Ahhh, I see. I'm not 100% sure that works, because the stack is getting very complicated here, but nothing jumps out at me as a clear problem, so let's see if there's any fix for it.
The first thing is, I wonder if this works to the same degree with the other option: cut Turncoat, and add in Tajuru Archer and Beastcaller Savant.
For clarity, the way this one works is: use an Engineered Explosives to kill Beastcaller, imprinting it on Mimic Vat and triggering Verdant Succession. Play Moggcatcher for Bloodbond March triggers, then make a token copy of Beastcaller, using the Archer's trigger to kill the Moggcatcher and make a hasty token. Then we shuffle the Beastcaller back in, and use the Succession triggers to get it back, which also bounces Moggcatcher. Critically, we can't use both triggers to get two hasty Moggcatchers, because of the severe timing restrictions involved.
There are two problems here: we have no way to get Tajuru Archer back after the megastage transition, and we only use up one Engineered Explosives in the same time frame. We could potentially solve all that by going back to the old Izzet Guildmage plan with Nylea's Disciple, but I'm not sure that plan actually works. Because Dark-Dwellers casts the instants themselves, not copies, I'm pretty sure we need some kind of [c]
Thousand-Year Storm[/c] effect to let us build the hyperstage, and all those effects go infinite when combined with Natural Order in the gigastage.
Failing that, we have to find some way to turn an Engineered Explosives into a way to get back Tajuru Archer in the megastage transition, without going infinite.
Hmm, we could throw in a third color, and have to crack an Explosives for 3 to destroy Tajuru Archer, which would waste an Explosives. That would nullify Centaur Safeguard, of course, so we need a replacement, but it could be a good way to solve those two particular problems.
Edit: Okay, so going with Tajuru Archer handles the problem of creating two Moggcatchers with one run through the combo. But, it still doesn't handle the problem of creating an unwanted Metallurgeon token. I believe you can do the same thing as what I described before: Create a stage for Metallurgeon, then each time you sacrifice Engineered Explosives to destroy Beastcaller Savant, you also destroy the original Metallurgeon, and can create a token copy of it, allowing you to extend the Metallurgeon stage. So I don't know how to handle this.
So, I had an interesting idea - let's say we wanted to go back to using Boggart Mob. We can target it using for example Godtoucher, but unfortunately Godtoucher also targets Child of Alara, so we can go through the megastage transition without spending the life. But here's a possibility - we could replace Mimic Vat and Horobi, Death's Wail with Soul Foundry and Brudiclad, Techor Engineer. So, instead of creating tokens by destroying them via Mimic Vat, we use Cowardice to send them back to our hand and imprint them on a Soul Foundry. Now, when we tap Godtoucher, we can target Child of Alara, but we can't destroy it.
It would be nice if we could now get rid of Mimic Vat, but unfortunately I don't see how we are going to create token copies of our enchantments. I had an idea that we could go back to using Splinter Twin and Crown of the Ages, but for now, let's just keep Mimic Vat in the deck.
For the moment, that still goes infinite, because it also gives haste to Mirrorworks copies of our artifact stage creature. I don't know if there's any way around that, but if there is, that's a very promising strategy!
With the infinite you discovered, if we can find a way to prevent copying Battle Cry: that way, we need a hasty copy, and to have the nontoken in hand, to continue. The problem is that the. I don't know how to build the stack up, since we can only resolve the non-copy card Rebuild. We can do it with the changeling tech, because each new Battle trigger can turn into one new spellcast, but that strategy has a host of other problems, too...
Hi,
I very loosely follow your progress here, and wanted to ask a question:
If you were to design and add a card to Magic in order to get to some new level of iteration, (omega^4, omega^omega, epsilon 0 etc) how 'unreasonable' would the card have to be? Could it look like an actual card that could exist and let you encode something like Beklemishev's worms?
Well, we are hoping to get our omega^4 deck working with no fake cards needed - I'm pretty sure there's a way. Getting to omega^5 seems quite difficult at this point, it might require several made up cards to make it work smoothly, although I haven't really put much thought into it.
As I said earlier in a discussion on the potential limits, I don't really know how to construct an omega^omega structure, at least not using the stack. I did however just think of a way to create an omega^omega structure using creatures on the battlefield, with +0/+X counters for various X.
So, we will make use of Thousand-Year Storm to keep increasing the number of times an instant or sorcery gets copied. So we will have an instant/sorcery that says something like:
"As an additional cost to cast this spell, remove a +0/+X counter from target creature you control, where X is at least 2."
"Put a +0/+(X-1) counter on that creature."
and an instant sorcery that says something like:
"As an additional cost to cast this spell, remove a +0/+1 counter from target creature you control."
"Create a token copy of that creature. For each counter on that creature, put a counter of the same type on the token copy."
And then, we create a deck that has the ability to cast those above two instants/sorceries as many times as we want, as long as we have creatures with +0/+X counters on them. Also, we need to be able to put a +0/+X counter on a creature for some relatively large X, but only a finite number of times.
This gets us to omega^omega in the fast-growing hierarchy. When you have a X creatures with one +0/+1 counter each (and no other counters on them), and the Thousand-Year Storm counter is at Y, we can cast the second spell X times, taking the counter from Y to Y+X. If we have one creature with two +0/+1 counters on it, then casting the second spell gets us about Y creatures with one +0/+1 counter each, so we can cast Y more spells and take the TYS counter from Y to about 2Y. So a creature with three +0/+1 counters will take Y to f_2(Y), a creature with four counters will take Y to f_3(Y) and so on. Next, for a creature with a single +0/+2 counter we cast the first spell, creating a creature with Y +0/+1 counters, so we get about f_Y(Y), or f_omega(Y). Then a creature with one +0/+2 counter and one +0/+1 counter can be targeted by the second spell to create Y creatures with one +0/+2 counter each, so we get f_{omega+1}(Y). Continuing in the fashion, a creature with two +0/+2 counters will take Y to f_{omega*2}(Y), a creature with one +0/+3 counter will take Y to f_{omega^2}(Y), a creature with one +0/+4 counter will take Y to f_{omega^3}(Y), and so on. So the whole structure is at the omega^omega level, and if we can recurse over that structure (say by having an ability that creatures a +0/+X counter, where X is say the number of creatures), we can get f_{omega^omega + alpha}(Y) for some smaller alpha.
Then, we could use +X/+0 counters to get up to omega^{omega*2}, or general +X/+Y counters to get to omega^{omega^2}, but it gets more and more complicated and contrived.
Looking at the above spells, the first doesn't generally do anything positive, while the second seems pretty strong. I guess it wouldn't be too hard to balance the spells, say by giving the first spell some positive effect (maybe generating mana or something), while the second can be nerfed by giving it a high mana cost or some drawback. The real problem is that Wizards has gone away from having lots of different +X/+Y counters, and everything is +1/+1 now. So we wouldn't get spells that dealt with general +0/+X counters. Still, the above spells seem like they could fit in a reasonable card game, if not our current state of MtG, rather than being totally contrived cards that are only designed to create a massive function.
As for encoding something at the level of epsilon_0, I have no idea how we would do that. Beklemishev's worms seems like the most likely possibility, since it doesn't rely on a tree structure or complicated arithmetic functions. But I don't know how we would implement the reduction procedure: if we use the stack to represent integer sequences, then the reduction procedure means resolving the stack until we find an ability representing a smaller number than the top ability of the stack; then we need to recreate the part of the stack we just resolved, except with the top ability decremented; then we copy that part of the stack X times where X keeps increasing. I don't really see how we can recreate the stack that we just resolved, unless it gets copied onto the battlefield or something. Or we could represent the integer sequence on the battlefield. But, since the battlefield is unordered, we need something to represent the order, like the toughness of a creature or something like that. But then the reduction procedure seems equally ridiculous. So this remains a pipe dream, for now.
For Omega^4, I believe all we need is a green 1 drop along these lines:
Weenieslaying Archer G
Creature - elf
When ~ enters the battlefield, deal 1 damage to target creature with flying.
1/1
I think that would solve our woes with Metallurgeon, and it even seems fairly likely to see print some day.
For something extensible, I don't know if it would work perfectly, but an enchantment that says something like "whenever a nontoken creature becomes the target of an ability, you may exile it. If you do, destroy target permanent that activated an ability targeting that creature this turn" or some such. I don't even know if that's possible in the rules, but when combined with the exile clause on Dual Nature, that could potentially get us up to omega^25 by letting us turn one upper-layer trigger into a targeting of a higher stage creature.
As for omega^omega.... God. Deedlit's idea already melted my brain a bit. I wouldn't know where to start.
In somewhat better news, I might have found a way out of our conundrum! If we go back to Scattershot Archer and Gratuitous Violence, we remove all the infinites, because no targeting and it's a one-drop. The problem is that it would also kill Horobi, which is a no-go. I'd thought that was a dead end because anything pumping Horobi would also pump SSG, but if we just forego the red Mana stage at the top, we can get it working with a Long-Forgotten Gohei!
I haven't pulled up a full version yet, but in principle that should still give us f_{w^4+w4+4}(x) at least. There's not much space either way, and it depends on whether the Scattershot plan saves Rust Tick, which I don't remember.
EDIT: Okay, I have a decklist, but it's a card over.
This list actually has the option to add back Simian Spirit Guide, because Wrap in Vigor can save Horobi from damage death without pumping spirits' p/t. We just need to find one cut from this list, and we're roughly back where we started before finding the last two infinites.
Also, re Beklemishev worms: If we were to actually try to do it, and I don't think it's a good means of allocating resources, I think the best way would be to build a variant of the Magic turing machine: have tokens of two different types, where their toughness corresponds to their position in the sequence and their power corresponds to their value. You could have two creatures with "whenever an A dies, make a B" and vice versa, and then have some effect that gives all A's -1/-1 and all B's +1/+1, and vice versa. Each time it resolves moves one tape forward and the other tape back, and transfers the last/first token on one to the other.
Get all those cards without using infinite-happy color/type hacking, and we'd be maybe 1% of the way to epsilon_0.
I really like this thought excercise, but unfortunately I don't have enough time to read through all the 72 pages of this discussion. Will you ever continue to work on your description in https://sites.google.com/site/deedlitsplace/ultracombo? Or is there a more recent description of the steps, stages and challenges so far?
At least it convinced me to finally join this message board again
I am really glad, that the current decklists do no longer seem to include effects like Grip of Chaos. I feel that cheating luck by always drawing exactly the right card is one thing, but sequntially targeting always exactly the right random target from amongst unimaginable number of available target is something else. It might be interesting to see if we could also keep track of the ballpark probability of this scenario playing out as desired. It would be great, if the probability still stays in "imaginable numbers" (that do not need fast growing hierarchies to express).
One question concering the challenge itself:
Do I assume correctly, that any possible infinite damage combo in the deck is prohibited, even if our "optimal luck" never reaches that state? i.E. if there is any imaginable way to create an infinite damage combo with the cards in the deck it is no longer legal?
Another thing about the mathematics that struck me as strange:
Is the usage of Omega in the fast growing hierarchy consistent with the definition of ordinals?
It is clear to me, how the concept of Omega introduced in the desrcription is consistent in itself and very powerful. But in the example
F_{\Omega}(64)=F_{64}(64)<F_{65}(64)
, Omega compares to be smaller than 65, and deffitely not bigger than all the nonnegative integers...
So in other words, the Omega in the fast growing hierarchy seems to introduce a new concept, which to me is not realy coupled with ordinals - except maybe for the ordinals notion of "next higher number" with Omega and Epsilon.
Can some math-savy person point me into the right direction where this is resolved?
Heh, the ultracombo article. When I started writing it, I had every intention of finishing it. But, as the gigastage deck started coalescing, I lost the motivation to complete a description of what would (perhaps) become an outdated deck. Maybe if this deck never quite comes together, I will write up the older version.
As for this version, we haven't started writing up anything for it, as it is still in the development stages. I can summarize it briefly I suppose.
The setup is a little different from the previous version. Like before, the basic mechanic is to generate more and more Psychic Battle and Bloodbond March enchantments, and the number of these enchantments are basically our "current number" throughout the combo. However, in this version we removed Dual Nature, since it causes certain problems (currently the problem is with Child of Alara I think). So to get lots of copies of enchantments, we destroy them (using Psychatog in the above deck), and then imprint them on a Mimic Vat to generate a token copy. Then we use Skull of Orm to bring the enchantment back so we can sacrifice it again. This is less efficient then Dual Nature, but that won't affect the final estimate.
The primary stage is similar to the previous version - we have an artifact creature (either Metallurgeon or Rust Tick) that functions as our stage resource, and the stage is built up with alternating Psychic Battle and Bloodbond March groups of triggers.
The hyperstage is the biggest difference in the new version. In the previous version, we had Spellweaver Volute in the hyperstage andSpellweaver Helix in the megastage - in this version, those two cards are bumped up to the megastage and gigastage respectively, and the hyperstage is what's new here. The new spell triggerer is Goblin Dark-Dwellers, which can cast an instant or sorcery of CMC 3 or less when it enters the battlefield. With Panharmonicon, it can cast multiple spells. So we use Battle Cry, or Goryo's Vengeance couple with Muzzio, Visionary Architect, to get lots of Metallurgeons or Rust Ticks; we use Rebuild to regain our hyperstage resource, but at the cost of losing all our stage creatures.
The hyperstage mechanism is actually pretty complicated, as we couldn't get anything simple to work out. So, Rebuild has to replenish our hyperstage resource (which will turn out to be Moggcatcher tokens). It does this by bringing Engineered Explosives back to our hand, so that it can be cast again with a counter, and sacrificed. (Note that if we just bring Engineered Explosives back from the graveyard to the battlefield, it won't get a counter and we can't use it properly - this is quite handy.) Sacrificing Explosives will destroy Scattershot Archer, which can then be imprinted on a Mimic Vat to create a hasted copy. (Engineered Explosives can be brought back from the graveyard using Muzzio or Salvaging Station, while Scattershot Archer can be brought back using Verdant Succession.) The Scattershot Archer can then be activated to destroy Moggcatcher and Strongarm Thug, with the aid of Dearly Departed, Abzan Falconer, and Gratuitous Violence. The Moggcatcher can be imprinted to create a Moggcatcher token, and our hyperstage resource is renewed; the Strongarm Thug can be imprinted to create a token copy, which along with Panharmonicon can bring back both the Moggcatcher and Strongarm Thug to our hand. The Moggcatcher can then be tapped to bring Goblin Dark-Dwellers from the graveyard, which triggers the casting of our cheap instants, including Rebuild to bring Engineered Explosives back to our hand again.
