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.
Yeah, I forgot when I was writing the Winter Sky decks that it lets us start with effectively 8 cards. That allows for some slightly better starts.
Yeah I think exchange of words has some shenanigans with layers and other copy effects like protean thaumaturge, but I don't see a way to make it beneficial.
For iterated BB we were using something like BB^3(X)=BB(BB(BB(X)))
BB_2(X) = BB^BB(X)(X)
BB_3(X) = BB_2^BB_2(X)(X)
Its a bit difficult to say how many true BB iterations we get, as we need to spend a few copies of echo of aeons setting up, as there are only a handful of creatures in play when we start echoing. It looks like that list needs 10 mana set aside so we don't dead end, and at least 2 iterations to start a trivial computation to begin sizing up, I'd guess we don't need more than 3-8?? of those to get big enough for real computation, depending on how efficient we can make small waterfall programs.
So approximately BB^X-15(X) where X is the amount of mana we have before casting storm god's thunder for Echo of Aeons.
Yeah I think exchange of words has some shenanigans with layers and other copy effects like protean thaumaturge, but I don't see a way to make it beneficial.
For iterated BB we were using something like BB^3(X)=BB(BB(BB(X)))
BB_2(X) = BB^BB(X)(X)
BB_3(X) = BB_2^BB_2(X)(X)
Its a bit difficult to say how many true BB iterations we get, as we need to spend a few copies of echo of aeons setting up, as there are only a handful of creatures in play when we start echoing. It looks like that list needs 10 mana set aside so we don't dead end, and at least 2 iterations to start a trivial computation to begin sizing up, I'd guess we don't need more than 3-8?? of those to get big enough for real computation, depending on how efficient we can make small waterfall programs.
So approximately BB^X-15(X) where X is the amount of mana we have before casting storm god's thunder for Echo of Aeons.
Would the initial computations be trivial? My thinking was:
Draw #2: Storm King's Thunder at X=11, resolve 6 copies of it, War Report copied 66 times for 2046 life. Resolve the other 5 Thunders.
Draw #3: Thunder at X=2039, copied 55 times. Resolve 28, Report copied 57,092 times for 1.7 million life. Resolve the other 28 Thunders.
Draw #4: Thunder at X=1.7 million, copied 57,092 times. Resolve 28,546, Report copied 4.8^10^10 times for 1.5*10^12 life. Resolve the other 28,546.
Draw #5: Thunder at X=1.5*10^12, copied 4.8^10^10 times. Resolve 2.4*10^10, Report copied 3.6*10^22 times for 1.1*10^24 life...
We end up almost doubling the number of digits each time. After all 18 copies, we should end up with well over 10^100,000 life, then can put that into Eiganjo Uprising (which gets copied additional times). So when we flashback Echo, we can spend the first draw setting up, then we can use the second draw for a computation with over that many creatures. And we're also working with over that many copies of Echo of Eons on the flashback, so we aren't worrying much about precise numbers.
Use Lotus/Channel/Mirror for infinite mana. On the last loop, play Doubling Season, while it's on the stack activate Conjurer's Bauble targeting nothing, then run Mirror's reshuffle in response. Draw Bauble back, along with the other 7 cards.
For 13-card, we can add Finest Hour and draw it before combat with the "main" Bauble. Which is kind of unfortunate, honestly. I liked having one where non-Mirror was better.
Oh you are right, I forgot about the initial Echo of Aeons getting copied and thought we had to do the first computation with more like a hundred creatures.
I don't see how that would help. Firecat Blitz was used because, in addition to making creatures with haste, it has flashback. Kindred Charge can't replace Irenicus's Vile Duplication because the delegendarizing is neccesary.
[...]
Not sure about some of the numbers, or how to write the damage for the iterated Busy Beaver deck.
Chancellor of the Dross doesn't deal damage.
For 6 cards, we can take Parallel Lives, Astral Dragon, Mirage Phalanx and add Black Lotus, Show and Tell, Omniscience, getting (still) >2^^35.
