Oh, I think I see what you are doing. But I'm not sure that it is enough. So we evaluate the top hyperstage to compute the function N -> F_{w^2}(N). Then, the top group of Psychic Battle triggers below that top hyperstage is supposed to compute the function F_{w^2+1}, then next group of Bloodbond March triggers below that is supposed to compute the function F_{w^2+2}, and so on. So the top layer of Psychic Battle triggers will indeed compute the function f_{w^2+1}(N), where N is the number of Psychic Battle triggers, in the sense that the numbers we see in the topmost hyperstage will be around that number. But after Child of Alara destroys everything, we won't see those numbers on the lower hyperstage. So when we destroy the nontoken Clockwork Gnomes and create a new token, and tap it, the number of Psychic Battle triggers we get will be equal to the small number of Psychic Battles that we have at this lower hyperstage. So we don't iterate F_{w^2+1}, we keep reapplying F_{w^2) N times where N is the small number of Psychic Battles.
Edit: So, I haven't had any new ideas for the Chalice of the Void deck. We can borrow Stakfish's stage sequence to get seven stages for the Soul Foundry deck:
Edit: Stakfish, a question: Even if we can't get Chalice of the Void to work, is there any mileage can we gain from restricting zone changing, with Millikin / Myr Welder? For example, can Muzzio be saved?
Edit: Random thought. What if, in the Chalice of the Void deck, we replace Changeling Hero and Anaba Ancestor with something more restrictive, like maybe Boggart Mob and Mad Auntie? I guess I don't see how this would fix the problem; it would allow Panharmonicon back in, and we couldn't Champion Vedalken Orrery anymore, if that helps. Hmm, I guess Mad Auntie is a 3 CMC anyway, so we can't use that, at least not directly.
I'm not seeing how this works. We can't use the instants triggered by the Acorn Harvest of the current megastage transition, since those will resolve before the Smite the Monstrous that destroys the Child of Alara, and wipes out all our nonland permanents. If we try to use Hunting Pack and Smite the Monstrous after Child of Alara wipes everything out, then we can get Beasts, but we won't get anything else on the battlefield, so we can't take advantage of the combo.
No wait, we have Changeling Hero Championing the Orrery, so that comes back and we can replay everything. But isn't this a problem? We can have Goblin Dark-Dwellers in our hand, and have Orrery on the battlefield and Smite the Monstrous copies (or Psychic Battle triggers, even if we don't have copies) on the stack, below the Child of Alara breakpoint. It looks like then we can keep replaying and bouncing the Dark-Dwellers to greatly extend the lower hyperstage. Am I missing something?
Hmm... Mirrorwing Dragon is an interesting idea, but having to resolve the previous Smite the Monstrous seems to be too expensive, as we only get Smite from the previous megastage transition.
I think Verdant Succession will search for Bloodbond March, since that is the current name of the creature when it dies. It might be worth asking on the Rules forum.
Edit: the Mirrorwing Dragon / Smite idea would work for the gigastage I think, so if we had an idea that used lands to bring stuff back, we could combine the two.
Nice, that's very clever. I don't see a problem with being able to delay the targeting ability after the tapping ability, but I guess it's something we should keep an eye on.
For the ending layers, it will be better to have Consecrated Sphinx rather than Precursor Golem, since then we will be able to get through the deck much more quickly, and probably the last five Reforges will be able to access the whole deck. The first Reforge draws seven cards, of which four can be two copies of Spider Spawning, Spellweaver Helix, and Consecrated Sphinx. Then we still have three more cards, and the second Reforge allows us to draw 21 more cards, which should be enough to get going; if we need to, we can get the third Reforge cast by drawing another Spider Spawning. (It would be nice to get another copy of Consecrated Sphinx for the second cast, but I don't see an easy way to do that with the remaining three cards.)
Edit: Unfortunately, I have found a serious problem with the deck, and I don't know how to fix it. Each time we resolve Child of Alara or Worldfire, we eliminate all of our permanents, so we need to find a way to build it back up somehow. We do have all the floating mana that we can carry over, so the idea was the use this to rebuiild our enchantments. This was fine when we were using Allay to bounce Copy Enchantment to make more Dual Nature copies. But, now, creating more enchantments relies crucially on our Mimic Vats and Mirror of Fates. So we will only be able to create a relatively small number of enchantments, and the lion share of our mana is left floating.
Cogwork Assembler won't work because it targets and gives haste. If we could use Thousand-Year Storm, that should work once we resolve down to the next casting of an instant/sorcery, since the storm count keeps rising throughout a hyperstage/megastage. But it looks like this deck relies on not having any spell copiers around.
All good points. It still might be nice if there were another way to get Centaur Safeguard back. Assembly Hall always comes to my mind, but I guess it will allow Muzzio to go infinite once we get one Muzzio in the graveyard, one in our hand and a token copy on the battlefield, which shouldn't be too hard to manage. Perhaps some way to use the fact that Centaur Safeguard is multicolored? Reborn Hope and Supply // Demand would be nice ways to bring it back, except they are cheap sorceries. It can get various properties with the Maze cards, including flying...
We can switch black mana with red mana if we so desire - the Simian Spirit Guide / Goblin Kites stage is nice, but it's worth considering all avenues.
Ah right, I forgot for a moment we still needed Mimic Vat in the Soul Foundry deck, in order to make more enchantments. So that kills off any later 1,2, or 4 CMC creatures. Does anyone have an idea for how to make lots of enchantments without Mimic Vat? Dual Nature is off the table, since we have Brudiclad, Telchor Engineer.