The megastage, like the hyperstage of our previous version, uses Spellweaver Volute as our spell triggerer, and it triggers on the casting of an sorcery. So we use Acorn Harvest as our sorcery (which has CMC greater than 3, so no conflict with Goblin Dark-Dweller), which we can flashback for mana (which we can get cheaply) and 3 life. So life becomes are megastage resource. The instant that renews our hyperstage resource, and the instant that renews our megstage resource but eliminates all of our hyperstage resource, are combined into one: Smite the Monstrous. When we cast Acorn Harvest, we get many copies of Smite the Monstrous via Thousand-Year Storm. Most of the copies can be used to bounce Goblin Dark-Dwellers, which can then be replayed to cast our cheap instants and build up the hyperstage. (Note: we can't rebuild the hyperstage all at once, rather it gradually gets built as it resolves, with the lower Smite the Monstrous triggers standing as placeholders for hyperstage layers until the eventually get resolved and replaced by Battle Cry/Rebuild.) A few more Smite the Monstrous can be used to bounce large creatures that we need to return to our hand. The last Smite the Monstrous is used to destroy Child of Alara, which destroys all nonland permanents, and therefore all of our hyperstage resources (Moggcatcher tokens), but also destroys Centaur Safeguard, which allows us to gain 3 life, renewing our megastage resource. Note that we can't use multiple copies of Smite the Monstrous to destroy Child of Alara and therefore Centaur Safeguard multiple times, because - hmm, I'm forgetting the exact way that works. Stakfish, could you go over that again?
The gigastage uses Spellweaver Helix to cast sorceries, which can only be triggered by a sorcery we have more than one of, so no flashbacking Acorn Harvest to trigger it. So only Spider Spawning can trigger it, which requires a black mana to cast it via flashback. The we get a Frightshroud Courier stage that produces black mana, and a few stages after that; the last deck gets us to around F_{w^4 + w5 + 4}, assuming it works properly.
As for the challenges the deck presents, there have been many. Having four different stage types in the main combo leads to a lot of possible conflict with one level potentially affecting another in undesirable ways. And the newest hyperstage is partcularly complicated; the more complicated, the greater the chance of a flaw or a hidden infinite. Probably the greatest lingering problem is the potential infinite that can come from the megastage and gigastage transitions potentially renewing lower level resources improperly. For example, the way the megastage transition is supposed to work is that we spend three life, go to a higher hyperstage, and gain three life back; but to do so we need to use up a minimal amount of resources from below the megastage transition so as not to go infinite. (Basically, we need to use a few Metallurgeon/Rust Tick triggers to set up the megastage transition). Unfortunately, passing to the higher hyperstage allows us to bring Engineered Explosives and Goblin Dark-Dwellers back to our hand, and keep them in our hand when we pass back down to the lower hyperstage. This allows us to add a couple Moggcatcher tokens, which more then compensates for a couple of lost Metallurgeons, so that goes infinite. So we need to find a way for the megastage transition to use up those extra uses of Engineered Explosives that we gain, and that has been plaguing us for a while. We may have solved it with the necessity to resolve Verdant Succession to gain certain green creatures back, but I'm not totally sure there isn't a hidden infinite somewhere.
Another problem is that Iijil has left, and he was the best one at finding problems and infinities in our prospective decks.
Stakfish, feel free to point out any further details that are worth mentioning.
Yeah, I also would prefer to use Psychic Battle over Grip of Chaos, so that the probabilities remain "reasonable". I had a discussion with Iijil over this, and he was of the opinion that we should just present the deck that had the maximum possible damage. I guess that makes sense. I think, if our deck winds up favoring Grip of Chaos, we would write up the article about that deck, but include an addendum on how things change if we want to replace Grip of Chaos with Psychic Battle.
So long as Grip of Chaos is not in the deck, there is really nothing that requires chance other than card drawing, and with Mirror of Fate we can arrange the library however we want to. So the probability of getting the combo off only includes the cards we draw up until we start using Mirror of Fate, so really it can be no worse (and in fact will be much better than) 1 in 60!, which I would consider firmly in "imaginable numbers".
About your question: Yes, any possible infinite damage combo is prohibited; I'm not sure what you mean by "optimal luck" never reaching that state, could you clarify?
I played around certain times with combos that would be finite if the opponent always acted in a way to keep the maximum damage down, rather than cooperate to go infinite; but Iijil and Stakfish seem to like the rules as they are.
Yes, the fast-growing hierarchy is consistent with the definition of ordinals. Now, F_w (64) is not greater than F_m (64) for all finite ordinals m, and cannot possibly be, since F_m (64) can be arbitrarily large. But, F_w (n), as a function of n, is faster growing than F_m (n) for any fixed m; we have F_w (n) = F_n (n) < F_m (n) for n < m, but once n passes m we have F_w (n) = F_n (n) > F_m (n). So past a certain point F_w (n) will always be greater. More generally, if we have two ordinals a < b < epsilon_0, then F_b will be a faster growing function than F_a. So the ordinals match up orderwise with their corresponding functions.
This might strike one as an academic point, since F_w (n) = F_n (n) doesn't seem like a major leap forward from the finite ordinals. But really it is. To see the big difference, look at what happens with F_{w+1} (n). For example, take F_{w+1} (4). This is equal to F_w (F_w (F_w (F_w (4)))). First we have F_w (4) = F_4 (4) ~ an exponential stack of 10's of height an exponential stack of 10's of height an exponential stack of 10's of height about 10^10^10^21. Big, but not that big given F_m on finite ordinals. But then we go to F_w (F_w (4)) = F_{F_4 (4)) (F_4 (4)) - now, that big number we just described goes into both the variable and the subscript of F, so now we are at an extremely high level in the finite hierarchy. Then we plug the extremely big result of that into the next F_w, so the extremely big result goes into both the variable and the subscript again. Then we plug that value into F_w one final time. Clearly, this is much bigger than an F_m (n) that we can easily describe without this iteration process. That's the power of diagonalization at limit ordinals.
That just about covers it, yeah. I want to note that in the older decks with both Psychic Battle AND Grip of Chaos, the luck factor was pretty negligible: as long as each Grip trigger never reselected the target to be one of a few critical nontokens out of the ever-growing mass of token copies, it didn't matter. It's the difference between "Grip has to hit this one thing out of countless millions every time" and "Grip has to not hit this one thing out of countless millions every time" that makes me feel more comfortable with it.
For the megastage, the reason we can't use multiple copies of Smite the Monstrous to destroy Child is because, while we can kill Centaur Safeguard, bring it back with Succession, then kill it again to gain 6 life, once we've done that we don't have any more copies of the Safeguard in our library to fetch with Verdant Succession. We just resolved two Child of Alara triggers in a row, so there's no way we can shuffle one back in with Mirror of Fate or Perpetual Timepiece, so when the next Succession trigger resolves, we'll fail to find and both our Safeguards will be stuck in the graveyard. We also don't have any other way to get it back yet: our other graveyard return mechanisms are Strongarm Thug and Bloodbond March, but it's not a mercenary, and we don't have any way to bounce it back to our hand and recast it: The first thing we have that can target Centaur Safeguard is Goblin Kites, which is several resources removed from anything we can generate at that point in the combo.
If you understand the concepts in those, all you need to get is how we use Mimic Vat, Cowardice, Horobi, Death's Wail, Bloodbond March, and Psychic Battle to turn creatures with tap abilities that can target themselves into stages, and you'll be able to look at any deck in this thread and at least have a vague sense of how it works. In particular, any time there's a big collection of cards in a hyperstage or megastage and such, try to match cards up to what parts of the steps lijil described they can accomplish. Even if you don't understand how our gigastage works just yet, you can pretty quickly figure out that Worldfire is supposed to delete all I.
I think you're spot-on with the challenges, though I imagine lijil will be back before long. The complexity of the hyperstage is a huge challenge, not only because it allows for so many more possible infinites but also because it doesn't leave much room for further stages. I think the ultracombo used about as many slots to get to the stages on top of the main structure as we do to get through the hyperstage alone, which is why it had 14 stages on top and we have 4-5. By far the biggest issue is the infinites, though. Especially without lijil's eye, it's been a slow slog to eliminate the ones we know about, and we may yet find even more.
On another note, it's a shame about the ultracombo article. I think one challenge that's limited the people reliably working on this to me, Deedlit, and at least recently lijil, has been a lack of accessibility to today's decks. I was interested in this challenge since early 2016, but after reading SadisticMystic's article, I went onto this forum and found decks that looked nothing like his and made no sense (wait, don't creatures that target themselves go infinite?). It was only when I reached a comment by Ijil on page 25ish explaining the hyperstage in algorithmic terms that I was able to put it all together. If you want to contribute to the project, you can't just read an article and start thinking, you have to first read it, then read about 70 pages of forum posts, many of which are dead ends. When I posted my standard combo on reddit, there was a lot of interest across the community, and a lot of people commented that they were following this thread or were interested in it. I'm hopeful that a finalized write-up for the... ubercombo? will get some new eyes on the deck who may find tricks we haven't discovered.
Even if we can't kill it with Explosives, we can use a Psychic Battle trigger below the transition to kill it and get a token. Then, we can use a saved Muzzio activation to get it back, and kill it again, making a second token. The next Bloodbond March trigger brings it back. We activate both the tokens, to add two Psychic Battle layers and a Bloodbond March layer, so now we have 1 more Psychic Battle layer than we had to start with. Then, we resolve one of those triggers to kill Rust Tick, and make a token.
Then, when the hyperstage starts, we use our first Muzzio activation to get it back, at which point we're back to our normal position, but we have one more Psychic Battle and Bloodbond March layer in the stage below it.
We can fix it by going back to Metallurgeon, or by forcing the hyperstage transition to use up a Muzzio activation.
Oh phooey... I guess being able to save Muzzio through the hyper stage transition is what causes the infinite. So there's currently no other setup for the main stage other than Metallurgeon?
If not, then it looks like the best we can do is to remove the Merfolk stage and end with World at War, getting to w^4+w4+4. I'm not seeing any cuts, although the need for both Salvaging Station and Goblin Welder is driving me nuts.
Hi, new to this whole shenaniganry, I'm trying to understand the ultracombo list, as it sounds like that's the starting point of the new thing, but I'm stuck at one point where I can't get my mental picture of the gamestate to agree with what y'all are describing.
Near the beginning, when you first cast the Drake, I understand this as still being with the original 4 dual nature "exile all tokens named dual nature" triggers on the stack. If that's correct, seeing as Allay hasn't tried to resolve yet, it's still on the stack. That being the case, how are you enchanting it with the copy of Spellweaver Volute after the 11th Drake trigger?
Additionally, even if y'all aren't in the mood for a full write-up of the current list, linking to the critical posts would be really helpful. There's a lot of referencing back to old systems or ideas without links or explanations, so reading backwards is really difficult, and due to the number of false starts and failed branches, it's also very difficult to try and read forward from the start. The two posts Stakfish recently linked to were helpful at the meta level, but some sort of ledger with "this post explains how X card works" would also go a long way to making this subject accessible
So, one issue with the Ultracombo write-up is that, because the deck involved has been in flux the whole time, the startup is no longer accurate even to the most current Ultracombo list. In that case, I think that Allay thing is an actual bug in the setup, which would reduce the amount of damage it can deal.
We also have not been good about explaining in simple terms how our new discoveries work, myself included. I'm gonna try to write out most of those concepts, but I'm not going to touch on up-arrow notation or the fast-growing hierarchy, that side of the math. For that, you should check out one of the write-ups.
So, basically every deck we talk about today, including the Ultracombo and the gigastage we're working on now, start with the same basic set of engine cards, which is the first section we put in the lists. The initial setup just tries to get them out while using as few resources as possible. Going through the list:
Omniscience lets us ignore casting costs from the hand, so we don't have to worry about getting white mana for Opalescence or black for Bloodbond March.
Vedalken Orrery lets us play things at instant speed, which is important because we're trying to build a massive stack of triggered abilities and it's nice to play spells in response.
Cowardice and Horobi, Death's Wail mean that any time we target a creature with a spell or ability, no matter what that thing would normally do, we instead either kill that creature or bounce it to our hand. If we want to bounce it, we stack the Cowardice trigger above the Horobi one. If we want to kill it, we do the opposite.
Psychic Battle lets us get extra mileage out of each ability: because our opponent's deck is all lands and we control the order of our library, we always win the clash, so each Psychic Battle lets us reselect the target of that spell or ability, which triggers Cowardice and Horobi again. So, for instance, if we had 5 Psychic Battles, Vedalken Orrery, a Coal Stoker, and a Prodigal Pyromancer token with haste, we could tap Prodigal Pyromancer, targeting Stoker. The first activation would bounce Stoker, we replay it, and get RRR. Then the first Psychic Battle trigger resolves, we retarget the ability to the replayed Stoker, and bounce/replay it again, going up to 6 mana.
Cephalid Shrine lets us control whether any given spell resolves: basically all our cards are singletons, and we can always refuse to pay 0 mana and get the spell countered. This is important, because sometimes we want to have access to a spell before all the triggers that happen when you cast it resolve. For instance:
Bloodbond March, especially when we create many copies, lets us cast a creature, get several Bloodbond March triggers, counter the creature, and use the first trigger to bring it back to the battlefield. It's just like if we cast the spell, but now, if it dies, all we have to do to get it back is wait until the next one of those Bloodbond March triggers resolves, and it will come back.
Mimic Vat is our main token-generating tool in the deck: Any time we need to make a copy of something, we can kill it, imprint it on an untapped Mimic Vat, tap the Mimic Vat to make a token, and then find some way to get the nontoken back on the battlefield. For instance, if it's a creature, we might transfer it from exile to the graveyard, then let a Bloodbond March trigger from when we cast it earlier resolve, bringing it back.
Mirror of Fate and Perpetual Timepiece, as long as we can keep making copies, let us pretend that the graveyard, exile, and our library are completely interchangeable: for instance, to get that imprinted creature back in our graveyard without imprinting something else on a tapped Mimic Vat, we could activate a Mirror of Fate to tuck that creature into our library, then tap a Perpetual Timepiece to mill it into our graveyard. For some past decks, we've instead used Izzet Guildmage and Pull from Eternity for this step, particularly when we want to make it harder to put things specifically back in the library: We just cast Pull at the very beginning, then keep copying it with Guildmage's ability as needed. It's the same basic principle.