I don't see how that would help. Firecat Blitz was used because, in addition to making creatures with haste, it has flashback. Kindred Charge can't replace Irenicus's Vile Duplication because the delegendarizing is neccesary.
[...]
Not sure about some of the numbers, or how to write the damage for the iterated Busy Beaver deck.
Chancellor of the Dross doesn't deal damage.
For 6 cards, we can take Parallel Lives, Astral Dragon, Mirage Phalanx and add Black Lotus, Show and Tell, Omniscience, getting (still) >2^^35.
My thinking was that it would be another chance to incorporate "for each Jadzi", but I'm not sure if that works out to showing up in the final count.
For Chancellor, I was thinking "damage" metaphorically as a way to score how much we've reduced the opponent's life, but it's true that that's not the most precise.
Usually our score is just (20 - opponent's life total), counting lifeloss just the same as damage (and "opponent loses X life" spells I'm pretty sure have been acceptable finishers in previous decks)
Taking a crack at a writeup for 1-16 cards, including some variations without infinite mana when relevant. If anyone has feedback or is interested in edit access, let me know.
Had to change 13-14 cards around a bit, I don't think Conjurer's Bauble actually works since you'd need to redraw Saw and play it on Bloodthorn Taunter to get enough activations to redraw Saw in the first place. With 13 cards, Codex Shredder can fix that by carrying over a mill activation from the last loop and then picking it up before combat, but with 14 cards I had to go back to the Chandra's Outrage strategy.
Haven't added 15-16 cards yet, I'm not sure how to explain computations well enough for this.
There is an error in the write-up for the 9-card solution.
"Mystic Sanctuary enters the battlefield tapped unless you control three or more other Islands." is a replacement effect, thus it is applied before it enters the battlefield. The first time copies of it are created, they will enter tapped and not get to put a card back; we need to target Mystic Sanctuary twice with Astral Dragon to start putting Saw in Half back.
(Edit) One more thing: when you write a list of cards, it's probably better to use something other than a comma as the separator (such as a semicolon), because some card names contain commas.
Since mana pools are emptied between steps and phases, the lich's mirror decks do still need to accumulate mana during the combat step when parts of the combo need to be run during that step. Is that still possible in the 11-card mirror deck?
Good catches. And hmm, mana pools being emptied between phases is a problem - that means we do need to get Black Lotus back online fast. I think 11-12 card can pull it off by carrying over a mill activation and then using the original Codex Shredder to get back the milled card, rather than getting a second early cast of Saw. But 13-card already made that trade, so it might need to switch back to the World at War strategy.
Edit: Fixed the issues and added 15-16 card writeups.
Because Comeuppance is our trigger and it’s our turn, it goes on the stack before the opponent’s triggers, and therefore resolves after them.
This part in the description of the computation is wrong. Comeuppance doesn't trigger, it creates a replacement effect. So the damage that it deals to the Arcbonded creature is dealt at the same time as all of the other Arcbond damage.
If that wasn't the case we could go infinite if we are able to set up a computation with multiple arcbonded creature, because the slight asymmetry of arcbond allows us to change the computation after an arbitrary time by changing the order of the arcbond triggers.
The trigger that is ours and goes on the stack before the opponent's triggers is actually the Arcbond trigger itself. We controlled arcbond when it resolved, so that trigger is ours, even when we don't control the arcbonded creature.
Because Comeuppance is our trigger and it’s our turn, it goes on the stack before the opponent’s triggers, and therefore resolves after them.
This part in the description of the computation is wrong. Comeuppance doesn't trigger, it creates a replacement effect. So the damage that it deals to the Arcbonded creature is dealt at the same time as all of the other Arcbond damage.
If that wasn't the case we could go infinite if we are able to set up a computation with multiple arcbonded creature, because the slight asymmetry of arcbond allows us to change the computation after an arbitrary time by changing the order of the arcbond triggers.
