MTG Salvation

Welp, it's been a long time since I posted here! Sorry about that, I had a bunch of stuff going on and this kind of fell by the wayside.

Ever since Alex Churchill posted his construction for encoding a UTM into Magic: the Gathering, there have been thoughts about how to perhaps translate that into the maximum damage challenge. I see four immediate problems that we face:

1) Alex's construction was for a four or five player game, whereas this challenge is for a two player game, with one player a goldfish with only basic lands in the deck. Making a version that basically uses just one deck may be difficult, especially given a 60 card limit.

2) In Alex's construction you could stop the execution of the UTM at various points. This would be a problem for the maximum damage challenge, since it means that you could run a program that kept going forever, and just choose to stop it whenever you pleased.

3) In order to create a specific, 18-symbol UTM, Alex made a very complicated construction using Rotlung Reanimator[c/]s and Artificial Evolution in order to make a copy of that UTM exactly. In order to do that, the decks basically had to have the freedom to make just about anything with Artificial Evolution. But instead of making a complicated UTM, it would seem to be much simpler to just create a simple infinite combo with all the power at one's disposal. (Note: I haven't actually tried to do this, but it does seem very likely that there is an infinite combo with all the freedom that the decks have.)

4) Note that while Alex had the decks set up a UTM, in order to have the UTM mimic an arbitrary Turing machine, you had to "program" it - that is, you had to set up the tape to a very specific configuration. Alex's construction doesn't actually run any programs, it just sets up the system. In order to have create an entry that would achieve BB(250), say, you would have to able to set up the initial tape to any configuration corresponding to any 250-state Turing machine. As with 3), the only way I can see being able to construct something that complicated, would be a deck or decks that have the power to construct any desired tape. But that would be too much power, since then would could implement Turing machines that output arbitrarily high numbers.

I think 3) and 4) are particularly problematic here - both the setup of the UTM, and the setup of the initial tape to implement a sufficiently powerful Turing machine, are very complicated. It seems very difficult to be able to do this without having the power to set up an infinite combo, which is comparatively a much simpler thing. Of course, we could cut out the UTM middleman and just have the deck implement a particular Turing machine that outputs a large number, but we still have that same problem I think.

So yeah, while achieving Busy Beaver numbers sounds very enticing, it seems like an incredibly difficult thing to try to pull off, which is why I haven't put a lot of work into it.

I still have to look at a bunch of recent posts, like J_kibbs deck, and the recent explanations of Stakfish and FortyTwo on the Chalice of the Void deck. Hopefully we can get discussion started up again.

1) and 2) are mostly addressed with the 2 player setup that jfb1337 posted

3) is also partially addressed with that construction, as the TM locks up the stack while running. But the fatal issue is that we can make a second Rotlung Reanimator that has the same trigger and order the triggers to make an infinite loop for a while then resolve the triggers in the other order to halt the machine.

4) Is not a problem, it is the goal. As by definition, any turing machine of n stated that outputs more than the BB(n) never halts. We would never be able to get to our attack step and actually deal the damage.

I think the problem with being able to order the death triggers is really the last hurdle, but I don't see any way to overcome it, short of WotC going crazy and printing enough rotlung reanimator+hungry lynx variants to render artificial evolution moot. Anything powerful enough to let us set up the UTM can also set up an infinite machine but with an extra escape rule we can invoke after an arbitrary amount of cycles, as even the smallest UTM is bigger than a non-halting machine.

Hmm, I need further explanation of jfb1337's setup. Which TM's can it execute? Of course "arbitrary TM's" is too much, as the set of all TM's have arbitrarily large inputs. Does starting with N mana allow one to set up exactly the TM's with N states? Why?

At first glance, it looks like his deck goes infinite, since we can retrace Raven's Crime to cast the other spells. Grim Discovery can get the land and Composite Golem back, which can be replayed to get the black mana plus more.

What I was saying with 4) was that we have to be able to execute very complicated TM's while still being restricted in the set of TM's that we can execute. If you are saying that jfb1337's setup can execute all N-state Turing machines for a large N, while not being able to execute any larger Turing machine, that's great - could you explain further?

Yeah the details still would still need to be worked out, and that loop does look to be a problem, the setup does need to be finite. but fixing that seems secondary to resolving the death triggers issue.