Finally, we have some other mechanism for making tokens of cards we can't profitably make with Mimic Vat. In past decks, that was Dual Nature, but nowadays we use Mirrorworks to prevent infinites. That lets us make lots of copies of artifacts by bouncing and replaying them, so we never run out of new Mimic Vats, Mirror of Fates, or Perpetual Timepieces.
Right now, to copy enchantments, we do something like this: spend a green mana to flashback Ray of Revelation, which kills the enchantment. We imprint it on a new Mimic Vat, and activate it to make a token copy. Then, we sacrifice a Mirror of Fate token to shuffle both the enchantment and Ray of Revelation into our library, and tap a Perpetual Timepiece to mill them both. Then, we activate a Skull of Orm to return the enchantment from our graveyard to our hand, and replay it. Now we're right back where we started, except we have an additional copy of the enchantment, we've spent 16G, if you count paying for Mirrorworks triggers, and used up 4 artifact tokens: Mimic Vat, Mirror of Fate, Perpetual Timepiece, and Skull of Orm. We can also generate green and generic mana by bouncing artifacts, like Mana Vault and Simic Keyrune. While it's expensive to do that at first, once we've made enough copies of Psychic Battle this way, we can do this many, many times from just one ability that reads "target artifact". That also means we can't use an enchantment as a limiting factor later, because we can just use some artifacts to make more.
The other thing that threw me when I was getting started was how token stages work. So, let's say we're targeting artifacts with Rust Tick. When we activate Rust Tick's ability and get a lot of Psychic Battle triggers, we can use each trigger to do one of three things: we can bounce another artifact and replay it to make token copies with Mirrorworks, we can bounce the nontoken Rust Tick and replay it, giving us a big stack of Bloodbond March triggers, or we can kill the nontoken Rust Tick, imprint it on a Mimic Vat, and make a new hasty token copy. But if we do that, it's stuck in exile. The only we we have to get it back, at least without using something higher up, is by resolving a Bloodbond March trigger. But we can't make new Bloodbond March triggers to do it, because that requires casting it and we can't cast Rust Tick from exile. So we have to resolve down until the top of the stack is a Bloodbond March trigger from Rust Tick. That in turn requires that we cast it earlier, which means we bounced it with a Psychic Battle trigger below THAT.
So the end result is that, any creature that can tap to target itself and also something we need can make this giant stack of alternating batches of Psychic Battle and Bloodbond March triggers, where each one feeds into the other. When we run out of Psychic Battle triggers at the top of the stack, we use the last one to kill Rust Tick, make a new token copy with Mimic Vat, and bring it back with the first Bloodbond March trigger below it. When we run out of Bloodbond March triggers in that batch, we just use the top Psychic Battle trigger below it to bounce Rust Tick and replay it for more Bloodbond March triggers. Each different batch of triggers on the stack is another layer, so with N Rust Tick tokens, we get N recursive layers (well, 2N, but we round down for convenience). For instance, to match the number from the old Megacombo, we would only need to make 408 hasty Rust Tick tokens. That closes off artifacts as a resource we can use to limit ourselves later.
Two important things: the only way we have of giving anything haste is Mimic Vat, so the nontoken Rust Tick can't do anything on its own. And because we can't keep making Bloodbond March batches after killing our Tick, we can't build a loop. Put another way, to make a new Rust Tick, we need a Psychic Battle and a Bloodbond March trigger next to each other. We can only use one Psychic Battle trigger per batch, and each batch costs one Tick activation, plus the cost of a Bloodbond March trigger below it. That came from a separate Tick, but we can use each one, so think of that as costing 1/n, where n is the number of Bloodbond March triggers that activation made. So to get 1 Rust Tick back out, we have to spend 1+1/n Rust Ticks. The difference is tiny, but enough to make it so we can't loop.
Hyperstages, megastages, and gigastages all basically work the same: you spend some resource (a token, 3 life, a black mana) to put a bunch of triggers on the stack. Most of those can generate a lot of the next resource down (the hyperstage makes lots of Rust Ticks, for instance), but the last one lets you destroy all of the resource you generated to make a new, replacement one. That deletion step is important, because otherwise you can save a Rust Tick until lower down and use it to pay for the costs to keep going, and go infinite. Because that's not something you can just make with one ability, each one of these casts some subset of instants and sorceries as its trigger. Our hyperstage uses a token creature that can tap to make Goblin Dark-Dwellers enter the battlefield, which in turn lets us cast instants with converted mana cost 3 or less as a trigger. Not sorceries, I'll get to that later.
For instance, if instead of using Rust Tick at the bottom we used Metallurgeon, we could have the hyperstage start casting Battle Cry, untapping all the token copies we made for much bigger stages. Then, when we need to delete all our Metallurgeons, we would instead cast Rebuild, which would kill all our tokens, bounce Vedalken Orrery which is important so that we can't do any trick stack shenanigans in the middle, and also some artifact that will let us generate more of our resource, but can't otherwise be reset. We use 0-mana artifacts, which we can't bounce with Cowardice: Cowardice only works on creatures, and our artifact-animating spells use converted mana cost to set toughness, so a 0 mana artifact becomes a 0/0 creature and dies. In the past, the hyperstage used mana, so we bounced a mox. The new version uses a token, so we bounce Engineered Explosives, which we then crack to kill some creature that lets us regenerate our hyperstage. We've tried both having it directly kill the creature, and having it kill something else that can somehow generate a new token copy. Right now, we do the latter, but I have hopes that we can get the former working. At the moment, this step closes off white creatures (can untap with Battle Cry), goblins (we can search them out easily to replace them), humans (that's how we specifically target our hyperstage creature, Moggcatcher, creatures with flying (we target humans by giving them flying, because there isn't a convenient creature that can just target a human), and creatures with +1/+1 counters (we give humans flying by giving them a +1/+1 counter, then giving creatures with +1/+1 counters flying). Engineered explosives also closes off creatures with converted mana cost less than or equal to the number of colors of mana we can generate before reaching them in our list, because we can kill them with Explosives instead. 3-drops, however, are always safe, because even if we can kill them with explosives, doing so would also kill our Mimic Vats so we can't imprint them.
The megastage keys off of instants of any cost, not just 3 or less. It uses Spellweaver Volute to make it so, any time we cast a sorcery, we get many copies of some instant that lets us generate more copies of the token we use in the hyperstage. Generally speaking, anything that can target the token, the intermediate creature we use to make copies of it, or Goblin Dark-Dwellers itself is fair game here. That's also why we can't use sorceries in the hyperstage, or have any sorceries with cmc 3 or less in the deck: otherwise we could cast a sorcery with Dark-Dwellers, which triggers volute, which lets us replay Dark Dwellers, which lets us trigger Volute again, etc. The only sorcery we can set this off with is by flashbacking Acorn Harvest, which costs 3 life.
Then, to delete all our hyperstage creature (Moggcatcher at the moment), we use the same instant to kill Child of Alara. That destroys our Orrery, our Omniscience, all our enchantment copies (though we keep our mana), our hyperstage and stage tokens, and is also the only way so far to kill Centaur Safeguard. The death trigger gains 3 life, but we also get a trigger to search our library for a card with the same name and put it directly onto the battlefield, via Verdant Succession. We can't respond to that trigger, because we can't save Vedalken Orrery, but we run two copies, so we just alternate which one is on the battlefield and in the library/graveyard/exile. This also means that we can't have access to 3 colors of mana at this point: even if it kills Mimic Vats, we could keep playing Explosives for 3 and cycling between the Safeguards to gain life and go infinite. We have a workaround to allow 3 colors, but it's janky and hard to make the gigastage safe afterwards. Right now, we use Smite the Monstrous, so past this point any creature whose power can be boosted to 4 or greater is unsafe.
The gigastage keys off black mana, and uses sorceries as its effects. We cast the sorceries with Spellweaver Helix, which can imprint multiple cards thanks to Panharmonicon. We flashback Spider Spawning while the second copy is imprinted on a Helix, and get to cast both a spell that gains life (Archangel's Light, for instance), and Worldfire as the reset. As a general rule, the last two of the big stages (or only two) will either start with a mana-based stage and finish with a life-based stage, using Worldpurge to clear all permanents and empty the mana so you can't save it, or start with a life-based stage and finish with a mana-based stage, using Worldfire to clear all permanents and hard set your life total to 1.
Either way, the thing that sets these cards apart is they remove any permanents, not just nonlands. So we use Worldpurge to get lands that gain life (like Radiant Fountain) off the battlefield, then we replay them to gain the life that we paid into the gigastage back. With Worldfire, we just use a land that produces black mana: Bayou usually so that it can also help cast Eureka at the very beginning.
The rest of the cards in the mega- and gigastage are there to make sure we can get our other permanents back after we blow up the world. That's extra important for Worldfire because we can't save them in our hand.
After that, we spend the rest of the combo trying to fit as many stages in as possible. While there are some exceptions (if it's not itself a stage creature, just an enabler that helps connect one stage creature to another, it can have a cmc we can reach with Engineered Explosives), those stages have to be built on creatures with converted mana costs of 3, 4, or 5+, with 4 not being allowed once we allow a fourth color of mana. They can't be white (or Battle Cry untaps them) or green (Verdant Succession) makes them too easy to get back out). They must have power less than 4. They can't be humans, goblins, have flying, or use +1/+1 counters. And each stage adds a new restriction.
For instance, we start with a Zombies stage to generate black mana. Then we use a red mana stage that also targets creatures with toughness 2 or less. Then we use a merfolk stage. Then we use Old Man of the Sea to rule out creatures with power 2 or less, so all remaining stage creatures must have power exactly equal to 3. Then we wrap up with Xathrid Gorgon.
In general, we keep adding stages until we either run out of deck slots or run out of stage creatures (different decks hit different limits first). After that, we try to add layers that generate lots of that last stage creature. Past decks have used Reality Spasm, which can untap the Mimic Vat with the creature imprinted, but right now we use Tribal Unity, which pumps all our Old Man of the Sea copies until they're big enough to target Xathrid Gorgon, and is more efficient.
Depending on how many slots are still open, we either end with World at War or Words of Wisdom. If we have more space, we find some way to turn a combat step into a lot of Tribal Unity (for instance, one white mana lets us play Sphinx's Revelation for many copies with Thousand-Year Storm, each of which can draw Tribal Unity, and we get lots of white mana each attack step with many copies of Druid's Repository), then cast World at War as many times as possible to get lots of combat steps. Because World at War won't do anything after we leave our first postcombat main phase, we can't use those extra combat steps to feed more World at Wars, so that's where we run out of steam.
If we don't have the space for all that, we use Consecrated Sphinx to turn our opponent drawing one card into us drawing many cards two at a time, each of which can let us recast Tribal Unity. That's why our only card draw spells make each player draw a card: there's no way to refill our opponent's deck, so we can only do that at most 53 times. Depending on how easy it is to set everything up, we either use Reforge the Soul, which we can usually cast 4-5 times before it would kill our opponent without dealing any damage, or Words of Wisdom, which is much more efficient. I'm not sure exactly how the ultracombo's top layers worked, but I think it was roughly similar.
Deedlit, it might be a good idea to add links to this comment, as well as yours on the first stage and lijil's on the hyperstage, and any others you know about that I don't, to the OP as a starting point.
In other news, I've found at least one cut we can make to the deck, as long as we keep Academy Rector around: Skull of Orm! We can make token copies of green enchantments just fine (kill them, make token with a vat, Mirror them to the library, search them out with Succession), which is enough for the bottom stage: we can just copy Bloodbond March. Then, we can kill Academy Rector to make copies of nongreen enchantments later on.
Though actually... how are we getting Rector back now? Ugh. That setup may not work anymore.
Very nice summary. I will definitely link it in the OP when I have time, right now I am abroad without a lot of time, and unsure of how to copy post links on mobile. But putting important posts in the OP is something I definitely should have been doing a long time ago.
Skull of Orm looks like a good cut! As for fetching Academy Rector, we can just use Misery Charm, can we not? That will allow the fifth stage back in, getting us to w^4 + w5 + 4.
Concerning the problem FireRogue517 mentioned, there was indeed an error with the early setup, which came about because I was greedy and tried to squeeze in another couple of copies of Dual Nature by having Copy Enchantment copy Dual Nature at strategic points. The additional Dual Nature means one more Dual Nature token is created, but when we bounce the Copy Enchantment (which is copying Dual Nature) card, we trigger the Dual Nature destruction abilities. I believe there was one point where doing this is okay, but there was another point where it was not. That problem could be easily fixed by simply not having Copy Enchantment copy Dual Nature at the wrong time; this will cost us a Dual Nature token, but not a big deal. Of course, the gigastage deck doesn't currently have Dual Nature in it, although perhaps we should keep an eye for its possible inclusion whenever it may become legal, since it may be more efficient.
I have updated the OP with links to a few of the explanatory posts.
EDIT: I've been wondering whether the "target artifact" combos like Arcum Dagsson or Goblin Trashmaster could be made to work after all. They would certainly go infinite in the old version of the combo, but in this new version we have a lot of new moving parts, and maybe those can't be refreshed as easily as the artifacts. But I'm not sure.
If it still goes infinite, then I think we can still make it work by getting rid of Mirrorworks. Just replace Mirror of Fate and Mirrorworks with Izzet Guildmage and Pull from Eternity, I think. That resolves the problem of requiring more Psychic Battle triggers of our stage artifact, since we will need lots of mana for the stage transition and one copy of Mana Vault and a Keyrune won't be enough. However, we may have the Muzzio problem of being able to bring a copy of whatever we are using to target/sacrifice an artifact below the hyperstage transition, and getting an extra use out of them. Stakfish, do you know an artifact combo that would be safe from this happening?
EDIT: It just occurred to me that getting rid of Mirrorworks can also solve the problem we had with the Soul Foundry deck. That deck also used Muzzio, so we have to switch that out as well, but perhaps we can squeeze out an extra stage or two with that deck.
Hi guys. Been working on and off on this project for about a month now. It’s kinda become my low key obsession as of late. I’m not going to be posting a deck list just yet, but I should be shortly. I have been doing most of my work entirely in the dark after hearing about this project a few years back. It’s beem pretty fun just seeing how creative I can be and how important every card slot really is. Part of my reason for not posting yet is that I want to be sure I’m actually bringing something worthy to the discussion. I’m going to do a full read through of the 70 or so pages of this thread to be sure I’m doing things a uniquely as I think I am. Also I want to have a primer/guide of sorts for my list so that once I post it I can also explain how it works. In some ways I think it’s simpler but the details matter and these type of projects can get messy to try to explain.