Ooh, that latest deck looks very nice! I don't see any immediate problems. One thing that I'm worried about: We have to make sure that we don't gain any Anaba Ancestor tokens by going through the megastage, but we also have to make sure that we don't lose any either. Otherwise, we lose a token or tokens each time we go to the higher hyperstage and back down again, so we won't get the full recursion going. Of course, it is okay to tap one or more Anaba Ancestor tokens to complete the transition, so long as we get them back later.
It does seem like there is plenty of room for an eighth stage. Also, white mana is still left open. White mana can target white creatures, green creatures, Humans, Birds, Clerics, Merfolk, or Kithkin - those are all I can remember. I can't see anything that will work though. Too many mana producers are in the 1 or 2 CMC range, or green. It's too bad that Wilderness Hypnotist is a Wizard, as well.
Is Verdant Succession indispensable for this deck? It's really good, but it does mess up green for the end stages.
Edit: No wait, having copies of Hurkyl's Recall won't help, since resolving one copy will bring all copies of Vedalken Orrery back to our hand, and we need to wait for a trigger to bring Vedalken Orrery back. So it seems like we can have Thousand-Year Storm and Sphinx's Revelation.
If there is no maximum to the amount of damage your deck can deal, using any possible sequence of play, then the deck is illegal. So you can't just make a choice that prevents the deck from going infinite, the deck will still be illegal.
With Soul Foundry, we don't need to actually bounce or kill Godtoucher! It is enough to bring it from the graveyard/library into our hand, so that we can imprint it onto Soul Foundry. So Wirewood Herald will do the trick. I just noticed, though, that if we use the Herald to bring back Godtoucher, we won't be able to bring back the Herald as well. So I guess we can go back to using Verdant Succession, which will require rejuggling the end stage sequence. Using double Heralds plus Assembly Hall is another possibility.
I'm certainly interested in what we can do in Standard, although I'm not quite familiar with exactly which cards are in Standard, and it's something of a pain to keep checking which cards are in Standard and which aren't. So I'll let you take the lead Stakfish, and I'll contribute what I can.
Okay, some interesting interactions there. Seize the Day can get a lot of copies and create a lot of new combat phases, and each one can allow Stolen Identity to be cast twice. And then Stolen Identity can get two layers for Precursor Golem. (Seize the Day does not get two layers, since we have to resolve all the copies of Seize the Day before we actually get to process all the new combat phases and gain all those layers worth of new Golems.) So, if we feed this into Teferi, Temporal Mage / White Suns' Zenith / Ojutai Exemplars, we would wind up with one more layer then before, getting us to 2^^^^^^^^^^22 (10 arrows).
However, without Teferi and White Suns' Zenith, I don't see anything as powerful to do with Stolen Identity; we can create more Mizzium Transreliquats, which can turn into Doubling Seasons or whatever we need it to, but that's just the first layer. The other thing we can do with Seize the Day is to get combat phases we can use for Tilonalli's Summoner and Neheb, the Eternal. But this doesn't look as powerful either. Let's let C,D,E,I,X be the number of Cradle of Vitality's, Doubling Seasons, Essence Slivers, Intruder Alarms, and creatures that we have. (Of course we can turn all our Transreliquats into the appropriate creatures at the appropriate times.) Let T be the number of extra mana we spend on Tilonalli's Summoner. Then we get T*2^D new creatures, each of which triggers I alarms, each of which untaps X creatures, so we get X*I*T*2^D untaps in all. For each untap, we can tap it to deal P damage where P is its power; this triggers E Essence Slivers, each of which triggers C Cradle of Vitalities, each of which adds P*2^D +1/+1 counters to some creature, which can itself be tapped. So the power P of one creature tranfers to a power P*(E*C*2^D) to the next creature. This happens X*I*T*2^D times, so after the damage chain is complete we go from a creature of power P to a creature of power P*(E*C*2^D)^(X*I*T*2^D), and we get about that much life, our opponent loses about that much life, and we get access to about that much mana. Note that this is just multiplication, albeit by a relatively big number. Each combat phase we also get to cast Stolen Identity twice, so our number of creatures gets 3 layers worth if improvement (i.e. if we have X creatures before, we will get about X^^^X creatures afterwards), but the damage chain itself is just an exponential chain 2 levels higher, so it will not be fundamentally bigger.
So, as far as I can see this gets a smaller final damage number than before, although that could be fixed by readding in Teferi, Temporal Archmage and White Suns' Zenith.
Deedlit or anyone else who thinks they have an answer: I jump through a lot of hoops to make chorus a very potent mana generator, do u think I could possibly just skip many or even all of those hoops and just try to go super wide on pure token generation and rely solely on mana echos? It’s fun seeing what chains etc can do but I’m totally up for dropping inefficient coolness for more optimized lines.