The main setup is with some large number of Rotlungs and Cats, and Noxious Ghoul set to various creatures to make and shrink tokens acting as a tape. We can easily make enough to encode a UTM to avoid running into the finite number of creature types we have. Then the complexity of the Turing machine we run is limited by how far out on the initial tape we can go to set up the biggest BB machine we can.

The setup is kinda better explained here: http://nethack4.org/pastebin/unfinished-mtg-tc-combo.html though that list does go infinite, and doesn't do a great job of proving if it is actually Turing complete, which would also need to be more formally examined if the other issues can be resolved.

Allowing for a large but finite amount of setup would limit the size of the TM we can emulate, and then only being able to set it off once and importantly have no opportunities for relevant decisions or any interaction while it is running means we are limited by the busy beaver number of whatever size TM we were able to set up.

But again the death trigger ordering thing is a real weak point of this strategy, as we can effectively make a simple machine that prints '1's forever halt after an arbitrary amount of time by just resolving the death triggers in the other order and getting to a halting state.

Edit: As for the chalice deck, I need to refresh on that myself. But I think things still weren't quite working yet.

Edit: and just to update the surprising amount of progress we've already made in the standard deck. It only took a few days to find a stage combo instead of a few weeks, and we already have a bunch of layers extending it to nearly what we had last year. We are a turn slower, but are basically only a boreal druid reprint away from turn 2.

So, I haven't gotten around to refamiliarizing myself with the Chalice of the Void deck, which looks like it might take some effort. Anyway, it appears that there are some problems that we still need to fix with the deck. With my older decks, I don't think that we actually have any outstanding problems, it's just that we haven't really given them a thorough look. So, I thought we might go back to them, and see how close they are to being finished.

It's been quite a while since I've looked at those though, so I have to refamiliarize myself with those as well. I'm also not sure what our most updated version of those decks were - here is a decklist I found for the Bramblewood Paragon deck:



Can we give this deck a thorough vetting? Perhaps we can get one of these versions ready for prime time faster than the Chalice of the Void deck.

Also these decks haven't been updated with new cards for a while, nothing is immediately jumping out at me, but escape and adventure seem like helpful and powerful mechanics. Maybe too powerful?

Also, triumphant surge is tantalizingly close to being the perfect smite the monstrous

Hmm... I guess we should always be checking the new expansions to see if there is anything of use.

Exiling cards is not that big a deal now that we have Mirror of Fate, so Escape seems akin to Flashback. Adventure is certainly an unusual and interesting mechanic - the obvious use is to somehow fetch it as a creature card, and then cast the instant or sorcery. So I guess, we could use an adventure card as one of the trigger sorceries. Interestingly, adventure cards are not instants or sorcery cards when they are in the graveyard, so Goblin Dark-Dwellers can't cast them, which is nice. So, how could we use mana or life to fetch a creature card, and how would this be better than what we have already?

Bolas's Citadel is an interesting card. Again, the obvious use is to cast one of the trigger sorceries. It would seem it would most easily be for the gigastage though, since if we used it for the megastage, what's to stop use from using it to cast the gigastage sorcery? It seems like that could work, but again the question is how this is an improvement. I guess one way it could be better is, we could have it cost 1 or 2 life rather than 3, which might be easier to work with?

There's also Precognition Field and Experimental Frenzy, again looking at trigger sorceries. I don't think we can use them for both trigger sorceries, since I don't think we can have both the megastage and gigastage be mana-based; having the megastage be mana-based means we need to use Worldpurge in the gigastage, but that would eliminate all our gigastage mana. But, we could use it for the gigastage, or we could possibly use it for the megastage, and have the gigastage sorcery be of a color that we don't have. (So perhaps Acorn Harvest, with no green) I dunno.

I guess there are a lot of interesting new cards, but I can't think of anything that jumps out - the problem is that I'm not sure exactly what we are looking for to improve the gigastage part of the combo. Perhaps we could improve the layer sequence at the end, although we have precious few cards to work with there.


Edit: Hmm, Adventure cards can actually help the ending layers. Use On Alert to untap many copies of Xathrid Gorgon, then use Usher to Safety to bounce Silverflame Squire many times. Coupled with Consecrated Sphinx and Sphinx of Enlightenment, that takes us up to F_{w^4 + w6 + 5}, an improvement of two layers.