I’ll be the first to admit that I won’t know if my sequencing can be improved on. The numbers just scale so fast it’s too difficult a task for me to try to figure out if one method is scaling any faster than another. But I’m hopeful that I can get a few more sets of eyes looking at my ideas, that maybe we can find an optimal sequence or configuration.
I’m going to try to have my list and guide finished, and posted, by the end of this coming week. Till then, happy enormous number hunting!
Yeah, so it’s turning out to be far more work to write my primer than I thought. I worked on it for almost 10 hours yesterday. I’m actually a bit worried it’ll be too big to post. It’s a 48k sized document, just as a text file currently, and I’m still not quite finished writing it yet. Obviously I’ll have to clean it up formatting wise etc, but yeah, she’s huge for sure.
Just a quick little preview of sorts and a bit of history on me and projects like this. I actually found this 60 card challenge after I started digging around the net to see if anyone was doing a challenge similar to one I had made up myself. I wanted to see, in an edh legal environment, what I could do with 7 cards without going infinite. My challenge was strictly looking for number of objects in play, so i didn’t need a haste enabler to attack or anything. I just wanted to see how much stuff could I put on board with a full starting hand. Mana reserves could be arbitrarily large as long as it didn't allow me to go infinite.
So my 7 cards ended up being:
Riku of two reflections
Opalescence
Parallel lives
Parallel evolution
Rites of replication
Radiate
Mystic retrieval
It costs about 60 mana to go all the way though the full sequence if we start with nothing in play.
So the sequence is:
Play Riku
Play opalescence, copy with Riku
Play parallel lives, copy with Riku, get 2 more token lives.
Cast evolution, Riku it. Let both of these fully resolve.
Recast evolution from the yard, Riku it again, let these resolve.
So me and a friend actually did the math up to this point once. We figured that we have a number of permanents in play that is represented by a number that was around 35(ish) million digits long. That's pretty decent for only 4 cards I'd say.
So we continue on by casting rites kicked, targeting lives, and Riku it. Let the copy resolve but then cast radiate, targeting the original, and then Riku copy the radiate, also targeting the original rites. This will be incredibly complex to resolve as the many rites copies will resolve independently and influence the next wave coming behind it. Also each radiate will make a larger wave if we cast/stack things correctly.
So let all that nonsense resolve. We have an empty stack and 1 card left in hand.
We cast mystic retrieval targeting rites or radiate, then Riku copy it to target the other, and pick them both back up.
Then do the rites/radiate thing again just as we did before only far more powerfully this time around.
Again back to empty stack, no cards in hand, but I'm not quite done just yet.
We flash back retrieval from yard, and Riku copy it, to get back rites and radiate one last time.
Again we do the rites/radiate thing once again. We let it all resolve and we are finally finished.
So I invented this project at least 3 years ago. I’ve had my head pretty well wrapped around large, finite, number generating for quite some time. I’ll be the first to admit my understanding of the notation need to express this stuff is awful, but from a conceptual standpoint I can at least grasp what is going on most of the time. Stuff like this is just the tip of the iceberg with my 60 card variant, but it’s a good proof of concept that I can proficiently take small starting resources and make egregiously large outputs without going infinite.
Hopefully I can still get my list/primer posted by the end of the week.
edit 1: cleaned up the spelling and general sloppiness.
One minor correction: You can't copy Opalescence with Riku, but I imagine that is just a typo.
The number you get after four Parallel Evolutions is a lot more than 35 million digits long:
After the first Parallel Evolution, you copy the two Parallel lives tokens, and each copy gets multiplied by 2^3 (since you have 3 Parallel Lives total) so you wind up with 2 + 2*2^3 = 18 Parallel Lives tokens.
After the second, you get 18 + 18 * 2^19 = 9437202 tokens total.
After the third, you get 9437202 + 9437202 * 2^9437203 ~ 1.42 * 10^2,840,888
After the fourth, you apply the formula one more time to get more than 10^10^2,840,887 Parallel Lives tokens.
Next comes the Rites and Radiates. each copy of Rite will add another "10^" to the exponential tower (the highest exponent will drop by an infinitesimal amount each time, but it will never dip below 2,840,887), and the first Radiate creates more than 10^10^2,840,887 Rites, so you will wind up with more than an exponential tower of 10^10^2,840,887 10's. In Knuth arrow notation, this is written 10^^(10^10^2,840,887). (More generally, a^^b is defined as a^(a^(...(a^a)...)) with b copies of a.) Similarly, the second Radiate will create more than 10^^(10^10^2,840,887) copies of Rite, so we will get more than 10^^10^^(10^10^2,840,887) token copies in the end. Since we wind up with six copies of Radiate in total, the final number will be more than 10^^10^^10^^10^^10^^10^^(10^10^2,840,887) token copies. We can simplify this with triple arrow notation: a^^^b = a^^(a^^...(a^^a)...) with b copies of a. So the final number is more than 10^^^7 but less than 10^^^8.
If I may make a suggestion, we could improve the number by replacing Riku of Two Reflections with a spell copier that we can have multiples of, like Swarm Intelligence. This would mean we don't get copies of Parallel Lives to start with, so casting Parallel Lives early on doesn't help. So perhaps we could replace that with [c]Clone Legion. We'll get only two copies of Clone Legion; the first will take us to 27 Parallel Lives and Swarm Intelligences, the second to 3623878683 each. That is a lot less than before, but now look what happens with the Radiates; The first cast gets copied 3623878683 times so we wind up with more than 10^^^3623878684 Parallel Lives and Swarm Intelligences. We then cast Radiate two more times, so we wind up with more than 10^^^10^^^10^^^3623878684 creatures, or between 10^^^^4 and 10^^^^5 creatures in the end.
Another improvement: Replace Mystic Retrieval with Bound // Determined. We can only cast Bound once, but since it is an instant, we can cast it while Rite of Replication is still on the stack. So we cast it after all the Radiates resolve, but while the original Rite is still on the stack. I just noticed that we can resolve the copies of the original Rite before we start resolving Radiates; so after the Rites resolve we will have more than 10^^3623878684 Swarm Intelligences, then the Radiates resolve and we go to 10^^^10^^3623878684 copies. Then we cast Bound, getting more than 10^^^(10^^3623878684) copies, and each one can fetch Radiate and recast it, increasing the final number to 10^^^^(10^^^(10^^3623878684)) creatures.
So, getting back to the gigastage deck, I was examining again the idea of switching out Mimic Vat for Soul Foundry. Unfortunately Soul Foundry does not grant its created tokens with haste, so the idea is to add Brudiclad to give tokens haste. This in turn runs afoul of artifacts because of Mirrorworks, so we want to remove that. That means that we will have trouble using Mirror of Fate, so we go back to Pull from Eternity and Izzet Guildmage.
With those changes in hand, we bring in Godtoucher to bounce Boggart Mob. Godtoucher can also target Child of Alara, but now we can only bounce it back to our hand, which does not trigger the destruction of permanents. So I think this is safe.
So good news. I’ve finished a rough draft of my guide/primer. Bad news, it’s a really rough draft. Lots of spelling errors etc I’ll need to fix and other general sloppiness I’ll need to clean up. But it’s complete. If I add anything it’s just for flavor sake or very minor details. I’m gonna be pretty busy the next day or two but I’m hopeful I can maybe get it posted by Thursday afternoon or maybe Friday at the latest.
Glad you enjoyed the challenge. It’s been a few years since I looked into it tbh. I was thinking about it while I was at work and I’m pretty sure these 6 cards would destroy my old 7 handily. It only works with a set amount of mana so let’s say it’s the same as my original list used up, 60.
So
Opalesence
Doubling season
Thousand-year storm
Rite of replication
Radiate
Reiterate
Not sure you even need 7 with this list. 60 mana gets pretty insane here.
Okay, so you can cast the first five spells, then cast Reiterate six times with buyback.
After casting the enchantments you cast Rite of Replication (unkicked, so that we can cast Reiterate the most times), which doesn't get copied. We can choose to target either Doubling Season or Thousand-Year Storm; I think it makes more sense to target Thousand-Year Storm, so that Radiate will make copies of Doubling Season, which we need to do in order to get exponential growth. Then you cast Radiate, which gets one copy from Thousand-Year Storm. That copy creates one copy if Rite of Replication, which targets Doubling Season. So we create two token copies of Doubling Season.
We don't want to resolve either Radiate or Rite, since we need to copy them. So we cast Reiterate next, with buyback. The Thousand-Year Storm triggers, creating two copies of Reiterate. So we get three Reiterates total, and each time we create a copy of Radiate. The next Reiterate will create three copies of Reiterate from Thousand-Year Storm, then 4,5,6,7. So we get a total of 3 + 4 + 5 + 6 + 7 + 8 = 33 Reiterates in total.
The first Radiate will target the three Doubling Seasons, getting us to 3 + 2^3 = 11, then 11 + 2^11 = 2059, then 2059 + 2^2059 ~ 6.6 * 10^619 Doubling Seasons.
The second Radiate will target all 6.6 * 10^619 Doubling Seasons, so we get more than 10 ^^ (10^619) > 10 ^^^ 2 Doubling Seasons in the end. Then the third will get more than 10 ^^ 10 ^^ (10^619) > 10 ^^^ 3 Doubling Seasons, and so on, until the 33rd generates more then 10 ^^^ 33 Doubling Seasons.
That's more than the old 7, but less than the improvements that I mentioned. The major problem is that we aren't getting more Thousand-Year Storms. So I guess it makes sense to use one of the Reiterates to copy Rite of Replication rather than Radiate, so that we can get both enchantments going.
So, let's go back to the first casting of Reiterate. We don't need more Thousand-Year Storms until the next Reiterate is cast, so let's use the first two Reiterate copies to copy Radiate; that takes us to more than 10 ^^ (10^619) Doubling Seasons. Then we use the original Reiterate to copy Thousand-Year Storm, which creates 10 ^^ (10^619) Thousand-Year Storms.
We then cast Reiterate the second time, and now we get more than 10 ^^ (10^619) copies. Each one takes X Doubling Seasons to 10 ^^ X Doubling Seasons, so by the end we will have more than 10 ^^^ (10 ^^ (10^619)) Doubling Seasons and Thousand-Year Storms. The same thing happens for each of the next Reiterate castings, so by then end we will have between 10 ^^^^ 6 and 10 ^^^^ 7 creatures. More than before, but still less than the last deck I mentioned. (Of course, you do have a seventh card to make things bigger!)
Edit: So, the following seems like a good entry into the seven card challenge:
So, we start off by casting the enchantments. We cast Cackling Counterpart, targeting Doubling Season. We cast Radiate, getting one copy via Thousand-Year Storm. The copy copies Rite of Replication, targeting Thousand-Year Storm, creating two Thousand-Year Storm copies.
Next, we cast Increasing Vengeance, which triggers all three Thousand-Year Storms, each one creating two copies of Increasing Vengeance. So we will get seven copies of Increasing Vengeance in total. We can use the first to copy Cackling Counterpart, getting two more Doubling Seasons. Then the next six copies can copy Radiate. The first targets two Doubling Seasons and three Thousand-Year Storms, getting 11 and then 2059 Doubling Seasons, and then 3 + 3*2^2059 Thousand-Year Storms. The second Radiate will create more than 10 ^^ 2059 Doubling Seasons and Thousand-Year Storms, the third 10 ^^ 10 ^^ 2059, and by the sixth we have more than 10 ^^^ 6 Doubling Seasons, and Thousand-Year Storms.
Finally we cast Mystic Retrieval, which will trigger more than 10 ^^^ 6 Thousand-Year Storms. We can use the first trigger to fetch the three spells from the graveyard, and then cast the three again. Keep the Cackling Counterpart and Radiate on the stack, and only resolve the Increasing Vengeance card. Then each copy of Mystic Retrieval can fetch Increasing Vengeance. Each Increasing Vengeance spell can copy Radiate, which takes X to 10 ^^ X; casting Increasing Vengeance triggers many copies, so we take X to 10 ^^^ X; casting Mystic Retrieval triggers many copies, each of which can fetch Increasing Vengeance, so we take X to 10 ^^^^ X. So we wind up with more than 10 ^^^^ (10 ^^^ 6) creatures after Mystic Retrieval fully resolves. Then we can flashback it from the graveyard, so we get a final number of more than 10 ^^^^ (10 ^^^^ (10 ^^^ 6)).
Eh, that's okay I guess. I'm pretty sure we can do more.
Edit: Wait, I'm being stupid. Each Increasing Vegeance Spell can copy Mystic Retrieval, which can fetch Radiate from the graveyard. A single Radiate spell takes X to 10 ^^ X; a casting of Radiate creates many Thousand-Year Storm copies, which takes X to 10 ^^^ X. Each Increasing Vengeance can fetch a Radiate to recast it. Each Increasing Vengeance cast creates many copies, so it takes X to 10 ^^^^ X. Each Thousand-Year Storm trigger for Mystic Retrieval creates many copies of Mystic Retrieval, each of which can fetch Increasing Vengeance, so it takes X to 10 ^^^^^ X. And finally, casting Mystic Retrieval creates many Thousand-Year Storm triggers, so it takes X to 10 ^^^^^^ X.
So we wind up with more than 10 ^^^^^^ (10 ^^^^^^ (10 ^^^ 6) creatures. Much better.
The first thing is, I wonder if this works to the same degree with the other option: cut Turncoat, and add in Tajuru Archer and Beastcaller Savant.
For clarity, the way this one works is: use an Engineered Explosives to kill Beastcaller, imprinting it on Mimic Vat and triggering Verdant Succession. Play Moggcatcher for Bloodbond March triggers, then make a token copy of Beastcaller, using the Archer's trigger to kill the Moggcatcher and make a hasty token. Then we shuffle the Beastcaller back in, and use the Succession triggers to get it back, which also bounces Moggcatcher. Critically, we can't use both triggers to get two hasty Moggcatchers, because of the severe timing restrictions involved.