Unfortunately yes, while the damage chain is really cool, it is not really worth all the cards that it takes to set up. As I mentioned earlier, the damage chain will create mana equal to an exponential tower one higher than the exponential tower describing the number of Doubling Seasons. This is not enough to make a difference in the higher recursive layers. To put things in somewhat simple terms, without the damage chain, casting a noncreature spell with X Rikus results in roughly X^^(X+1) (an exponential tower of height X+1) new token creatures after the entire process is resolved. With the damage chain, casting a White Suns' Zenith with the same resources will get you roughly X^^(X+2) (an exponential tower of height X+2) mana after the entire process is resolved. Will that affect the higher layers? Let's see: in the first scenario, we start with X Rikus. Casting one noncreature spell gets us Y Rikus, where why is more than X^^X but less than X^^(X+1). Casting one more noncreature spell will result in Z Rikus, where Z is more than Y^^Y but less than Y^^(Y+1), so it winds up in between X^^(X^^X) and X^^(X^^(X+1)). Note that the former is X^^^3, and the latter is much less than X^^^4 = X^^(X^^(X^^X)). Another iteration gets us between X^^(X^^(X^^X)) and X^^(X^^(X^^(X+1))), or between X^^^4 and X^^^5. For the second scenario, after the first White Suns' Zenith we will get between X^^(X+1) and X^^(X+2), which is between X^^^2 and X^^^3. After the second White Suns' Zenith we will get between X^^(X^^(X+1)) and X^^(X^^(X+2)), which is between X^^^3 and X^^^4. So in both cases, after N spells we wind up between X^^^(N+1) and X^^^(N+2), so the difference is not enough to be discernable from the perspective of triple arrows. In fact, the difference is a long way away from being discernable, since the difference is between the final number being X+1 or X+2, whereas we would have to go past X^^X to get to X^^^(N+2).
I hope that is at least somewhat understandable.
Deedlit: thanks for the clarification on the chains. I figured it might not have mattered but thank u for explaining it. When u where explaining the arrow adding in the layers of my deck I was curious in the RR layer. RR actaully gets 2 casts of CC for each copy resolving not just 1(1 from hand another 1 from grave before going back to exile). I didn’t know if that was accounted for but I figured there should have been a 2 in the math somewhere. Again many thanks
I was aware of the ability to cast Cackling Counterpart twice per copy of Runic Repetition, but, as above, it doesn't make a difference in the higher layers. The reasoning is the same as before. Casting X copies of Cackling Counterpart takes you from X to about X^^^^^^X. So, with 2 castings of Cackling Counterpart per Runic Repetition copy instead of one, we iterate the function that takes X to X^^^^^^(2X) rather than X^^^^^^X. In a certain sense, this is a MUCH more powerful function, since taking X to X^^^^^X is such a powerful function and X^^^^^^(2X) is applying that function twice as many times. But it is not significant from the viewpoint of 7-arrows. Iterating the function X^^^^^^(2X), we get X^^^^^^(2* X^^^^^^(2X)), which is bigger than X^^^^^^(X^^^^^^(2X)), but MUCH less than X^^^^^^(X^^^^^^(2X+1)). Iterating the function again, we get a number that is bigger than X^^^^^^(X^^^^^^(X^^^^^^(2X))) but much less than X^^^^^^(X^^^^^^(X^^^^^^(2X+1)))). After N iterations, we will get a number between a sequence of N "X^^^^^^" followed by a 2X, and a sequence of N "X^^^^^^"'s followed by a 2X+1. Since 2X and 2X+1 are both much less than X^^^^^^X, the resulting value will be greater than X^^^^^^^(N+1) but much less than X^^^^^^^(N+2). So the 2X at the 6-arrow level is insignifcant at the 7-arrow level.
Hope this helps, and good luck with improving your deck!
Deedlit - a small maybe inconsequential note on the initial layer or chains: if we point the outcome of that chain at biomancer the next wave will start at that level x doubling seasons. Also the life gain also effects the chains because Serra avatar is growing with each life gain trigger and that is growing the chains etc. I’m not sure it’s super substantial but it’s actaully growing faster than u think.
What you say is true, but it doesn't affect the growth rate too much; it's still exponential. Let's say we just finished a token creation of A Doubling Seasons. This will eventually create a Master Biomancer with roughly 2^[cA^3] power, where c is much less than A. (c is about (B+1)(C+1), where B is the number of Intruder Alarms and C is the number of Rowan Kenrith emblems.) Our life total will also be at the level of 2^(cA^3). We then proceed to make another token creation of Doubling Seasons, which will create about 2^A Doubling Seasons this time. If you want, we can also create a Serra Avatar, but this is going to turn out not to be better than another Doubling Season. So we start out with Serra Avatar with a power of roughly 2^(cA^3), and we can add +1/+1 counters via Master Biomancer, which adds 2^(cA^3) * 2^(2^A) counters. This is roughly 2^(2^A) since 2^A is so much larger than cA^3 for large A. We can add counters to all our new creatures, which gets 2^2^A for all 2^A of them, and this increases our life by roughly 2^(2^A). So our Serra Angel still winds up at roughly 2^(2^A). We can then start tapping creatures for our damage chain; as I said previously, we can tap (2^A)^2(B+1)(C+1) times, and each time we take the power P of the tapper and add (2^(2^A))P +1/+1 tokens to the target, so each time the power gets multiplied by 2^(2^A). So we wind up with (2^(2^A)) * (2^(2^A))^((2^A)^2(B+1)(C+1)) = 2^[(2^A)^3 (B+1)(C+1) + 2^A]. Note that adding 2^A at the end is a very small difference, so it is roughly 2^(c(2^A)^3) where c = (B+1)(C+1). So now our Master Biomancer tokens and life is roughly 2^(c(2^A)^3), our the same formula over our new Doubling Season total of 2^A. The next token creation will bump our Doubling Seasons to 2^(2^A) and our Master Biomancer to 2^(c(2^(2^A))^3). So our number of creatures will be an ever-growing exponential tower, and the Master Biomancer counters will be an exponential tower of height one more.
TLDR: Life total gains will grow so much more than anything else this game, Diublecast + bonus round instead of TYS.