Edit: Heh nope, we can bounce those adventure cards when they are creatures, using our stage creatures.


Edit: Hmm, the Chalice of the Void deck doesn't use white, so we couldn't cast our Adventure creatures from exile. So perhaps we can fit them in that deck? But no, we can cast the Adventure cards as creatures, and get Bloodbond March triggers. Return them to the battlefield, and bounce them back to our hand with Xathrid Gorgon or Royal Assassin. Then we can repeatedly cast them as instants/sorceries, until we need to refresh our Bloodbond March triggers, at which point we can just cast them as creatures again. So that goes infinite.

I've been thinking a bit about the Turing machine idea, and about what cards are necessary and what can be replaced.

First of all, Artificial Evolution is completely necessary. No other card has a similar effect, and no variable other than creature type ha enough distinguishable values to represent states or registers.

Next; Hungry Lynx seems necessary for this particular TM method; I don't know of anything else that pumps toughness on a triggered ability.

Now, Rutlang Reanimator: Its purpose is to replace creatures that die during the loop. It's only required to replace something of the same creature type - though a card that does exactly that doesn't exist. Variants exist, such as Bishop of wings. Possibly persist/undying creatures could work - though the they'd have to be nontoken making deck space an issue. (they'd also have to be under our control).

Noxious Ghoul: Its purpose is to shrink all creatures being used for storage to cause triggers and progress the machine by one step. Replaceable by effects that deal damage to every creature. The most interesting I found of these is Arcbond, as casting it twice (as well as giving both players protection or enough life gain during the loop) sets up a loop whose only halt condition is for one of the two creatures to die, and it does not involve ETB triggers.

Elesh Norn: Is not necessary. Its purpose is to provide automatic death triggers to keep the loop running, as well as being the halt condition for the loop - when it dies, the loop stops. A replacement I thought of was Marauding Raptor which would mean ETB triggers and death triggers wouldn't be interleaved, however different ETBs would be; still an issue. However then I realized that the it's replaceable by a system of Noxious Ghouls and Rutlang Reanimators repeatedly killing and creating creatures automatically. Which still doesn't get around this issue.

The rest of the cards aren't necessary or have easy replacements: Composite Golem just isn't needed at all (its purposes in the original setup is to create easy death triggers (which we have other methods for), create infinite mana (which we actively don't want), and trigger the combo with a split second spell on the stack (not relevant for us)); Sheilds of Velis Vel just protects combo pieces from noxious ghouls which can be replaced by, e.g, having Hungry Lynx put counters on them counteracting the shrinking/damage; Fractured Identity is nice to have for setup because it does 3 things: creating token copies, creating death triggers, and donating things (tokens only though); and is replaceable by cards that do these things individually.

Now; the issue of trigger interleaving still exists. It can be partially helped if you can somehow require part of the combo to be controlled by the opponent - but this is hard. I thought the Elesh Norn setup required this, by being the only way to auto-kill creatures, but not those of its controller; however this doesn't work since it's not the only way to auto-kill creatures within the original setup. One potential way might be to have the NG-variant be something that only effects the opponent's board, like Goblin Chainwhirler - but I don't know how to repeatedly trigger that ETB. (makes me wish un-cards were legal - Grusilda, Monster Masher could combine it with Polyraptor)


There are 2 main places where this is a problem:
- The "run a step of the TM" trigger shouldn't be interleaved with the "keep the loop going" trigger. Otherwise, arbitrarily many triggers of the first kind can be stored on the stack, and then when the machine reaches a halting state (i.e. triggers of the second kind stop happening), you'd still be able to run the machine for as many additional steps as you saved before.
The original setup with Elesh Norn has this problem because NG's "when an X ETBs, shrink all non-X" and RR "when an X dies, make an X" happen simultaneously when you're creating a 0/0
Replacing with Raptor has the same issue because NG's trigger is interleavable with Raptor's "when a creature ETBs, damage it"
Using only noxious ghouls has the issue that multiple NG triggers can be interleaved.
Using Arcbond has potentially this issue that its "when this is damaged" trigger is interleaved with death triggers; unless it can be arranged for the opponent to control all relevant death triggers.