There are two problems here: we have no way to get Tajuru Archer back after the megastage transition, and we only use up one Engineered Explosives in the same time frame. We could potentially solve all that by going back to the old Izzet Guildmage plan with Nylea's Disciple, but I'm not sure that plan actually works. Because Dark-Dwellers casts the instants themselves, not copies, I'm pretty sure we need some kind of [c]
Thousand-Year Storm[/c] effect to let us build the hyperstage, and all those effects go infinite when combined with Natural Order in the gigastage.
Failing that, we have to find some way to turn an Engineered Explosives into a way to get back Tajuru Archer in the megastage transition, without going infinite.
Edit: Okay, so going with Tajuru Archer handles the problem of creating two Moggcatchers with one run through the combo. But, it still doesn't handle the problem of creating an unwanted Metallurgeon token. I believe you can do the same thing as what I described before: Create a stage for Metallurgeon, then each time you sacrifice Engineered Explosives to destroy Beastcaller Savant, you also destroy the original Metallurgeon, and can create a token copy of it, allowing you to extend the Metallurgeon stage. So I don't know how to handle this.
Can we go back to Scattershot Archer? Maybe something like:
2 Psychic Battle
3 Cowardice
4 Horobi, Death's Wail
5 Bloodbond March
6 Cephalid Shrine
7 Mimic Vat
8 Omniscience
9 Vedalken Orrery
10 Mirror of Fate
11 Karn, Silver Golem
12 Perpetual Timepiece
13 Allay
14 Skull of Orm
15 Mirrorworks
16 Mana Vault
17 Simic Keyrune
18 Rust Tick
19 Muzzio, Visionary Architect
20 Goryo's Vengeance
21 Rebuild
22 Goblin Dark-Dwellers
23 Moggcatcher
24 Moggcatcher
25 Assembly Hall
26 Goblin Turncoat
27 Panharmonicon
28 Engineered Explosives
29 Scattershot Archer
30 Scattershot Archer
31 Gratuitous Violence
32 Dearly Departed
33 Abzan Falconer
35 Acorn Harvest
36 Smite the Monstrous
37 Child of Alara
38 Centaur Safeguard
39 Centaur Safeguard
40 Spellweaver Helix
41 Worldfire
42 Spider Spawning
43 Spider Spawning
44 Titania, Protector of Argoth
45 Archangel's Light
46 Bayou
47 Eureka
48 Mox Emerald
49 Llanowar Dead
50 Everglove Courier
51 Eastern Paladin
52 Frightshroud Courier
53 Simian Spirit Guide
54 Goblin Kites
56 Xathrid Gorgon
57 Reality Spasm
58 Thousand-Year Storm
59 Consecrated Sphinx
60 Words of Wisdom
It would be nice if we could now get rid of Mimic Vat, but unfortunately I don't see how we are going to create token copies of our enchantments. I had an idea that we could go back to using Splinter Twin and Crown of the Ages, but for now, let's just keep Mimic Vat in the deck.
So perhaps we can start with something like:
2 Psychic Battle
3 Cowardice
4 Brudiclad, Telchor Engineer
5 Bloodbond March
6 Cephalid Shrine
7 Soul Foundry
8 Omniscience
9 Vedalken Orrery
10 Mirror of Fate
11 Karn, Silver Golem
12 Perpetual Timepiece
13 Mimic Vat
14 Ray of Revelation
15 Skull of Orm
16 Mirrorworks
17 Mana Vault
18 Obelisk of Bant
19 Rust Tick
20 Muzzio, Visionary Architect
21 Goryo's Vengeance
22 Rebuild
23 Goblin Dark-Dwellers
24 Boggart Mob
25 Godtoucher
26 Wirewood Herald
27 Engineered Explosives
29 Acorn Harvest
30 Smite the Monstrous
31 Thousand-Year Storm
32 Child of Alara
33 Tireless Mercenaries
34 Celestial Gatekeeper
35 Celestial Gatekeeper
36 Spellweaver Helix
37 Worldfire
38 Spider Spawning
39 Spider Spawning
40 Molderhulk
41 Divine Congregation
42 Bayou
43 Eureka
44 Mox Emerald
45 Fault Riders
46 Grassland Crusader
47 Hazdhur the Abbot
48 Mirror Gallery
50 Streambed Aquitects
51 Benthicore
52 Devout Chaplain
53 Royal Assassin
54 Simian Spirit Guide
55 Goblin Kites
56 Old Man of the Sea
57 Xathrid Gorgon
58 Tribal Unity
59 Consecrated Sphinx
60 Words of Wisdom
8 stages would be great, but I imagine there's a problem or two in there.
With the infinite you discovered, if we can find a way to prevent copying Battle Cry: that way, we need a hasty copy, and to have the nontoken in hand, to continue. The problem is that the. I don't know how to build the stack up, since we can only resolve the non-copy card Rebuild. We can do it with the changeling tech, because each new Battle trigger can turn into one new spellcast, but that strategy has a host of other problems, too...
I very loosely follow your progress here, and wanted to ask a question:
If you were to design and add a card to Magic in order to get to some new level of iteration, (omega^4, omega^omega, epsilon 0 etc) how 'unreasonable' would the card have to be? Could it look like an actual card that could exist and let you encode something like Beklemishev's worms?
As I said earlier in a discussion on the potential limits, I don't really know how to construct an omega^omega structure, at least not using the stack. I did however just think of a way to create an omega^omega structure using creatures on the battlefield, with +0/+X counters for various X.
So, we will make use of Thousand-Year Storm to keep increasing the number of times an instant or sorcery gets copied. So we will have an instant/sorcery that says something like:
"As an additional cost to cast this spell, remove a +0/+X counter from target creature you control, where X is at least 2."
"Put a +0/+(X-1) counter on that creature."
and an instant sorcery that says something like:
"As an additional cost to cast this spell, remove a +0/+1 counter from target creature you control."
"Create a token copy of that creature. For each counter on that creature, put a counter of the same type on the token copy."
And then, we create a deck that has the ability to cast those above two instants/sorceries as many times as we want, as long as we have creatures with +0/+X counters on them. Also, we need to be able to put a +0/+X counter on a creature for some relatively large X, but only a finite number of times.
This gets us to omega^omega in the fast-growing hierarchy. When you have a X creatures with one +0/+1 counter each (and no other counters on them), and the Thousand-Year Storm counter is at Y, we can cast the second spell X times, taking the counter from Y to Y+X. If we have one creature with two +0/+1 counters on it, then casting the second spell gets us about Y creatures with one +0/+1 counter each, so we can cast Y more spells and take the TYS counter from Y to about 2Y. So a creature with three +0/+1 counters will take Y to f_2(Y), a creature with four counters will take Y to f_3(Y) and so on. Next, for a creature with a single +0/+2 counter we cast the first spell, creating a creature with Y +0/+1 counters, so we get about f_Y(Y), or f_omega(Y). Then a creature with one +0/+2 counter and one +0/+1 counter can be targeted by the second spell to create Y creatures with one +0/+2 counter each, so we get f_{omega+1}(Y). Continuing in the fashion, a creature with two +0/+2 counters will take Y to f_{omega*2}(Y), a creature with one +0/+3 counter will take Y to f_{omega^2}(Y), a creature with one +0/+4 counter will take Y to f_{omega^3}(Y), and so on. So the whole structure is at the omega^omega level, and if we can recurse over that structure (say by having an ability that creatures a +0/+X counter, where X is say the number of creatures), we can get f_{omega^omega + alpha}(Y) for some smaller alpha.
Then, we could use +X/+0 counters to get up to omega^{omega*2}, or general +X/+Y counters to get to omega^{omega^2}, but it gets more and more complicated and contrived.
Looking at the above spells, the first doesn't generally do anything positive, while the second seems pretty strong. I guess it wouldn't be too hard to balance the spells, say by giving the first spell some positive effect (maybe generating mana or something), while the second can be nerfed by giving it a high mana cost or some drawback. The real problem is that Wizards has gone away from having lots of different +X/+Y counters, and everything is +1/+1 now. So we wouldn't get spells that dealt with general +0/+X counters. Still, the above spells seem like they could fit in a reasonable card game, if not our current state of MtG, rather than being totally contrived cards that are only designed to create a massive function.
As for encoding something at the level of epsilon_0, I have no idea how we would do that. Beklemishev's worms seems like the most likely possibility, since it doesn't rely on a tree structure or complicated arithmetic functions. But I don't know how we would implement the reduction procedure: if we use the stack to represent integer sequences, then the reduction procedure means resolving the stack until we find an ability representing a smaller number than the top ability of the stack; then we need to recreate the part of the stack we just resolved, except with the top ability decremented; then we copy that part of the stack X times where X keeps increasing. I don't really see how we can recreate the stack that we just resolved, unless it gets copied onto the battlefield or something. Or we could represent the integer sequence on the battlefield. But, since the battlefield is unordered, we need something to represent the order, like the toughness of a creature or something like that. But then the reduction procedure seems equally ridiculous. So this remains a pipe dream, for now.
Weenieslaying Archer G
Creature - elf
When ~ enters the battlefield, deal 1 damage to target creature with flying.
1/1
I think that would solve our woes with Metallurgeon, and it even seems fairly likely to see print some day.
For something extensible, I don't know if it would work perfectly, but an enchantment that says something like "whenever a nontoken creature becomes the target of an ability, you may exile it. If you do, destroy target permanent that activated an ability targeting that creature this turn" or some such. I don't even know if that's possible in the rules, but when combined with the exile clause on Dual Nature, that could potentially get us up to omega^25 by letting us turn one upper-layer trigger into a targeting of a higher stage creature.
As for omega^omega.... God. Deedlit's idea already melted my brain a bit. I wouldn't know where to start.
In somewhat better news, I might have found a way out of our conundrum! If we go back to Scattershot Archer and Gratuitous Violence, we remove all the infinites, because no targeting and it's a one-drop. The problem is that it would also kill Horobi, which is a no-go. I'd thought that was a dead end because anything pumping Horobi would also pump SSG, but if we just forego the red Mana stage at the top, we can get it working with a Long-Forgotten Gohei!
I haven't pulled up a full version yet, but in principle that should still give us f_{w^4+w4+4}(x) at least. There's not much space either way, and it depends on whether the Scattershot plan saves Rust Tick, which I don't remember.
EDIT: Okay, I have a decklist, but it's a card over.
2 Psychic Battle
3 Cowardice
4 Horobi, Death’s Wail
5 Bloodbond March
6 Cephalid Shrine
7 Mimic Vat
8 Omniscience
9 Vedalken Orrery
10 Mirror of Fate
11 March of the Machines
12 Perpetual Timepiece
13 Phantatog
14 Skull of Orm
15 Mirrorworks
16 Mana Vault
17 Selesnya Keyrune
18 Metallurgeon
19 Battle Cry
20 Rebuild
21 Goblin Dark-Dwellers
22 Moggcatcher
23 Strongarm Thug
24 Panharmonicon
25 Engineered Explosives
26 Salvaging Station
27 Scattershot Archer
28 Gratuitous Violence
29 Thousand-Year Storm
30 Dearly Departed
31 Abzan Falconer
32 Wrap in Vigor
34 Acorn Harvest
35 Smite the Monstrous
36 Child of Alara
37 Centaur Safeguard
38 Centaur Safeguard
39 Verdant Succession
40 Academy Rector
41 Spellweaver Helix
42 Worldfire
43 Spider Spawning
44 Spider Spawning
45 Molderhulk
46 Natural Order
47 Goblin Welder
48 Underground Sea
49 Misery Charm
50 Mox Pearl
51 Polluted Dead
52 Frightshroud Courier
54 Goblin Kites
55 Wilderness Hypnotist
56 Streambed Aquitects
57 Old Man of the Sea
58 Xathrid Gorgon
59 Tribal Unity
60 Consecrated Sphinx
61 Words of Wisdom
This list actually has the option to add back Simian Spirit Guide, because Wrap in Vigor can save Horobi from damage death without pumping spirits' p/t. We just need to find one cut from this list, and we're roughly back where we started before finding the last two infinites.
Also, re Beklemishev worms: If we were to actually try to do it, and I don't think it's a good means of allocating resources, I think the best way would be to build a variant of the Magic turing machine: have tokens of two different types, where their toughness corresponds to their position in the sequence and their power corresponds to their value. You could have two creatures with "whenever an A dies, make a B" and vice versa, and then have some effect that gives all A's -1/-1 and all B's +1/+1, and vice versa. Each time it resolves moves one tape forward and the other tape back, and transfers the last/first token on one to the other.
Get all those cards without using infinite-happy color/type hacking, and we'd be maybe 1% of the way to epsilon_0.
If I recall correctly, the problem with Rust Tick was the same as with Metallurgeon; targeting the Human (in this case Muzzio, Visionary Architect) with Skyshroud Archer. So I think there isn't an obvious problem with Muzzio and Scattershot Archer.
If that is okay, we can maybe save three cards and get something like:
2 Psychic Battle
3 Cowardice
4 Horobi, Death’s Wail
5 Bloodbond March
6 Cephalid Shrine
7 Mimic Vat
8 Omniscience
9 Vedalken Orrery
10 Mirror of Fate
11 March of the Machines
12 Perpetual Timepiece
13 Phantatog
14 Skull of Orm
15 Mirrorworks
16 Mana Vault
17 Simic Keyrune
18 Rust Tick
19 Muzzio, Visionary Architect
20 Goryo's Vengeance
21 Rebuild
22 Goblin Dark-Dwellers
23 Moggcatcher
24 Strongarm Thug
25 Panharmonicon
26 Engineered Explosives
27 Scattershot Archer
28 Gratuitous Violence
29 Thousand-Year Storm
30 Dearly Departed
31 Abzan Falconer
32 Wrap in Vigor
34 Acorn Harvest
35 Smite the Monstrous
36 Child of Alara
37 Centaur Safeguard
38 Centaur Safeguard
39 Verdant Succession
40 Spellweaver Helix
41 Worldfire
42 Spider Spawning
43 Spider Spawning
44 Molderhulk
45 Natural Order
46 Bayou
47 Mox Emerald
48 Eureka
49 Polluted Dead
50 Frightshroud Courier
51 Simian Spirit Guide
52 Goblin Kites
54 Streambed Aquitects
55 Old Man of the Sea
56 Xathrid Gorgon
57 Tribal Unity
58 Military Intelligence
59 World at War
60 Reforge the Soul
So it looks like we save two cards, using the extra card slot to get a partial layer. Do you see any problem with the above?
I wonder if it might be possible to replace Verdant Succession; that might allow an Everglove Courier layer prior to the Frightshroud Courier layer.