Well, Doublecast + Bonus Round doesn't work well alone; we need a spell copier like Djinn Illuminatus to make it go. And, while Doublecast + Bonus Round + Djinn Illuminatus is better than just Djinn Illuminatus, it's not as good as Djinn Illuminatus plus two exile-for-retrieval spells. Again, each exile-for-retrieval spell cast implements an incredibly fast-growing function f(x), so rather than using Doublecast + Bonus Round + Djinn Illuminatus to increase this to f(3x), with two more cards we can implement f(f(f(x)), which is much greater.
By ETT's, do you mean cards like Praetor's Counsel? Wait, what do you mean that "ETT gets TT back 16 times and none of them are copied"? When you cast Praetor's Counsel, you will get many copies via Riku, Djinn Illuminatus, or Thousand-Year Storm, and each copy will fetch Timetwister from the graveyard.
30 copies of Praetor's Counsel is not that much. By the time you get around to casting Praetor's Counsel, you can get a gajillion copies of Thousand-Year Storm via all the token copies of Mirage Mirror we are creating througout the whole combo. And each of the Thousand-Year Storms triggers to create a gajillion copies of Praetor's Counsel. So that certainly seems a lot better. Of course, we can increase that a bit by adding Doublecast and Bonus Round, but it would be much better to add another Praetor's Counsel, since after the first Praetor's Counsel we can increase the number of Thousand-Year Storms and the instant/sorcery count tremendously, and then the second Praetor's Counsel will key off of those much bigger numbers. The numbers increase MUCH more than exponentially, and much more than you get from Doublecast and Bonus Round.
I don't understand your analogy. It's not like we can just add two cards for free. There is a 60 card limit, so we have to be sure there those two cards do the best job at increasing the final number. If you remove the 60 card limit, then sure, you can add everything and the kitchen sink, as long as things don't go infinite.
I don't think you get x^x. Doublecast and Bonus Round activate only when a spell is cast, as does Replicate. So say you cast Doublecast. You get X copies. You then cast Bonus Round. You get about X copies from Djinn Illuminatus and you also get X copies from Doublecast, for 2X total. Then you cast Timetwister, which gets X copies from Djinn Illuminatus, and 2X from Bonus Round, for 3X total. So it's not a big deal really. Even if it were X^X, that's not noticeable when you are dealing with numbers this large (of the many Knuth arrow variety).
It's true that adding Doublecast and Bonus Round will increase the final damage, no matter how small. But it would be better to use those card slots for adding more exile-for-retrieval cards, since those currently take X to 2^^^^^^^^^^^X, a much bigger improvement. Still, rather than just fill out the deck with exile-for-retrieval cards, it would be more interesting to look for cards that can extend the sequence, and therefore the number of Knuth arrows. Right now the deck ends the sequence with
Can we extend this to a sequence of five or more? That would be the really big improvement.
Edit: It's true that in a normal sense, if X is very large than (2/3)X is "much smaller" than X. And it's true that, as we continue the combo, the difference between our number starting from X versus (2/3)X will get bigger and bigger. But the point is, there are much stronger things that we can do instead of going from (2/3)X to X. For example, if we replace the cards that go from (2/3)X to X with cards that can go form (2/3)X to 2^{(2/3)X}, that will get us a much bigger number. And this time, when we continue the combo, the difference will again get bigger and bigger, but this time in favor of 2^{(2/3)X}.
In regards to this deck... it's a bit hard to explain if you don't understand Knuth arrows, but I will give it a try. So we know that casting Praetor's Counsel generates and incredibly powerful combo, taking X to some f(X) where f(X) is an incredibly fast-growing function. For instance f is much stronger than exponentiation, or repeated exponentiation, or anything even close to that. So let's say you have Praetor's Counsel along with Doublecast and Bonus Round. The latter two will get us 3X copies of Praetor's counsel, so we can generate f(3X). This is, in a normal sense, much bigger than f(X), so in a sense Doublecast and Bonus Round are doing a wonderful job. But if we replace Doublecast and Bonus Round with another copy of Praetor's Counsel, now we can cast the first Praetor's Counsel to get f(X), and another Praetor's Counsel to get f(f(X)). f(f(X)) is MUCH bigger than f(3X), since f(X) is much bigger than 3X. Even if 3X were X^X this would remain true. So just adding more exile-for-retrieval cards would be better.
Oh right, the Fork trick only works with cards that *target* cards in the graveyard, and we can't have Goblin Flectomancer. So scratch that idea.
I saw your second edit, see my previous edit to post #1841. Doublecast doesn't go infinite, but it doesn't help a lot. If we cast Doublcast, we can get X copies via Djinn Illuminatus and Riku of two Reflections. Then we cast some other spell, and get X copies via Djinn and Riku, and another X copies via Doublecast. So it's just X versus 2X, which hardly makes a difference. It's the same with Thousand-Year Storm, except the difference is even less, since we get more copies for the second spell than we get with Doublecast.