The trigger that is ours and goes on the stack before the opponent's triggers is actually the Arcbond trigger itself. We controlled arcbond when it resolved, so that trigger is ours, even when we don't control the arcbonded creature.
That makes sense, fixed it.
Thinking back to the talk about higher iterations of Busy Beaver - I'm not sure about including this in the writeup (16 is such a nice number, and I like ending on the first iterated Busy Beaver) but one way to get a number of iterations of computations based on the output of previous computations in 17 cards would be to replace Echo of Eons with Emergency Powers and Learn from the Past. Emergency Powers lets us redraw Learn a limited number of times, each time using Storm King's Thunder to get more copies of it and using a few of those copies per computation.
Thunder for X=125, then Emergency Powers. On the first Powers, drop Coat of Arms and play War Report for 88 life, then do Thunder>Learn to start looping Thunder/Report. On the second one, drop Goblin Boom Keg, then that series of Learns can start start doing whatever sort-of computations are possible without Dralnu's Crusade, starting with a small board but building to bigger ones. Then on the third one we can play Dralnu's Crusade and start having every six Learns correspond to a proper computation.
Also in the write-up for the 9-card solution, "After the first Saw, we have over 2^^^3 Doubling Season tokens" is now incorrect: 2^^^3 = 2^^2^^2 = 2^^4 = 2^2^2^2 = 65536, while the number of Doubling Seasons is 69. However, making Astral Dragon tokens with the next Saw in Half adds another exponentiation, so the result still exceeds 2^^^6.
fantastic writeups!
One fun thing you can mention is that Chancellor of the dross does the damage slightly 'faster' if we are on the draw, as our upkeep triggers would resolve before theirs if they had any.
Also you should probably mention that our waterfall machines are limited by the number of MTG creature types, but we only need a handful of them to make a Turing machine.
I'm a little sad that the Urza, lord high artificer deck that just barely worked got outclassed but saw in half is pretty insane too.
Also in the write-up for the 9-card solution, "After the first Saw, we have over 2^^^3 Doubling Season tokens" is now incorrect: 2^^^3 = 2^^2^^2 = 2^^4 = 2^2^2^2 = 65536, while the number of Doubling Seasons is 69. However, making Astral Dragon tokens with the next Saw in Half adds another exponentiation, so the result still exceeds 2^^^6.
fantastic writeups!
One fun thing you can mention is that Chancellor of the dross does the damage slightly 'faster' if we are on the draw, as our upkeep triggers would resolve before theirs if they had any.
Also you should probably mention that our waterfall machines are limited by the number of MTG creature types, but we only need a handful of them to make a Turing machine.
I'm a little sad that the Urza, lord high artificer deck that just barely worked got outclassed but saw in half is pretty insane too.
Thanks! I've revised the 9-card start (again) and added the notes about Chancellor and waterfall.
Another thing probably worth mentioning about computation is that it is an open question if Dralnu's Crusade is even required for Turing Completeness which would improve those last two decks by a full card. The problem with removing it is that all of the tokens would just have one type making computation much more volatile. If we ever get a Bishop of wings that makes multityped creatures, we can cut it.
Minor comment; the 7 card deck mentions that tetration is "like untapping devilish valet". However, none of the prior decks involve untapping devillish valet.
Another thing probably worth mentioning about computation is that it is an open question if Dralnu's Crusade is even required for Turing Completeness which would improve those last two decks by a full card. The problem with removing it is that all of the tokens would just have one type making computation much more volatile. If we ever get a Bishop of wings that makes multityped creatures, we can cut it.
Yeah, those are unfortunate. Added a note about the Dralnu's Crusade question.
Minor comment; the 7 card deck mentions that tetration is "like untapping devilish valet". However, none of the prior decks involve untapping devillish valet.
Right, that was from the other 6-card strategy. Changed to mention Astral Dragon instead.