I really like this thought excercise, but unfortunately I don't have enough time to read through all the 72 pages of this discussion. Will you ever continue to work on your description in https://sites.google.com/site/deedlitsplace/ultracombo? Or is there a more recent description of the steps, stages and challenges so far?
At least it convinced me to finally join this message board again
I am really glad, that the current decklists do no longer seem to include effects like Grip of Chaos. I feel that cheating luck by always drawing exactly the right card is one thing, but sequntially targeting always exactly the right random target from amongst unimaginable number of available target is something else. It might be interesting to see if we could also keep track of the ballpark probability of this scenario playing out as desired. It would be great, if the probability still stays in "imaginable numbers" (that do not need fast growing hierarchies to express).
One question concering the challenge itself:
Do I assume correctly, that any possible infinite damage combo in the deck is prohibited, even if our "optimal luck" never reaches that state? i.E. if there is any imaginable way to create an infinite damage combo with the cards in the deck it is no longer legal?
Another thing about the mathematics that struck me as strange:
Is the usage of Omega in the fast growing hierarchy consistent with the definition of ordinals?
It is clear to me, how the concept of Omega introduced in the desrcription is consistent in itself and very powerful. But in the example
F_{\Omega}(64)=F_{64}(64)<F_{65}(64)
, Omega compares to be smaller than 65, and deffitely not bigger than all the nonnegative integers...
So in other words, the Omega in the fast growing hierarchy seems to introduce a new concept, which to me is not realy coupled with ordinals - except maybe for the ordinals notion of "next higher number" with Omega and Epsilon.
Can some math-savy person point me into the right direction where this is resolved?
Heh, the ultracombo article. When I started writing it, I had every intention of finishing it. But, as the gigastage deck started coalescing, I lost the motivation to complete a description of what would (perhaps) become an outdated deck. Maybe if this deck never quite comes together, I will write up the older version.
As for this version, we haven't started writing up anything for it, as it is still in the development stages. I can summarize it briefly I suppose.
The setup is a little different from the previous version. Like before, the basic mechanic is to generate more and more Psychic Battle and Bloodbond March enchantments, and the number of these enchantments are basically our "current number" throughout the combo. However, in this version we removed Dual Nature, since it causes certain problems (currently the problem is with Child of Alara I think). So to get lots of copies of enchantments, we destroy them (using Psychatog in the above deck), and then imprint them on a Mimic Vat to generate a token copy. Then we use Skull of Orm to bring the enchantment back so we can sacrifice it again. This is less efficient then Dual Nature, but that won't affect the final estimate.
The primary stage is similar to the previous version - we have an artifact creature (either Metallurgeon or Rust Tick) that functions as our stage resource, and the stage is built up with alternating Psychic Battle and Bloodbond March groups of triggers.
The hyperstage is the biggest difference in the new version. In the previous version, we had Spellweaver Volute in the hyperstage andSpellweaver Helix in the megastage - in this version, those two cards are bumped up to the megastage and gigastage respectively, and the hyperstage is what's new here. The new spell triggerer is Goblin Dark-Dwellers, which can cast an instant or sorcery of CMC 3 or less when it enters the battlefield. With Panharmonicon, it can cast multiple spells. So we use Battle Cry, or Goryo's Vengeance couple with Muzzio, Visionary Architect, to get lots of Metallurgeons or Rust Ticks; we use Rebuild to regain our hyperstage resource, but at the cost of losing all our stage creatures.
The hyperstage mechanism is actually pretty complicated, as we couldn't get anything simple to work out. So, Rebuild has to replenish our hyperstage resource (which will turn out to be Moggcatcher tokens). It does this by bringing Engineered Explosives back to our hand, so that it can be cast again with a counter, and sacrificed. (Note that if we just bring Engineered Explosives back from the graveyard to the battlefield, it won't get a counter and we can't use it properly - this is quite handy.) Sacrificing Explosives will destroy Scattershot Archer, which can then be imprinted on a Mimic Vat to create a hasted copy. (Engineered Explosives can be brought back from the graveyard using Muzzio or Salvaging Station, while Scattershot Archer can be brought back using Verdant Succession.) The Scattershot Archer can then be activated to destroy Moggcatcher and Strongarm Thug, with the aid of Dearly Departed, Abzan Falconer, and Gratuitous Violence. The Moggcatcher can be imprinted to create a Moggcatcher token, and our hyperstage resource is renewed; the Strongarm Thug can be imprinted to create a token copy, which along with Panharmonicon can bring back both the Moggcatcher and Strongarm Thug to our hand. The Moggcatcher can then be tapped to bring Goblin Dark-Dwellers from the graveyard, which triggers the casting of our cheap instants, including Rebuild to bring Engineered Explosives back to our hand again.
The megastage, like the hyperstage of our previous version, uses Spellweaver Volute as our spell triggerer, and it triggers on the casting of an sorcery. So we use Acorn Harvest as our sorcery (which has CMC greater than 3, so no conflict with Goblin Dark-Dweller), which we can flashback for mana (which we can get cheaply) and 3 life. So life becomes are megastage resource. The instant that renews our hyperstage resource, and the instant that renews our megstage resource but eliminates all of our hyperstage resource, are combined into one: Smite the Monstrous. When we cast Acorn Harvest, we get many copies of Smite the Monstrous via Thousand-Year Storm. Most of the copies can be used to bounce Goblin Dark-Dwellers, which can then be replayed to cast our cheap instants and build up the hyperstage. (Note: we can't rebuild the hyperstage all at once, rather it gradually gets built as it resolves, with the lower Smite the Monstrous triggers standing as placeholders for hyperstage layers until the eventually get resolved and replaced by Battle Cry/Rebuild.) A few more Smite the Monstrous can be used to bounce large creatures that we need to return to our hand. The last Smite the Monstrous is used to destroy Child of Alara, which destroys all nonland permanents, and therefore all of our hyperstage resources (Moggcatcher tokens), but also destroys Centaur Safeguard, which allows us to gain 3 life, renewing our megastage resource. Note that we can't use multiple copies of Smite the Monstrous to destroy Child of Alara and therefore Centaur Safeguard multiple times, because - hmm, I'm forgetting the exact way that works. Stakfish, could you go over that again?
The gigastage uses Spellweaver Helix to cast sorceries, which can only be triggered by a sorcery we have more than one of, so no flashbacking Acorn Harvest to trigger it. So only Spider Spawning can trigger it, which requires a black mana to cast it via flashback. The we get a Frightshroud Courier stage that produces black mana, and a few stages after that; the last deck gets us to around F_{w^4 + w5 + 4}, assuming it works properly.
As for the challenges the deck presents, there have been many. Having four different stage types in the main combo leads to a lot of possible conflict with one level potentially affecting another in undesirable ways. And the newest hyperstage is partcularly complicated; the more complicated, the greater the chance of a flaw or a hidden infinite. Probably the greatest lingering problem is the potential infinite that can come from the megastage and gigastage transitions potentially renewing lower level resources improperly. For example, the way the megastage transition is supposed to work is that we spend three life, go to a higher hyperstage, and gain three life back; but to do so we need to use up a minimal amount of resources from below the megastage transition so as not to go infinite. (Basically, we need to use a few Metallurgeon/Rust Tick triggers to set up the megastage transition). Unfortunately, passing to the higher hyperstage allows us to bring Engineered Explosives and Goblin Dark-Dwellers back to our hand, and keep them in our hand when we pass back down to the lower hyperstage. This allows us to add a couple Moggcatcher tokens, which more then compensates for a couple of lost Metallurgeons, so that goes infinite. So we need to find a way for the megastage transition to use up those extra uses of Engineered Explosives that we gain, and that has been plaguing us for a while. We may have solved it with the necessity to resolve Verdant Succession to gain certain green creatures back, but I'm not totally sure there isn't a hidden infinite somewhere.
Another problem is that Iijil has left, and he was the best one at finding problems and infinities in our prospective decks.
Stakfish, feel free to point out any further details that are worth mentioning.
Yeah, I also would prefer to use Psychic Battle over Grip of Chaos, so that the probabilities remain "reasonable". I had a discussion with Iijil over this, and he was of the opinion that we should just present the deck that had the maximum possible damage. I guess that makes sense. I think, if our deck winds up favoring Grip of Chaos, we would write up the article about that deck, but include an addendum on how things change if we want to replace Grip of Chaos with Psychic Battle.
So long as Grip of Chaos is not in the deck, there is really nothing that requires chance other than card drawing, and with Mirror of Fate we can arrange the library however we want to. So the probability of getting the combo off only includes the cards we draw up until we start using Mirror of Fate, so really it can be no worse (and in fact will be much better than) 1 in 60!, which I would consider firmly in "imaginable numbers".
About your question: Yes, any possible infinite damage combo is prohibited; I'm not sure what you mean by "optimal luck" never reaching that state, could you clarify?
I played around certain times with combos that would be finite if the opponent always acted in a way to keep the maximum damage down, rather than cooperate to go infinite; but Iijil and Stakfish seem to like the rules as they are.
Yes, the fast-growing hierarchy is consistent with the definition of ordinals. Now, F_w (64) is not greater than F_m (64) for all finite ordinals m, and cannot possibly be, since F_m (64) can be arbitrarily large. But, F_w (n), as a function of n, is faster growing than F_m (n) for any fixed m; we have F_w (n) = F_n (n) < F_m (n) for n < m, but once n passes m we have F_w (n) = F_n (n) > F_m (n). So past a certain point F_w (n) will always be greater. More generally, if we have two ordinals a < b < epsilon_0, then F_b will be a faster growing function than F_a. So the ordinals match up orderwise with their corresponding functions.
This might strike one as an academic point, since F_w (n) = F_n (n) doesn't seem like a major leap forward from the finite ordinals. But really it is. To see the big difference, look at what happens with F_{w+1} (n). For example, take F_{w+1} (4). This is equal to F_w (F_w (F_w (F_w (4)))). First we have F_w (4) = F_4 (4) ~ an exponential stack of 10's of height an exponential stack of 10's of height an exponential stack of 10's of height about 10^10^10^21. Big, but not that big given F_m on finite ordinals. But then we go to F_w (F_w (4)) = F_{F_4 (4)) (F_4 (4)) - now, that big number we just described goes into both the variable and the subscript of F, so now we are at an extremely high level in the finite hierarchy. Then we plug the extremely big result of that into the next F_w, so the extremely big result goes into both the variable and the subscript again. Then we plug that value into F_w one final time. Clearly, this is much bigger than an F_m (n) that we can easily describe without this iteration process. That's the power of diagonalization at limit ordinals.
For the megastage, the reason we can't use multiple copies of Smite the Monstrous to destroy Child is because, while we can kill Centaur Safeguard, bring it back with Succession, then kill it again to gain 6 life, once we've done that we don't have any more copies of the Safeguard in our library to fetch with Verdant Succession. We just resolved two Child of Alara triggers in a row, so there's no way we can shuffle one back in with Mirror of Fate or Perpetual Timepiece, so when the next Succession trigger resolves, we'll fail to find and both our Safeguards will be stuck in the graveyard. We also don't have any other way to get it back yet: our other graveyard return mechanisms are Strongarm Thug and Bloodbond March, but it's not a mercenary, and we don't have any way to bounce it back to our hand and recast it: The first thing we have that can target Centaur Safeguard is Goblin Kites, which is several resources removed from anything we can generate at that point in the combo.
I also want to add that, if you want some further understanding of this deck, there are a few forum comments that are really, really informative about how the decks in this combo work. In particular, I found
Deedlit's explanation of the first stage we found and lijil's explanation of how hyperstages work really helpful when I was trying to get up to speed.
If you understand the concepts in those, all you need to get is how we use Mimic Vat, Cowardice, Horobi, Death's Wail, Bloodbond March, and Psychic Battle to turn creatures with tap abilities that can target themselves into stages, and you'll be able to look at any deck in this thread and at least have a vague sense of how it works. In particular, any time there's a big collection of cards in a hyperstage or megastage and such, try to match cards up to what parts of the steps lijil described they can accomplish. Even if you don't understand how our gigastage works just yet, you can pretty quickly figure out that Worldfire is supposed to delete all I.
I think you're spot-on with the challenges, though I imagine lijil will be back before long. The complexity of the hyperstage is a huge challenge, not only because it allows for so many more possible infinites but also because it doesn't leave much room for further stages. I think the ultracombo used about as many slots to get to the stages on top of the main structure as we do to get through the hyperstage alone, which is why it had 14 stages on top and we have 4-5. By far the biggest issue is the infinites, though. Especially without lijil's eye, it's been a slow slog to eliminate the ones we know about, and we may yet find even more.
On another note, it's a shame about the ultracombo article. I think one challenge that's limited the people reliably working on this to me, Deedlit, and at least recently lijil, has been a lack of accessibility to today's decks. I was interested in this challenge since early 2016, but after reading SadisticMystic's article, I went onto this forum and found decks that looked nothing like his and made no sense (wait, don't creatures that target themselves go infinite?). It was only when I reached a comment by Ijil on page 25ish explaining the hyperstage in algorithmic terms that I was able to put it all together. If you want to contribute to the project, you can't just read an article and start thinking, you have to first read it, then read about 70 pages of forum posts, many of which are dead ends. When I posted my standard combo on reddit, there was a lot of interest across the community, and a lot of people commented that they were following this thread or were interested in it. I'm hopeful that a finalized write-up for the... ubercombo? will get some new eyes on the deck who may find tricks we haven't discovered.
Even if we can't kill it with Explosives, we can use a Psychic Battle trigger below the transition to kill it and get a token. Then, we can use a saved Muzzio activation to get it back, and kill it again, making a second token. The next Bloodbond March trigger brings it back. We activate both the tokens, to add two Psychic Battle layers and a Bloodbond March layer, so now we have 1 more Psychic Battle layer than we had to start with. Then, we resolve one of those triggers to kill Rust Tick, and make a token.
Then, when the hyperstage starts, we use our first Muzzio activation to get it back, at which point we're back to our normal position, but we have one more Psychic Battle and Bloodbond March layer in the stage below it.
We can fix it by going back to Metallurgeon, or by forcing the hyperstage transition to use up a Muzzio activation.
If not, then it looks like the best we can do is to remove the Merfolk stage and end with World at War, getting to w^4+w4+4. I'm not seeing any cuts, although the need for both Salvaging Station and Goblin Welder is driving me nuts.