- The Hungry Lynx trigger shouldn't be interleaved with death triggers that can cause creatures to be created. Otherwise, the p/t of the creature that gets created depends on the ordering, which allows for a computation to be changed at an arbitrary point. Lynx triggers are safe to be interleaved with each other if they are the only death triggers. Unfortunately, I don't see any way around this - the vanilla creatures that need to be controlled by the same player as the Lynxs need to be replaced from a RR variant when they die, and I don't know of any effect that gives an opponent creatures as a triggered ability we could use.

Yeah, the adventures seem to get close but have some problem or another...

Sweet oblivion allow us to have one card control both the library->graveyard and graveyard->exile transitions. Shame its a sorcery though...

Underworld breach is too powerful and the other spells are too generic, either obviously going infinite or obviously not helping. And the escape creatures, though interesting with Bloodbond march,also seem lacking.

Edit:
As for the turing machine, giving our opponent options is not a good strategy because if they can let us to loop they will.

I think being able to make different creature types is needed for Rotlung reanimator, as that is how the TM evaluates different rules. The obviously wont print one that replaces with the same creature type as that would make a 2 card combo with any sacrifice outlet. (Bishop of Wings+Divine Visitation+Woe Strider coming to a FNM near you)

Either way, I really don't see a way around making a simple looping TM with a pair of rotlung Reanimators that trigger each other, like "when an Ape dies create a 2/2 white bear" and "when a bear dies create a 2/2 green ape" to keep looping. Then also having a third set to "when an Ape dies create a 2/2 red Wall", where the red wall is the HALT instruction.

Running such a machine would mostly consist of stacking the death triggers so that the wall is never created. and then after an arbitrary amount of time, finally allow the wall to come down and halt the machine, and then resolve down and attack with an arbitrary number of 2/2 walls.

What I mean about giving the opponent stuff is not giving them choices, but using the fact that their triggered abilities will go on the stack on top of ours. For example, if you could somehow set it up such that the only way to run the machine is to have the opponent control all the hungry lynxs, and for us to control the rest, then a death would cause all their lynx triggers to resolve first (in an order that won't matter), followed by our triggers which culd otherwise cause problems if they were allowed to be interleaved with the lynxs. Though I don't see a way to require this.

The way this TM works isn't that different creature types represent different rules or instructions (like they do in Alex Churchil's more well-known TM); it's in implementation of The Waterfall Model in which creatures are representing variables; at each step you decrement every variable (damage/shrink every creature) and then whenever a variable hits 0 (a creature dies) you increment some other variables (pump other creatures) including, except in the halting case, the variable that hit 0 (requiring replacing that token). This only requires rotlung reanimators that replace the same creature type - though of course such a card would never be printed. Except maybe on a PW ultimate? Regardless, the existing RR and variants still work.

The issue you mention with a pair of RRs triggering each other is an example of the first king of problem mentioned. It's not in of itself fatal, but demonstrates that you cannot use ETB triggers to progress the loop (meaning Noxious Ghoul is out), and must let all death triggers resolve before being able to progress the loop. However I don't see any way of requiring that to happen.

I think we're still a very long way off from being able to solve all these issues with a TM based setup.

Hmm, I'm not great with nonstandard Turing machines. I know some of the tricks for proving Bitwise Cyclic Tag as Turing complete, but not much more than that.

How many different creature types do we need to simulate a Turing Machine with this method?
If we can avoid making copies of the setup cards and just rely on pump spells to etc to set the initial conditions, that would dodge some of the problems with giving us too much choice.

Arcbond seems promising as a constant set of triggers below any death trigger.

jfb1337: Good to see you still working on the Busy Beaver deck, I wish you the best of luck!


FortyTwo: Just noticed your old post bringing up Kelemne's Captain. While it does come with a destructive effect, we also need a beneficial effect to warrant us activating the ability. I don't know of any card that has a triggered ability for becoming monstrous or adding +1/+1 counters. Something like an ability that removes +1/+1 counters won't work, because we aren't forced to use that ability before the destructive trigger from Kelemne's Captain is resolved.


Edit: Hmm, I guess there is Generous Patron? So we could combine that card with donation shenanigans, so that we could activate the monstrous ability and the exchange the Kalemne's Captain with the opponent, so that Generous Patron triggers. So that is a possibility. But, drawing a card is a pretty powerful effect in this deck. It would seem to moot Acorn Harvest later, for instance. Also, if we want to position it in between Goblin Dark-Dwellers and Child of Alara, we would have to destroy whatever creature tokens are used in the hyperstage - but we only destroy artifacts and enchantments. So it would have to be an enchantment creature? I don't know of one suitable.

