchange of words knockoff true polymorph only changing text, does silly things with multiples and opalescence.
Magar of the magic strings not sure exactly how this could be useful, but it is certainly a powerful effect.