Near the beginning, when you first cast the Drake, I understand this as still being with the original 4 dual nature "exile all tokens named dual nature" triggers on the stack. If that's correct, seeing as Allay hasn't tried to resolve yet, it's still on the stack. That being the case, how are you enchanting it with the copy of Spellweaver Volute after the 11th Drake trigger?
Additionally, even if y'all aren't in the mood for a full write-up of the current list, linking to the critical posts would be really helpful. There's a lot of referencing back to old systems or ideas without links or explanations, so reading backwards is really difficult, and due to the number of false starts and failed branches, it's also very difficult to try and read forward from the start. The two posts Stakfish recently linked to were helpful at the meta level, but some sort of ledger with "this post explains how X card works" would also go a long way to making this subject accessible
We also have not been good about explaining in simple terms how our new discoveries work, myself included. I'm gonna try to write out most of those concepts, but I'm not going to touch on up-arrow notation or the fast-growing hierarchy, that side of the math. For that, you should check out one of the write-ups.
So, basically every deck we talk about today, including the Ultracombo and the gigastage we're working on now, start with the same basic set of engine cards, which is the first section we put in the lists. The initial setup just tries to get them out while using as few resources as possible. Going through the list:
Right now, to copy enchantments, we do something like this: spend a green mana to flashback Ray of Revelation, which kills the enchantment. We imprint it on a new Mimic Vat, and activate it to make a token copy. Then, we sacrifice a Mirror of Fate token to shuffle both the enchantment and Ray of Revelation into our library, and tap a Perpetual Timepiece to mill them both. Then, we activate a Skull of Orm to return the enchantment from our graveyard to our hand, and replay it. Now we're right back where we started, except we have an additional copy of the enchantment, we've spent 16G, if you count paying for Mirrorworks triggers, and used up 4 artifact tokens: Mimic Vat, Mirror of Fate, Perpetual Timepiece, and Skull of Orm. We can also generate green and generic mana by bouncing artifacts, like Mana Vault and Simic Keyrune. While it's expensive to do that at first, once we've made enough copies of Psychic Battle this way, we can do this many, many times from just one ability that reads "target artifact". That also means we can't use an enchantment as a limiting factor later, because we can just use some artifacts to make more.
The other thing that threw me when I was getting started was how token stages work. So, let's say we're targeting artifacts with Rust Tick. When we activate Rust Tick's ability and get a lot of Psychic Battle triggers, we can use each trigger to do one of three things: we can bounce another artifact and replay it to make token copies with Mirrorworks, we can bounce the nontoken Rust Tick and replay it, giving us a big stack of Bloodbond March triggers, or we can kill the nontoken Rust Tick, imprint it on a Mimic Vat, and make a new hasty token copy. But if we do that, it's stuck in exile. The only we we have to get it back, at least without using something higher up, is by resolving a Bloodbond March trigger. But we can't make new Bloodbond March triggers to do it, because that requires casting it and we can't cast Rust Tick from exile. So we have to resolve down until the top of the stack is a Bloodbond March trigger from Rust Tick. That in turn requires that we cast it earlier, which means we bounced it with a Psychic Battle trigger below THAT.
So the end result is that, any creature that can tap to target itself and also something we need can make this giant stack of alternating batches of Psychic Battle and Bloodbond March triggers, where each one feeds into the other. When we run out of Psychic Battle triggers at the top of the stack, we use the last one to kill Rust Tick, make a new token copy with Mimic Vat, and bring it back with the first Bloodbond March trigger below it. When we run out of Bloodbond March triggers in that batch, we just use the top Psychic Battle trigger below it to bounce Rust Tick and replay it for more Bloodbond March triggers. Each different batch of triggers on the stack is another layer, so with N Rust Tick tokens, we get N recursive layers (well, 2N, but we round down for convenience). For instance, to match the number from the old Megacombo, we would only need to make 408 hasty Rust Tick tokens. That closes off artifacts as a resource we can use to limit ourselves later.
Two important things: the only way we have of giving anything haste is Mimic Vat, so the nontoken Rust Tick can't do anything on its own. And because we can't keep making Bloodbond March batches after killing our Tick, we can't build a loop. Put another way, to make a new Rust Tick, we need a Psychic Battle and a Bloodbond March trigger next to each other. We can only use one Psychic Battle trigger per batch, and each batch costs one Tick activation, plus the cost of a Bloodbond March trigger below it. That came from a separate Tick, but we can use each one, so think of that as costing 1/n, where n is the number of Bloodbond March triggers that activation made. So to get 1 Rust Tick back out, we have to spend 1+1/n Rust Ticks. The difference is tiny, but enough to make it so we can't loop.
Hyperstages, megastages, and gigastages all basically work the same: you spend some resource (a token, 3 life, a black mana) to put a bunch of triggers on the stack. Most of those can generate a lot of the next resource down (the hyperstage makes lots of Rust Ticks, for instance), but the last one lets you destroy all of the resource you generated to make a new, replacement one. That deletion step is important, because otherwise you can save a Rust Tick until lower down and use it to pay for the costs to keep going, and go infinite. Because that's not something you can just make with one ability, each one of these casts some subset of instants and sorceries as its trigger. Our hyperstage uses a token creature that can tap to make Goblin Dark-Dwellers enter the battlefield, which in turn lets us cast instants with converted mana cost 3 or less as a trigger. Not sorceries, I'll get to that later.
For instance, if instead of using Rust Tick at the bottom we used Metallurgeon, we could have the hyperstage start casting Battle Cry, untapping all the token copies we made for much bigger stages. Then, when we need to delete all our Metallurgeons, we would instead cast Rebuild, which would kill all our tokens, bounce Vedalken Orrery which is important so that we can't do any trick stack shenanigans in the middle, and also some artifact that will let us generate more of our resource, but can't otherwise be reset. We use 0-mana artifacts, which we can't bounce with Cowardice: Cowardice only works on creatures, and our artifact-animating spells use converted mana cost to set toughness, so a 0 mana artifact becomes a 0/0 creature and dies. In the past, the hyperstage used mana, so we bounced a mox. The new version uses a token, so we bounce Engineered Explosives, which we then crack to kill some creature that lets us regenerate our hyperstage. We've tried both having it directly kill the creature, and having it kill something else that can somehow generate a new token copy. Right now, we do the latter, but I have hopes that we can get the former working. At the moment, this step closes off white creatures (can untap with Battle Cry), goblins (we can search them out easily to replace them), humans (that's how we specifically target our hyperstage creature, Moggcatcher, creatures with flying (we target humans by giving them flying, because there isn't a convenient creature that can just target a human), and creatures with +1/+1 counters (we give humans flying by giving them a +1/+1 counter, then giving creatures with +1/+1 counters flying). Engineered explosives also closes off creatures with converted mana cost less than or equal to the number of colors of mana we can generate before reaching them in our list, because we can kill them with Explosives instead. 3-drops, however, are always safe, because even if we can kill them with explosives, doing so would also kill our Mimic Vats so we can't imprint them.
The megastage keys off of instants of any cost, not just 3 or less. It uses Spellweaver Volute to make it so, any time we cast a sorcery, we get many copies of some instant that lets us generate more copies of the token we use in the hyperstage. Generally speaking, anything that can target the token, the intermediate creature we use to make copies of it, or Goblin Dark-Dwellers itself is fair game here. That's also why we can't use sorceries in the hyperstage, or have any sorceries with cmc 3 or less in the deck: otherwise we could cast a sorcery with Dark-Dwellers, which triggers volute, which lets us replay Dark Dwellers, which lets us trigger Volute again, etc. The only sorcery we can set this off with is by flashbacking Acorn Harvest, which costs 3 life.
Then, to delete all our hyperstage creature (Moggcatcher at the moment), we use the same instant to kill Child of Alara. That destroys our Orrery, our Omniscience, all our enchantment copies (though we keep our mana), our hyperstage and stage tokens, and is also the only way so far to kill Centaur Safeguard. The death trigger gains 3 life, but we also get a trigger to search our library for a card with the same name and put it directly onto the battlefield, via Verdant Succession. We can't respond to that trigger, because we can't save Vedalken Orrery, but we run two copies, so we just alternate which one is on the battlefield and in the library/graveyard/exile. This also means that we can't have access to 3 colors of mana at this point: even if it kills Mimic Vats, we could keep playing Explosives for 3 and cycling between the Safeguards to gain life and go infinite. We have a workaround to allow 3 colors, but it's janky and hard to make the gigastage safe afterwards. Right now, we use Smite the Monstrous, so past this point any creature whose power can be boosted to 4 or greater is unsafe.
The gigastage keys off black mana, and uses sorceries as its effects. We cast the sorceries with Spellweaver Helix, which can imprint multiple cards thanks to Panharmonicon. We flashback Spider Spawning while the second copy is imprinted on a Helix, and get to cast both a spell that gains life (Archangel's Light, for instance), and Worldfire as the reset. As a general rule, the last two of the big stages (or only two) will either start with a mana-based stage and finish with a life-based stage, using Worldpurge to clear all permanents and empty the mana so you can't save it, or start with a life-based stage and finish with a mana-based stage, using Worldfire to clear all permanents and hard set your life total to 1.
Either way, the thing that sets these cards apart is they remove any permanents, not just nonlands. So we use Worldpurge to get lands that gain life (like Radiant Fountain) off the battlefield, then we replay them to gain the life that we paid into the gigastage back. With Worldfire, we just use a land that produces black mana: Bayou usually so that it can also help cast Eureka at the very beginning.
The rest of the cards in the mega- and gigastage are there to make sure we can get our other permanents back after we blow up the world. That's extra important for Worldfire because we can't save them in our hand.
After that, we spend the rest of the combo trying to fit as many stages in as possible. While there are some exceptions (if it's not itself a stage creature, just an enabler that helps connect one stage creature to another, it can have a cmc we can reach with Engineered Explosives), those stages have to be built on creatures with converted mana costs of 3, 4, or 5+, with 4 not being allowed once we allow a fourth color of mana. They can't be white (or Battle Cry untaps them) or green (Verdant Succession) makes them too easy to get back out). They must have power less than 4. They can't be humans, goblins, have flying, or use +1/+1 counters. And each stage adds a new restriction.
For instance, we start with a Zombies stage to generate black mana. Then we use a red mana stage that also targets creatures with toughness 2 or less. Then we use a merfolk stage. Then we use Old Man of the Sea to rule out creatures with power 2 or less, so all remaining stage creatures must have power exactly equal to 3. Then we wrap up with Xathrid Gorgon.
In general, we keep adding stages until we either run out of deck slots or run out of stage creatures (different decks hit different limits first). After that, we try to add layers that generate lots of that last stage creature. Past decks have used Reality Spasm, which can untap the Mimic Vat with the creature imprinted, but right now we use Tribal Unity, which pumps all our Old Man of the Sea copies until they're big enough to target Xathrid Gorgon, and is more efficient.
Depending on how many slots are still open, we either end with World at War or Words of Wisdom. If we have more space, we find some way to turn a combat step into a lot of Tribal Unity (for instance, one white mana lets us play Sphinx's Revelation for many copies with Thousand-Year Storm, each of which can draw Tribal Unity, and we get lots of white mana each attack step with many copies of Druid's Repository), then cast World at War as many times as possible to get lots of combat steps. Because World at War won't do anything after we leave our first postcombat main phase, we can't use those extra combat steps to feed more World at Wars, so that's where we run out of steam.
If we don't have the space for all that, we use Consecrated Sphinx to turn our opponent drawing one card into us drawing many cards two at a time, each of which can let us recast Tribal Unity. That's why our only card draw spells make each player draw a card: there's no way to refill our opponent's deck, so we can only do that at most 53 times. Depending on how easy it is to set everything up, we either use Reforge the Soul, which we can usually cast 4-5 times before it would kill our opponent without dealing any damage, or Words of Wisdom, which is much more efficient. I'm not sure exactly how the ultracombo's top layers worked, but I think it was roughly similar.
Deedlit, it might be a good idea to add links to this comment, as well as yours on the first stage and lijil's on the hyperstage, and any others you know about that I don't, to the OP as a starting point.
In other news, I've found at least one cut we can make to the deck, as long as we keep Academy Rector around: Skull of Orm! We can make token copies of green enchantments just fine (kill them, make token with a vat, Mirror them to the library, search them out with Succession), which is enough for the bottom stage: we can just copy Bloodbond March. Then, we can kill Academy Rector to make copies of nongreen enchantments later on.
Though actually... how are we getting Rector back now? Ugh. That setup may not work anymore.
Skull of Orm looks like a good cut! As for fetching Academy Rector, we can just use Misery Charm, can we not? That will allow the fifth stage back in, getting us to w^4 + w5 + 4.
Concerning the problem FireRogue517 mentioned, there was indeed an error with the early setup, which came about because I was greedy and tried to squeeze in another couple of copies of Dual Nature by having Copy Enchantment copy Dual Nature at strategic points. The additional Dual Nature means one more Dual Nature token is created, but when we bounce the Copy Enchantment (which is copying Dual Nature) card, we trigger the Dual Nature destruction abilities. I believe there was one point where doing this is okay, but there was another point where it was not. That problem could be easily fixed by simply not having Copy Enchantment copy Dual Nature at the wrong time; this will cost us a Dual Nature token, but not a big deal. Of course, the gigastage deck doesn't currently have Dual Nature in it, although perhaps we should keep an eye for its possible inclusion whenever it may become legal, since it may be more efficient.
EDIT: I've been wondering whether the "target artifact" combos like Arcum Dagsson or Goblin Trashmaster could be made to work after all. They would certainly go infinite in the old version of the combo, but in this new version we have a lot of new moving parts, and maybe those can't be refreshed as easily as the artifacts. But I'm not sure.
If it still goes infinite, then I think we can still make it work by getting rid of Mirrorworks. Just replace Mirror of Fate and Mirrorworks with Izzet Guildmage and Pull from Eternity, I think. That resolves the problem of requiring more Psychic Battle triggers of our stage artifact, since we will need lots of mana for the stage transition and one copy of Mana Vault and a Keyrune won't be enough. However, we may have the Muzzio problem of being able to bring a copy of whatever we are using to target/sacrifice an artifact below the hyperstage transition, and getting an extra use out of them. Stakfish, do you know an artifact combo that would be safe from this happening?