To improve something else that was bugging me, I used Python to get some more specific numbers for the iterated Busy Beaver deck, moving the lower bound up to 10^390,000:
Edit: Using a similar method, I believe the 7-card deck finishes its second Slaughter cast with 7,258,845,553,210 copies of Precursor Golem and 16,937,306,290,822 copies of Salvaging Station:
def slaughter(targets, stations, mana):
while targets >= 3:
targets -= 1
mana += stations * 3
activations = (mana-3)//4
stations += activations
mana -= activations*4
if targets == 2:
targets -= 1
mana += stations * 3
activations = (mana-7)//4
stations += activations
mana -= 7+activations*4
precursors = 1
if targets == 1:
targets -= 1
mana += stations * 3
precursors += mana//7
if targets == 0:
print("precursors:", precursors)
print("stations:", stations)
Edit: Using a similar method, I believe the 7-card deck finishes its second Slaughter cast with 7,258,845,553,210 copies of Precursor Golem and 16,937,306,290,822 copies of Salvaging Station:
That would be the numbers after the second Precursor Golem trigger on Slaughter, so before the second Slaughter cast.
We can however do better by using the mana from the last two slaughter deaths to create Precursor Golems, instead of only the mana from the last one. The Salvaging Stations we could create on the second to last death only give us 6 mana back before we resolve the next precursor golem trigger or cast the next spell and in either case getting just one more golem beforehand is worth more than the additional salvaging stations. (Though to optimize we can create Salvaging Stations on the second to last death at the cost of effectively 1 mana, so we can use that to finish with 0 to 6 additional stations 0 mana)
I updated my spreadsheet with that play pattern. We end up with 25 Salvaging Stations, 19 Precursor Golems and 36 Golem Tokens before the second Precursor Golem trigger on Slaughter will resolve.
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Exchange of Words and Magar of the Hidden Strings are interesting, although they both seem tricky to use.
If everything works, I think the current top decks are:
For iterated BB we were using something like BB^3(X)=BB(BB(BB(X)))
BB_2(X) = BB^BB(X)(X)
BB_3(X) = BB_2^BB_2(X)(X)
Its a bit difficult to say how many true BB iterations we get, as we need to spend a few copies of echo of aeons setting up, as there are only a handful of creatures in play when we start echoing. It looks like that list needs 10 mana set aside so we don't dead end, and at least 2 iterations to start a trivial computation to begin sizing up, I'd guess we don't need more than 3-8?? of those to get big enough for real computation, depending on how efficient we can make small waterfall programs.
So approximately BB^X-15(X) where X is the amount of mana we have before casting storm god's thunder for Echo of Aeons.
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.
Draw #1: War Report for 31 life, Storm King's Thunder at X=10.
Draw #2: Storm King's Thunder at X=11, resolve 6 copies of it, War Report copied 66 times for 2046 life. Resolve the other 5 Thunders.
Draw #3: Thunder at X=2039, copied 55 times. Resolve 28, Report copied 57,092 times for 1.7 million life. Resolve the other 28 Thunders.
Draw #4: Thunder at X=1.7 million, copied 57,092 times. Resolve 28,546, Report copied 4.8^10^10 times for 1.5*10^12 life. Resolve the other 28,546.
Draw #5: Thunder at X=1.5*10^12, copied 4.8^10^10 times. Resolve 2.4*10^10, Report copied 3.6*10^22 times for 1.1*10^24 life...
We end up almost doubling the number of digits each time. After all 18 copies, we should end up with well over 10^100,000 life, then can put that into Eiganjo Uprising (which gets copied additional times). So when we flashback Echo, we can spend the first draw setting up, then we can use the second draw for a computation with over that many creatures. And we're also working with over that many copies of Echo of Eons on the flashback, so we aren't worrying much about precise numbers.
2 Channel
3 Lich's Mirror
4 Conjurer's Bauble
5 Doubling Season
6 Astral Dragon
7 Saw in Half
8 Bloodthorn Taunter
9 Hornbash Mentor
10 Scattershot Archer
11 Rite of Passage
12 Glorious Sunrise
Use Lotus/Channel/Mirror for infinite mana. On the last loop, play Doubling Season, while it's on the stack activate Conjurer's Bauble targeting nothing, then run Mirror's reshuffle in response. Draw Bauble back, along with the other 7 cards.