Edit: So, I haven't had any new ideas for the Chalice of the Void deck. We can borrow Stakfish's stage sequence to get seven stages for the Soul Foundry deck:
2 Psychic Battle
3 Cowardice
4 Brudiclad, Telchor Engineer
5 Bloodbond March
6 Broken Ambitions
7 Soul Foundry
8 Omniscience
9 Vedalken Orrery
10 Pull from Eternity
11 Izzet Guildmage
12 Karn, Silver Golem
13 Canal Dredger
14 Mimic Vat
15 Ray of Revelation
16 Skull of Orm
17 Mana Vault
18 Obelisk of Bant
19 Metallurgeon
20 Battle Cry
21 Rebuild
22 Goblin Dark-Dwellers
23 Boggart Mob
24 Godtoucher
25 Wirewood Herald
26 Verdant Succession
27 Engineered Explosives
28 Salvaging Station
30 Acorn Harvest
31 Smite the Monstrous
32 Thousand-Year Storm
33 Child of Alara
34 Tireless Mercenaries
35 Celestial Gatekeeper
36 Celestial Gatekeeper
37 Spellweaver Helix
38 Worldfire
39 Spider Spawning
40 Spider Spawning
41 Spider Spawning
42 Molderhulk
43 Divine Congregation
44 Bayou
45 Eureka
46 Mox Emerald
47 Polluted Dead
48 Frightshroud Courier
50 Ghosthelm Courier
51 Devout Chaplain
52 Royal Assassin
53 Simian Spirit Guide
54 Goblin Kites
55 Old Man of the Sea
56 Sea Snidd
57 Reign of Chaos
58 Xathrid Gorgon
59 Tribal Unity
60 Reforge the Soul
Edit: Stakfish, a question: Even if we can't get Chalice of the Void to work, is there any mileage can we gain from restricting zone changing, with Millikin / Myr Welder? For example, can Muzzio be saved?
Edit: Random thought. What if, in the Chalice of the Void deck, we replace Changeling Hero and Anaba Ancestor with something more restrictive, like maybe Boggart Mob and Mad Auntie? I guess I don't see how this would fix the problem; it would allow Panharmonicon back in, and we couldn't Champion Vedalken Orrery anymore, if that helps. Hmm, I guess Mad Auntie is a 3 CMC anyway, so we can't use that, at least not directly.
No wait, we have Changeling Hero Championing the Orrery, so that comes back and we can replay everything. But isn't this a problem? We can have Goblin Dark-Dwellers in our hand, and have Orrery on the battlefield and Smite the Monstrous copies (or Psychic Battle triggers, even if we don't have copies) on the stack, below the Child of Alara breakpoint. It looks like then we can keep replaying and bouncing the Dark-Dwellers to greatly extend the lower hyperstage. Am I missing something?
I think Verdant Succession will search for Bloodbond March, since that is the current name of the creature when it dies. It might be worth asking on the Rules forum.
Edit: the Mirrorwing Dragon / Smite idea would work for the gigastage I think, so if we had an idea that used lands to bring stuff back, we could combine the two.
For the ending layers, it will be better to have Consecrated Sphinx rather than Precursor Golem, since then we will be able to get through the deck much more quickly, and probably the last five Reforges will be able to access the whole deck. The first Reforge draws seven cards, of which four can be two copies of Spider Spawning, Spellweaver Helix, and Consecrated Sphinx. Then we still have three more cards, and the second Reforge allows us to draw 21 more cards, which should be enough to get going; if we need to, we can get the third Reforge cast by drawing another Spider Spawning. (It would be nice to get another copy of Consecrated Sphinx for the second cast, but I don't see an easy way to do that with the remaining three cards.)
Edit: Unfortunately, I have found a serious problem with the deck, and I don't know how to fix it. Each time we resolve Child of Alara or Worldfire, we eliminate all of our permanents, so we need to find a way to build it back up somehow. We do have all the floating mana that we can carry over, so the idea was the use this to rebuiild our enchantments. This was fine when we were using Allay to bounce Copy Enchantment to make more Dual Nature copies. But, now, creating more enchantments relies crucially on our Mimic Vats and Mirror of Fates. So we will only be able to create a relatively small number of enchantments, and the lion share of our mana is left floating.
Cogwork Assembler won't work because it targets and gives haste. If we could use Thousand-Year Storm, that should work once we resolve down to the next casting of an instant/sorcery, since the storm count keeps rising throughout a hyperstage/megastage. But it looks like this deck relies on not having any spell copiers around.
One idea is to replace Simic Keyrune with Obelisk of Bant, and then replace Mirrorworks with Vitu-Ghazi Guildmage. Unfortunately, that gives us access to white mana, which lets us destroy Centaur Safeguard without casting Acorn Harvest. Sundered Growth is too expensive when cast with Goblin Dark-Dwellers; adding Izzet Guildmage makes the artifact targeting too cheap, and Izzet Guildmage will be able to cast Hurkyl's Recall.
Using storm cards is a possibility, but I didn't see anything useful. Anything we can do with a lot of Goblins or Beasts?
Someone mentioned gaining experience counters; we could also gain energy counters, but I don't know what to do with either.
We can switch black mana with red mana if we so desire - the Simian Spirit Guide / Goblin Kites stage is nice, but it's worth considering all avenues.
Edit: Wait, how about:
2 Psychic Battle
3 Cowardice
4 Horobi, Death's Wail
5 Bloodbond March
6 Chalice of the Void
7 Mimic Vat
8 Omniscience
9 Vedalken Orrery
10 Mirror of Fate
11 Karn, Silver Golem
12 Millikin
13 Phantatog
14 Mirrorworks
15 Mana Vault
16 Simic Keyrune
17 Skull of Orm
18 Clockwork Gnomes
19 Goryo's Vengeance
20 Muzzio, Visionary Architect
21 Muzzio, Visionary Architect
22 Hurkyl's Recall
23 Goblin Dark-Dwellers
24 Changeling Hero
25 Anaba Ancestor
26 Engineered Explosives
27 Myr Welder
29 Acorn Harvest
30 Smite the Monstrous
31 Child of Alara
32 Centaur Safeguard
33 Verdant Succession
34 Spellweaver Helix
35 Worldfire
36 Spider Spawning
37 Spider Spawning
38 Spider Spawning
39 Titania, Protector of Argoth
40 Multani's Decree
41 Bayou
42 Eureka
43 Elvish Spirit Guide
44 Vastwood Animist
45 Grassland Crusader
46 Western Paladin
47 Frightshroud Courier
49 Ghosthelm Courier
50 Devout Chaplain
51 Royal Assassin
52 Phantasmal Mount
53 Old Man of the Sea
54 Sea Snidd
55 Slingshot Goblin
56 Xathrid Gorgon
57 Reality Spasm
58 Precursor Golem
59 Consecrated Sphinx
60 Reforge the Soul
Edit: Nope, keep forgetting about having too low of a CMC.