EDIT: It just occurred to me that getting rid of Mirrorworks can also solve the problem we had with the Soul Foundry deck. That deck also used Muzzio, so we have to switch that out as well, but perhaps we can squeeze out an extra stage or two with that deck.
Hi guys. Been working on and off on this project for about a month now. It’s kinda become my low key obsession as of late. I’m not going to be posting a deck list just yet, but I should be shortly. I have been doing most of my work entirely in the dark after hearing about this project a few years back. It’s beem pretty fun just seeing how creative I can be and how important every card slot really is. Part of my reason for not posting yet is that I want to be sure I’m actually bringing something worthy to the discussion. I’m going to do a full read through of the 70 or so pages of this thread to be sure I’m doing things a uniquely as I think I am. Also I want to have a primer/guide of sorts for my list so that once I post it I can also explain how it works. In some ways I think it’s simpler but the details matter and these type of projects can get messy to try to explain.
I’ll be the first to admit that I won’t know if my sequencing can be improved on. The numbers just scale so fast it’s too difficult a task for me to try to figure out if one method is scaling any faster than another. But I’m hopeful that I can get a few more sets of eyes looking at my ideas, that maybe we can find an optimal sequence or configuration.
I’m going to try to have my list and guide finished, and posted, by the end of this coming week. Till then, happy enormous number hunting!
Jkibbs
Just a quick little preview of sorts and a bit of history on me and projects like this. I actually found this 60 card challenge after I started digging around the net to see if anyone was doing a challenge similar to one I had made up myself. I wanted to see, in an edh legal environment, what I could do with 7 cards without going infinite. My challenge was strictly looking for number of objects in play, so i didn’t need a haste enabler to attack or anything. I just wanted to see how much stuff could I put on board with a full starting hand. Mana reserves could be arbitrarily large as long as it didn't allow me to go infinite.
So my 7 cards ended up being:
Riku of two reflections
Opalescence
Parallel lives
Parallel evolution
Rites of replication
Radiate
Mystic retrieval
It costs about 60 mana to go all the way though the full sequence if we start with nothing in play.
So the sequence is:
Play Riku
Play opalescence, copy with Riku
Play parallel lives, copy with Riku, get 2 more token lives.
Cast evolution, Riku it. Let both of these fully resolve.
Recast evolution from the yard, Riku it again, let these resolve.
So me and a friend actually did the math up to this point once. We figured that we have a number of permanents in play that is represented by a number that was around 35(ish) million digits long. That's pretty decent for only 4 cards I'd say.
So we continue on by casting rites kicked, targeting lives, and Riku it. Let the copy resolve but then cast radiate, targeting the original, and then Riku copy the radiate, also targeting the original rites. This will be incredibly complex to resolve as the many rites copies will resolve independently and influence the next wave coming behind it. Also each radiate will make a larger wave if we cast/stack things correctly.
So let all that nonsense resolve. We have an empty stack and 1 card left in hand.
We cast mystic retrieval targeting rites or radiate, then Riku copy it to target the other, and pick them both back up.
Then do the rites/radiate thing again just as we did before only far more powerfully this time around.
Again back to empty stack, no cards in hand, but I'm not quite done just yet.
We flash back retrieval from yard, and Riku copy it, to get back rites and radiate one last time.
Again we do the rites/radiate thing once again. We let it all resolve and we are finally finished.
So I invented this project at least 3 years ago. I’ve had my head pretty well wrapped around large, finite, number generating for quite some time. I’ll be the first to admit my understanding of the notation need to express this stuff is awful, but from a conceptual standpoint I can at least grasp what is going on most of the time. Stuff like this is just the tip of the iceberg with my 60 card variant, but it’s a good proof of concept that I can proficiently take small starting resources and make egregiously large outputs without going infinite.
Hopefully I can still get my list/primer posted by the end of the week.
edit 1: cleaned up the spelling and general sloppiness.
Jkibbs
edit: i'm an idiot, should have just done this post as an edit to the orginal, mods please erase if you get a chance
One minor correction: You can't copy Opalescence with Riku, but I imagine that is just a typo.
The number you get after four Parallel Evolutions is a lot more than 35 million digits long:
After the first Parallel Evolution, you copy the two Parallel lives tokens, and each copy gets multiplied by 2^3 (since you have 3 Parallel Lives total) so you wind up with 2 + 2*2^3 = 18 Parallel Lives tokens.
After the second, you get 18 + 18 * 2^19 = 9437202 tokens total.
After the third, you get 9437202 + 9437202 * 2^9437203 ~ 1.42 * 10^2,840,888
After the fourth, you apply the formula one more time to get more than 10^10^2,840,887 Parallel Lives tokens.
Next comes the Rites and Radiates. each copy of Rite will add another "10^" to the exponential tower (the highest exponent will drop by an infinitesimal amount each time, but it will never dip below 2,840,887), and the first Radiate creates more than 10^10^2,840,887 Rites, so you will wind up with more than an exponential tower of 10^10^2,840,887 10's. In Knuth arrow notation, this is written 10^^(10^10^2,840,887). (More generally, a^^b is defined as a^(a^(...(a^a)...)) with b copies of a.) Similarly, the second Radiate will create more than 10^^(10^10^2,840,887) copies of Rite, so we will get more than 10^^10^^(10^10^2,840,887) token copies in the end. Since we wind up with six copies of Radiate in total, the final number will be more than 10^^10^^10^^10^^10^^10^^(10^10^2,840,887) token copies. We can simplify this with triple arrow notation: a^^^b = a^^(a^^...(a^^a)...) with b copies of a. So the final number is more than 10^^^7 but less than 10^^^8.
If I may make a suggestion, we could improve the number by replacing Riku of Two Reflections with a spell copier that we can have multiples of, like Swarm Intelligence. This would mean we don't get copies of Parallel Lives to start with, so casting Parallel Lives early on doesn't help. So perhaps we could replace that with [c]Clone Legion. We'll get only two copies of Clone Legion; the first will take us to 27 Parallel Lives and Swarm Intelligences, the second to 3623878683 each. That is a lot less than before, but now look what happens with the Radiates; The first cast gets copied 3623878683 times so we wind up with more than 10^^^3623878684 Parallel Lives and Swarm Intelligences. We then cast Radiate two more times, so we wind up with more than 10^^^10^^^10^^^3623878684 creatures, or between 10^^^^4 and 10^^^^5 creatures in the end.
Another improvement: Replace Mystic Retrieval with Bound // Determined. We can only cast Bound once, but since it is an instant, we can cast it while Rite of Replication is still on the stack. So we cast it after all the Radiates resolve, but while the original Rite is still on the stack. I just noticed that we can resolve the copies of the original Rite before we start resolving Radiates; so after the Rites resolve we will have more than 10^^3623878684 Swarm Intelligences, then the Radiates resolve and we go to 10^^^10^^3623878684 copies. Then we cast Bound, getting more than 10^^^(10^^3623878684) copies, and each one can fetch Radiate and recast it, increasing the final number to 10^^^^(10^^^(10^^3623878684)) creatures.
Looking forward to your full deck!
With those changes in hand, we bring in Godtoucher to bounce Boggart Mob. Godtoucher can also target Child of Alara, but now we can only bounce it back to our hand, which does not trigger the destruction of permanents. So I think this is safe.
So I was thinking of something like:
2 Psychic Battle
3 Cowardice
4 Brudiclad, Telchor Engineer
5 Bloodbond March
6 Cephalid Shrine
7 Soul Foundry
8 Omniscience
9 Vedalken Orrery
10 Pull from Eternity
11 Izzet Guildmage
12 Karn, Silver Golem
13 Perpetual Timepiece
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 Engineered Explosives
27 Salvaging Station
29 Acorn Harvest
30 Smite the Monstrous
31 Thousand-Year Storm
32 Child of Alara
33 Tireless Mercenaries
34 Celestial Gatekeeper
35 Celestial Gatekeeper
36 Spellweaver Helix
37 Worldfire
38 Spider Spawning
39 Spider Spawning
40 Molderhulk
41 Divine Congregation
42 Bayou
43 Eureka
44 Mox Emerald
45 Cloud of Faeries
46 Nectar Faerie
47 Centaur Archer
48 Maze Glider
50 Frightshroud Courier
51 Simian Spirit Guide
52 Goblin Kites
53 Wilderness Hypnotist
54 Streambed Aquitects
55 Old Man of the Sea
56 Xathrid Gorgon
57 Tribal Unity
58 Military Intelligence
59 World at War
60 Reforge the Soul
Glad you enjoyed the challenge. It’s been a few years since I looked into it tbh. I was thinking about it while I was at work and I’m pretty sure these 6 cards would destroy my old 7 handily. It only works with a set amount of mana so let’s say it’s the same as my original list used up, 60.
So
Opalesence
Doubling season
Thousand-year storm
Rite of replication
Radiate
Reiterate
Not sure you even need 7 with this list. 60 mana gets pretty insane here.
After casting the enchantments you cast Rite of Replication (unkicked, so that we can cast Reiterate the most times), which doesn't get copied. We can choose to target either Doubling Season or Thousand-Year Storm; I think it makes more sense to target Thousand-Year Storm, so that Radiate will make copies of Doubling Season, which we need to do in order to get exponential growth. Then you cast Radiate, which gets one copy from Thousand-Year Storm. That copy creates one copy if Rite of Replication, which targets Doubling Season. So we create two token copies of Doubling Season.
We don't want to resolve either Radiate or Rite, since we need to copy them. So we cast Reiterate next, with buyback. The Thousand-Year Storm triggers, creating two copies of Reiterate. So we get three Reiterates total, and each time we create a copy of Radiate. The next Reiterate will create three copies of Reiterate from Thousand-Year Storm, then 4,5,6,7. So we get a total of 3 + 4 + 5 + 6 + 7 + 8 = 33 Reiterates in total.
The first Radiate will target the three Doubling Seasons, getting us to 3 + 2^3 = 11, then 11 + 2^11 = 2059, then 2059 + 2^2059 ~ 6.6 * 10^619 Doubling Seasons.
The second Radiate will target all 6.6 * 10^619 Doubling Seasons, so we get more than 10 ^^ (10^619) > 10 ^^^ 2 Doubling Seasons in the end. Then the third will get more than 10 ^^ 10 ^^ (10^619) > 10 ^^^ 3 Doubling Seasons, and so on, until the 33rd generates more then 10 ^^^ 33 Doubling Seasons.
That's more than the old 7, but less than the improvements that I mentioned. The major problem is that we aren't getting more Thousand-Year Storms. So I guess it makes sense to use one of the Reiterates to copy Rite of Replication rather than Radiate, so that we can get both enchantments going.
So, let's go back to the first casting of Reiterate. We don't need more Thousand-Year Storms until the next Reiterate is cast, so let's use the first two Reiterate copies to copy Radiate; that takes us to more than 10 ^^ (10^619) Doubling Seasons. Then we use the original Reiterate to copy Thousand-Year Storm, which creates 10 ^^ (10^619) Thousand-Year Storms.
We then cast Reiterate the second time, and now we get more than 10 ^^ (10^619) copies. Each one takes X Doubling Seasons to 10 ^^ X Doubling Seasons, so by the end we will have more than 10 ^^^ (10 ^^ (10^619)) Doubling Seasons and Thousand-Year Storms. The same thing happens for each of the next Reiterate castings, so by then end we will have between 10 ^^^^ 6 and 10 ^^^^ 7 creatures. More than before, but still less than the last deck I mentioned. (Of course, you do have a seventh card to make things bigger!)
Edit: So, the following seems like a good entry into the seven card challenge:
Opalescence
Doubling Season
Thousand-Year Storm
Cackling Counterpart
Radiate
Increasing Vengeance
Mystic Retrieval
So, we start off by casting the enchantments. We cast Cackling Counterpart, targeting Doubling Season. We cast Radiate, getting one copy via Thousand-Year Storm. The copy copies Rite of Replication, targeting Thousand-Year Storm, creating two Thousand-Year Storm copies.
Next, we cast Increasing Vengeance, which triggers all three Thousand-Year Storms, each one creating two copies of Increasing Vengeance. So we will get seven copies of Increasing Vengeance in total. We can use the first to copy Cackling Counterpart, getting two more Doubling Seasons. Then the next six copies can copy Radiate. The first targets two Doubling Seasons and three Thousand-Year Storms, getting 11 and then 2059 Doubling Seasons, and then 3 + 3*2^2059 Thousand-Year Storms. The second Radiate will create more than 10 ^^ 2059 Doubling Seasons and Thousand-Year Storms, the third 10 ^^ 10 ^^ 2059, and by the sixth we have more than 10 ^^^ 6 Doubling Seasons, and Thousand-Year Storms.
Finally we cast Mystic Retrieval, which will trigger more than 10 ^^^ 6 Thousand-Year Storms. We can use the first trigger to fetch the three spells from the graveyard, and then cast the three again. Keep the Cackling Counterpart and Radiate on the stack, and only resolve the Increasing Vengeance card. Then each copy of Mystic Retrieval can fetch Increasing Vengeance. Each Increasing Vengeance spell can copy Radiate, which takes X to 10 ^^ X; casting Increasing Vengeance triggers many copies, so we take X to 10 ^^^ X; casting Mystic Retrieval triggers many copies, each of which can fetch Increasing Vengeance, so we take X to 10 ^^^^ X. So we wind up with more than 10 ^^^^ (10 ^^^ 6) creatures after Mystic Retrieval fully resolves. Then we can flashback it from the graveyard, so we get a final number of more than 10 ^^^^ (10 ^^^^ (10 ^^^ 6)).
Eh, that's okay I guess. I'm pretty sure we can do more.
Edit: Wait, I'm being stupid. Each Increasing Vegeance Spell can copy Mystic Retrieval, which can fetch Radiate from the graveyard. A single Radiate spell takes X to 10 ^^ X; a casting of Radiate creates many Thousand-Year Storm copies, which takes X to 10 ^^^ X. Each Increasing Vengeance can fetch a Radiate to recast it. Each Increasing Vengeance cast creates many copies, so it takes X to 10 ^^^^ X. Each Thousand-Year Storm trigger for Mystic Retrieval creates many copies of Mystic Retrieval, each of which can fetch Increasing Vengeance, so it takes X to 10 ^^^^^ X. And finally, casting Mystic Retrieval creates many Thousand-Year Storm triggers, so it takes X to 10 ^^^^^^ X.
So we wind up with more than 10 ^^^^^^ (10 ^^^^^^ (10 ^^^ 6) creatures. Much better.