Play Astral Dragon copying Doubling Season, then play Conjurer's Bauble, Bloodthorn Taunter, Hornbash Mentor, Scattershot Archer, Rite of Passage, Glorious Sunrise, and then Saw in Half making 64 Astral Dragons which copy Doubling Season 62 times, Bauble once, and Sunrise once. Bauble can't recover Saw before combat, but once we're in combat, we can draw past Lotus/Channel/Mirror and any other junk that may be present.
For 13-card, we can add Finest Hour and draw it before combat with the "main" Bauble. Which is kind of unfortunate, honestly. I liked having one where non-Mirror was better.
so yeah something like BB^(10^100000)(10^100000)
Edit: Replacing Rite of Passage with Test of Faith saves a setup draw for Glorious Sunrise decks, since we can pick it up in combat instead. This should make it possible to use Sunrise in 14-card, and to go back to Codex Shredder over Conjurer's Bauble in 12-card.
I don't see how that would help. Firecat Blitz was used because, in addition to making creatures with haste, it has flashback. Kindred Charge can't replace Irenicus's Vile Duplication because the delegendarizing is neccesary.
Chancellor of the Dross doesn't deal damage.
For 6 cards, we can take Parallel Lives, Astral Dragon, Mirage Phalanx and add Black Lotus, Show and Tell, Omniscience, getting (still) >2^^35.
For Chancellor, I was thinking "damage" metaphorically as a way to score how much we've reduced the opponent's life, but it's true that that's not the most precise.
Mirage Phalanx deck looks good.
Taking a crack at a writeup for 1-16 cards, including some variations without infinite mana when relevant. If anyone has feedback or is interested in edit access, let me know.
Had to change 13-14 cards around a bit, I don't think Conjurer's Bauble actually works since you'd need to redraw Saw and play it on Bloodthorn Taunter to get enough activations to redraw Saw in the first place. With 13 cards, Codex Shredder can fix that by carrying over a mill activation from the last loop and then picking it up before combat, but with 14 cards I had to go back to the Chandra's Outrage strategy.
Haven't added 15-16 cards yet, I'm not sure how to explain computations well enough for this.
"Mystic Sanctuary enters the battlefield tapped unless you control three or more other Islands." is a replacement effect, thus it is applied before it enters the battlefield. The first time copies of it are created, they will enter tapped and not get to put a card back; we need to target Mystic Sanctuary twice with Astral Dragon to start putting Saw in Half back.
(Edit) One more thing: when you write a list of cards, it's probably better to use something other than a comma as the separator (such as a semicolon), because some card names contain commas.
Edit: Fixed the issues and added 15-16 card writeups.
If that wasn't the case we could go infinite if we are able to set up a computation with multiple arcbonded creature, because the slight asymmetry of arcbond allows us to change the computation after an arbitrary time by changing the order of the arcbond triggers.
The trigger that is ours and goes on the stack before the opponent's triggers is actually the Arcbond trigger itself. We controlled arcbond when it resolved, so that trigger is ours, even when we don't control the arcbonded creature.
Thinking back to the talk about higher iterations of Busy Beaver - I'm not sure about including this in the writeup (16 is such a nice number, and I like ending on the first iterated Busy Beaver) but one way to get a number of iterations of computations based on the output of previous computations in 17 cards would be to replace Echo of Eons with Emergency Powers and Learn from the Past. Emergency Powers lets us redraw Learn a limited number of times, each time using Storm King's Thunder to get more copies of it and using a few of those copies per computation.
For startup, I'm thinking Black Lotus, Channel, Mycosynth Lattice, Eiganjo Uprising at X=8, War Report for 31 life, then Storm King's Thunder at X=5 followed by Learn from the Past. That redraws Uprising/Report/Thunder, as well as drawing Bishop of Wings, Artificial Evolution, and Emergency Powers. Play Bishop, hack it to gain life from Samurai, Uprising at X=14, gaining 56 life, then War Report for for 87 life, bringing us to 139.