I guess we have no other way to bring back our enchantments, so we could drop Skull of Orm?
Ooh, that latest deck looks very nice! I don't see any immediate problems. One thing that I'm worried about: We have to make sure that we don't gain any Anaba Ancestor tokens by going through the megastage, but we also have to make sure that we don't lose any either. Otherwise, we lose a token or tokens each time we go to the higher hyperstage and back down again, so we won't get the full recursion going. Of course, it is okay to tap one or more Anaba Ancestor tokens to complete the transition, so long as we get them back later.
It does seem like there is plenty of room for an eighth stage. Also, white mana is still left open. White mana can target white creatures, green creatures, Humans, Birds, Clerics, Merfolk, or Kithkin - those are all I can remember. I can't see anything that will work though. Too many mana producers are in the 1 or 2 CMC range, or green. It's too bad that Wilderness Hypnotist is a Wizard, as well.
Is Verdant Succession indispensable for this deck? It's really good, but it does mess up green for the end stages.
Edit: I thought about maybe transitioning from Grassland Crusader into Hazduhr the Abbot, supplemented by Mirror Gallery, but Hazduhr could be brought back by Goryo's Vengeance.
Another possibility was to use Sphinx's Revelation supplemented by Thousand-Year Storm, into Druids' Repository for the final layers. But, I'm guessing that we need to avoid Thousand-Year Storm, in order for two Hurkyl's Recalls to require two Anaba Ancestor taps, to nullify two extra tokens we get from Engineered Explosives and Goblin Dark-Dwellers being brought back to our hand.
Edit: No wait, having copies of Hurkyl's Recall won't help, since resolving one copy will bring all copies of Vedalken Orrery back to our hand, and we need to wait for a trigger to bring Vedalken Orrery back. So it seems like we can have Thousand-Year Storm and Sphinx's Revelation.
Yeah, that seems to be a problem with Perpetual Timepiece. We can get by without losing any cards by replacing Cephalid Shrine with Broken Ambitions to keep our ability to mill, and then replace Perpetual Timepiece with some card that can shuffle cards in our graveyard into our library, like Canal Dredger.
With Soul Foundry, we don't need to actually bounce or kill Godtoucher! It is enough to bring it from the graveyard/library into our hand, so that we can imprint it onto Soul Foundry. So Wirewood Herald will do the trick. I just noticed, though, that if we use the Herald to bring back Godtoucher, we won't be able to bring back the Herald as well. So I guess we can go back to using Verdant Succession, which will require rejuggling the end stage sequence. Using double Heralds plus Assembly Hall is another possibility.
So how about:
2 Psychic Battle
3 Cowardice
4 Brudiclad, Telchor Engineer
5 Bloodbond March
6 Broken Ambitions
7 Soul Foundry
8 Omniscience
9 Vedalken Orrery
10 Pull from Eternity
11 Izzet Guildmage
12 Karn, Silver Golem
13 Canal Dredger
14 Mimic Vat
15 Ray of Revelation
16 Skull of Orm
17 Mana Vault
18 Obelisk of Bant
19 Metallurgeon
20 Battle Cry
21 Rebuild
22 Goblin Dark-Dwellers
23 Boggart Mob
24 Godtoucher
25 Wirewood Herald
26 Verdant Succession
27 Engineered Explosives
28 Salvaging Station
30 Acorn Harvest
31 Smite the Monstrous
32 Thousand-Year Storm
33 Child of Alara
34 Tireless Mercenaries
35 Celestial Gatekeeper
36 Celestial Gatekeeper
37 Spellweaver Helix
38 Worldfire
39 Spider Spawning
40 Spider Spawning
41 Molderhulk
42 Divine Congregation
43 Undiscovered Paradise
44 Eureka
45 Mox Emerald
46 Cloud of Faeries
47 Nectar Faerie
48 Goblin Skycutter
49 Flamestick Courier
51 Empress Galina
52 Mirror Gallery
53 Streambed Aquitects
54 Old Man of the Sea
55 Xathrid Gorgon
56 Tribal Unity
57 Sylvan Echoes
48 Sentry Oak
59 World at War
60 Reforge the Soul
I'm certainly interested in what we can do in Standard, although I'm not quite familiar with exactly which cards are in Standard, and it's something of a pain to keep checking which cards are in Standard and which aren't. So I'll let you take the lead Stakfish, and I'll contribute what I can.
However, without Teferi and White Suns' Zenith, I don't see anything as powerful to do with Stolen Identity; we can create more Mizzium Transreliquats, which can turn into Doubling Seasons or whatever we need it to, but that's just the first layer. The other thing we can do with Seize the Day is to get combat phases we can use for Tilonalli's Summoner and Neheb, the Eternal. But this doesn't look as powerful either. Let's let C,D,E,I,X be the number of Cradle of Vitality's, Doubling Seasons, Essence Slivers, Intruder Alarms, and creatures that we have. (Of course we can turn all our Transreliquats into the appropriate creatures at the appropriate times.) Let T be the number of extra mana we spend on Tilonalli's Summoner. Then we get T*2^D new creatures, each of which triggers I alarms, each of which untaps X creatures, so we get X*I*T*2^D untaps in all. For each untap, we can tap it to deal P damage where P is its power; this triggers E Essence Slivers, each of which triggers C Cradle of Vitalities, each of which adds P*2^D +1/+1 counters to some creature, which can itself be tapped. So the power P of one creature tranfers to a power P*(E*C*2^D) to the next creature. This happens X*I*T*2^D times, so after the damage chain is complete we go from a creature of power P to a creature of power P*(E*C*2^D)^(X*I*T*2^D), and we get about that much life, our opponent loses about that much life, and we get access to about that much mana. Note that this is just multiplication, albeit by a relatively big number. Each combat phase we also get to cast Stolen Identity twice, so our number of creatures gets 3 layers worth if improvement (i.e. if we have X creatures before, we will get about X^^^X creatures afterwards), but the damage chain itself is just an exponential chain 2 levels higher, so it will not be fundamentally bigger.
So, as far as I can see this gets a smaller final damage number than before, although that could be fixed by readding in Teferi, Temporal Archmage and White Suns' Zenith.
Unfortunately yes, while the damage chain is really cool, it is not really worth all the cards that it takes to set up. As I mentioned earlier, the damage chain will create mana equal to an exponential tower one higher than the exponential tower describing the number of Doubling Seasons. This is not enough to make a difference in the higher recursive layers. To put things in somewhat simple terms, without the damage chain, casting a noncreature spell with X Rikus results in roughly X^^(X+1) (an exponential tower of height X+1) new token creatures after the entire process is resolved. With the damage chain, casting a White Suns' Zenith with the same resources will get you roughly X^^(X+2) (an exponential tower of height X+2) mana after the entire process is resolved. Will that affect the higher layers? Let's see: in the first scenario, we start with X Rikus. Casting one noncreature spell gets us Y Rikus, where why is more than X^^X but less than X^^(X+1). Casting one more noncreature spell will result in Z Rikus, where Z is more than Y^^Y but less than Y^^(Y+1), so it winds up in between X^^(X^^X) and X^^(X^^(X+1)). Note that the former is X^^^3, and the latter is much less than X^^^4 = X^^(X^^(X^^X)). Another iteration gets us between X^^(X^^(X^^X)) and X^^(X^^(X^^(X+1))), or between X^^^4 and X^^^5. For the second scenario, after the first White Suns' Zenith we will get between X^^(X+1) and X^^(X+2), which is between X^^^2 and X^^^3. After the second White Suns' Zenith we will get between X^^(X^^(X+1)) and X^^(X^^(X+2)), which is between X^^^3 and X^^^4. So in both cases, after N spells we wind up between X^^^(N+1) and X^^^(N+2), so the difference is not enough to be discernable from the perspective of triple arrows. In fact, the difference is a long way away from being discernable, since the difference is between the final number being X+1 or X+2, whereas we would have to go past X^^X to get to X^^^(N+2).
I hope that is at least somewhat understandable.
I was aware of the ability to cast Cackling Counterpart twice per copy of Runic Repetition, but, as above, it doesn't make a difference in the higher layers. The reasoning is the same as before. Casting X copies of Cackling Counterpart takes you from X to about X^^^^^^X. So, with 2 castings of Cackling Counterpart per Runic Repetition copy instead of one, we iterate the function that takes X to X^^^^^^(2X) rather than X^^^^^^X. In a certain sense, this is a MUCH more powerful function, since taking X to X^^^^^X is such a powerful function and X^^^^^^(2X) is applying that function twice as many times. But it is not significant from the viewpoint of 7-arrows. Iterating the function X^^^^^^(2X), we get X^^^^^^(2* X^^^^^^(2X)), which is bigger than X^^^^^^(X^^^^^^(2X)), but MUCH less than X^^^^^^(X^^^^^^(2X+1)). Iterating the function again, we get a number that is bigger than X^^^^^^(X^^^^^^(X^^^^^^(2X))) but much less than X^^^^^^(X^^^^^^(X^^^^^^(2X+1)))). After N iterations, we will get a number between a sequence of N "X^^^^^^" followed by a 2X, and a sequence of N "X^^^^^^"'s followed by a 2X+1. Since 2X and 2X+1 are both much less than X^^^^^^X, the resulting value will be greater than X^^^^^^^(N+1) but much less than X^^^^^^^(N+2). So the 2X at the 6-arrow level is insignifcant at the 7-arrow level.
Hope this helps, and good luck with improving your deck!
All Suns' Dawn
Bound // Determined
Flood of Recollection
Ill-Gotten Gains
Nostalgic Dreams
Treasured Find
Vengeful Rebirth
Volcanic Vision
Wildest Dreams
Woodland Guidance
So that's another 40 cards we could add right there.