Thunder for X=125, then Emergency Powers. On the first Powers, drop Coat of Arms and play War Report for 88 life, then do Thunder>Learn to start looping Thunder/Report. On the second one, drop Goblin Boom Keg, then that series of Learns can start start doing whatever sort-of computations are possible without Dralnu's Crusade, starting with a small board but building to bigger ones. Then on the third one we can play Dralnu's Crusade and start having every six Learns correspond to a proper computation.
One fun thing you can mention is that Chancellor of the dross does the damage slightly 'faster' if we are on the draw, as our upkeep triggers would resolve before theirs if they had any.
Also you should probably mention that our waterfall machines are limited by the number of MTG creature types, but we only need a handful of them to make a Turing machine.
I'm a little sad that the Urza, lord high artificer deck that just barely worked got outclassed but saw in half is pretty insane too.
For 5 cards, Sparkcaster in place of Storm Herd can be cast 38 times before having to kill a player.
A 4-card solution that is close but not quite best: Black Lotus, Channel, Uktabi Drake, Bronze Cudgels for 38 damage.
Its a shame Exponential Growth is double green, its a lot more efficient than wine of blood and iron
Another thing probably worth mentioning about computation is that it is an open question if Dralnu's Crusade is even required for Turing Completeness which would improve those last two decks by a full card. The problem with removing it is that all of the tokens would just have one type making computation much more volatile. If we ever get a Bishop of wings that makes multityped creatures, we can cut it.
Yeah, those are unfortunate. Added a note about the Dralnu's Crusade question.
Right, that was from the other 6-card strategy. Changed to mention Astral Dragon instead.
Thanks!
To improve something else that was bugging me, I used Python to get some more specific numbers for the iterated Busy Beaver deck, moving the lower bound up to 10^390,000:
def echoes(copies):
xvalue = 10
thundernum = 1
reports = 1
endlife = 18
carryover = 1
iterations = 1
while iterations < copies:
thundernum = xvalue*carryover + 1
xvalue = endlife - 7
reports = (thundernum-thundernum//2)*xvalue+1
endlife = reports*31
carryover = thundernum//2
iterations = iterations + 1
print("xvalue log:", math.log(xvalue,10))
print("thundernum log:", math.log(thundernum,10))
print("reports log:", math.log(reports,10))
print("endlife log:", math.log(endlife,10))
print("carryover log:", math.log(carryover,10))
print("iterations:", iterations)
echoes(18)
Edit: Using a similar method, I believe the 7-card deck finishes its second Slaughter cast with 7,258,845,553,210 copies of Precursor Golem and 16,937,306,290,822 copies of Salvaging Station:
while targets >= 3:
targets -= 1
mana += stations * 3
activations = (mana-3)//4
stations += activations
mana -= activations*4
if targets == 2:
targets -= 1
mana += stations * 3
activations = (mana-7)//4
stations += activations
mana -= 7+activations*4
precursors = 1
if targets == 1:
targets -= 1
mana += stations * 3
precursors += mana//7
if targets == 0:
print("precursors:", precursors)
print("stations:", stations)
slaughter(49,37,2)
We can however do better by using the mana from the last two slaughter deaths to create Precursor Golems, instead of only the mana from the last one. The Salvaging Stations we could create on the second to last death only give us 6 mana back before we resolve the next precursor golem trigger or cast the next spell and in either case getting just one more golem beforehand is worth more than the additional salvaging stations. (Though to optimize we can create Salvaging Stations on the second to last death at the cost of effectively 1 mana, so we can use that to finish with 0 to 6 additional stations 0 mana)
I updated my spreadsheet with that play pattern. We end up with 25 Salvaging Stations, 19 Precursor Golems and 36 Golem Tokens before the second Precursor Golem trigger on Slaughter will resolve.