What you say is true, but it doesn't affect the growth rate too much; it's still exponential. Let's say we just finished a token creation of A Doubling Seasons. This will eventually create a Master Biomancer with roughly 2^[cA^3] power, where c is much less than A. (c is about (B+1)(C+1), where B is the number of Intruder Alarms and C is the number of Rowan Kenrith emblems.) Our life total will also be at the level of 2^(cA^3). We then proceed to make another token creation of Doubling Seasons, which will create about 2^A Doubling Seasons this time. If you want, we can also create a Serra Avatar, but this is going to turn out not to be better than another Doubling Season. So we start out with Serra Avatar with a power of roughly 2^(cA^3), and we can add +1/+1 counters via Master Biomancer, which adds 2^(cA^3) * 2^(2^A) counters. This is roughly 2^(2^A) since 2^A is so much larger than cA^3 for large A. We can add counters to all our new creatures, which gets 2^2^A for all 2^A of them, and this increases our life by roughly 2^(2^A). So our Serra Angel still winds up at roughly 2^(2^A). We can then start tapping creatures for our damage chain; as I said previously, we can tap (2^A)^2(B+1)(C+1) times, and each time we take the power P of the tapper and add (2^(2^A))P +1/+1 tokens to the target, so each time the power gets multiplied by 2^(2^A). So we wind up with (2^(2^A)) * (2^(2^A))^((2^A)^2(B+1)(C+1)) = 2^[(2^A)^3 (B+1)(C+1) + 2^A]. Note that adding 2^A at the end is a very small difference, so it is roughly 2^(c(2^A)^3) where c = (B+1)(C+1). So now our Master Biomancer tokens and life is roughly 2^(c(2^A)^3), our the same formula over our new Doubling Season total of 2^A. The next token creation will bump our Doubling Seasons to 2^(2^A) and our Master Biomancer to 2^(c(2^(2^A))^3). So our number of creatures will be an ever-growing exponential tower, and the Master Biomancer counters will be an exponential tower of height one more.
Well, Doublecast + Bonus Round doesn't work well alone; we need a spell copier like Djinn Illuminatus to make it go. And, while Doublecast + Bonus Round + Djinn Illuminatus is better than just Djinn Illuminatus, it's not as good as Djinn Illuminatus plus two exile-for-retrieval spells. Again, each exile-for-retrieval spell cast implements an incredibly fast-growing function f(x), so rather than using Doublecast + Bonus Round + Djinn Illuminatus to increase this to f(3x), with two more cards we can implement f(f(f(x)), which is much greater.
30 copies of Praetor's Counsel is not that much. By the time you get around to casting Praetor's Counsel, you can get a gajillion copies of Thousand-Year Storm via all the token copies of Mirage Mirror we are creating througout the whole combo. And each of the Thousand-Year Storms triggers to create a gajillion copies of Praetor's Counsel. So that certainly seems a lot better. Of course, we can increase that a bit by adding Doublecast and Bonus Round, but it would be much better to add another Praetor's Counsel, since after the first Praetor's Counsel we can increase the number of Thousand-Year Storms and the instant/sorcery count tremendously, and then the second Praetor's Counsel will key off of those much bigger numbers. The numbers increase MUCH more than exponentially, and much more than you get from Doublecast and Bonus Round.
I don't understand your analogy. It's not like we can just add two cards for free. There is a 60 card limit, so we have to be sure there those two cards do the best job at increasing the final number. If you remove the 60 card limit, then sure, you can add everything and the kitchen sink, as long as things don't go infinite.
It's true that adding Doublecast and Bonus Round will increase the final damage, no matter how small. But it would be better to use those card slots for adding more exile-for-retrieval cards, since those currently take X to 2^^^^^^^^^^^X, a much bigger improvement. Still, rather than just fill out the deck with exile-for-retrieval cards, it would be more interesting to look for cards that can extend the sequence, and therefore the number of Knuth arrows. Right now the deck ends the sequence with
Cackling Counterpart <- Runic Repetition <- Timetwister <- exile-for-retrieval cards
Can we extend this to a sequence of five or more? That would be the really big improvement.
Edit: It's true that in a normal sense, if X is very large than (2/3)X is "much smaller" than X. And it's true that, as we continue the combo, the difference between our number starting from X versus (2/3)X will get bigger and bigger. But the point is, there are much stronger things that we can do instead of going from (2/3)X to X. For example, if we replace the cards that go from (2/3)X to X with cards that can go form (2/3)X to 2^{(2/3)X}, that will get us a much bigger number. And this time, when we continue the combo, the difference will again get bigger and bigger, but this time in favor of 2^{(2/3)X}.
In regards to this deck... it's a bit hard to explain if you don't understand Knuth arrows, but I will give it a try. So we know that casting Praetor's Counsel generates and incredibly powerful combo, taking X to some f(X) where f(X) is an incredibly fast-growing function. For instance f is much stronger than exponentiation, or repeated exponentiation, or anything even close to that. So let's say you have Praetor's Counsel along with Doublecast and Bonus Round. The latter two will get us 3X copies of Praetor's counsel, so we can generate f(3X). This is, in a normal sense, much bigger than f(X), so in a sense Doublecast and Bonus Round are doing a wonderful job. But if we replace Doublecast and Bonus Round with another copy of Praetor's Counsel, now we can cast the first Praetor's Counsel to get f(X), and another Praetor's Counsel to get f(f(X)). f(f(X)) is MUCH bigger than f(3X), since f(X) is much bigger than 3X. Even if 3X were X^X this would remain true. So just adding more exile-for-retrieval cards would be better.
I saw your second edit, see my previous edit to post #1841. Doublecast doesn't go infinite, but it doesn't help a lot. If we cast Doublcast, we can get X copies via Djinn Illuminatus and Riku of two Reflections. Then we cast some other spell, and get X copies via Djinn and Riku, and another X copies via Doublecast. So it's just X versus 2X, which hardly makes a difference. It's the same with Thousand-Year Storm, except the difference is even less, since we get more copies for the second spell than we get with Doublecast.