Or, we could just have it replace the current hyperstage, and possibly be more efficient and less troublesome? I suppose we could use it to draw Battle Cry, or whatever card we are using to create more artifact resource tokens. But, there is still the problem of being able to draw the higher instants sorceries. I guess we could make sure that all the higher instants and sorceries were of unavailable colors? That might be pretty tough, but I guess it is worth investigating.

Another possibility is, could we use Kalemne's Captain for an additional hyperstage? I guess it's possible. Since it's a separate structure from the gigastage, it's okay that Child of Alara and Worldfire destroy artifacts and enchantments, since we would only process the gigastage above the new hyperstage, where we would have exhausted all of the new stage and hyperstage resources. We couldn't use artifact tokens for the new stage though, since it can get targeted by the first stage artifact creature. Oh, and we can't use enchantment creature either because of our enchantment setup. So I guess this doesn't work.

But, I guess I'll look into the possibility of replacing the current hyperstage.


Edit: Meh, I don't like the draw trigger - nothing is forcing us to play the card when we draw it.

I was not expecting to use the act of putting +1/+1 counters on Kalemne's Captain as the beneficial effect.

I was more thinking that destroying some specific artifact/enchantment would be beneficial. Though I can't quite see how that would work with metallurgeon probably being able to kill it anyway... it's not like we get anything from killing something like Needlebug.

Yeah, it doesn't look like that can work.

Are there other cards like Kalemne's Captain, that causes all artifact tokens to be removed from play, and can trigger some beneficial ability? Such a card would have the potential to greatly simply the hyperstage, perhaps.

For specifically tokens? Aether snap? ...and that's about it?

Yeah, I'm not sure that there is much that we can trigger from Aether Snap, plus it is a sorcery so it will trigger Spellweaver Volute.

There is Bane of Progress, which I guess we can couple with Risen Reef to draw cards... but again, nothing is forcing us to play those cards before the artifact destruction.

There's also Furnace Dragon, which I suppose can be coupled with Dragon Tempest or Spit Fire - but those deal damage, which doesn't seem useful.


Edit: Oh, I didn't mean artifact tokens only, removing all artifacts would be perfectly fine.

Beyond those there's Fracturing Gust which gains way too much life.
And Consulate Crackdown which only hits opponent's things, so we'd need for it to come into play on their side somehow?

For Consulate Crackdown, I think we would need the beneficial effect to trigger off of one of our artifacts dying, in order to force us to put it into play on the opponent's side somehow. Hmm, but triggering off of our artifacts dying is too late.


Edit: So, boing back to the Chalice of the Void deck. The idea to use Highland Game didn't work - but, it appears that we can use Army of the Damned to spend 6 life, and get it back with two copies of Centaur Safeguard? So we get something like



which would get us 9 stages!

I don't remember if we can get going using Sphinx of Enlightenment without Consecrated Sphinx - if not, we can always switch back to Words of Wisdom. Oh, but do we need Thousand-Year Storm?

Of course, fixing the problems in the deck is the higher priority. It may not be possible to fix everything without losing more card slots, and the above change doesn't get us a more efficient 7 or 8 stage setup, since we need two more cards to get the K'rrik change working.

Yeah I think the problem was getting the right amount of Muzzio, Visionary Architect activations (and in the right states). It looked like there might have been a problem around chalice on 2?

Also, if I recall correctly, just one sphinx was enough to get started?

Edit: Looking more at the 'waterfall' TMs

Arcbond - we need to only be able to resolve exactly two of these, so TYS and friends are out. Platinum angel + Abyssal persecutor is an elegant way to ensure players don't die until the TM ends. (Rules question: does our deck get disqualified for going infinite if we can't stop the loop and the game would be a draw?)

Death triggers: I think Hungry Lynx is the problem here, what we need instead is something that triggers on come into play and boosts toughness of a creature type. That way the stack's ordering is not up to us: it's wait until arcbond kills something, a Rotlung Reanimator triggers, and that trigger leads to the pumping trigger, however it looks like all triggers of the required type (Kazuul Warlord) are 'may' abilities, or too generic (cathars' crusade).

Double death: If two or more of the 'waterclocks' zero out at the same time, the behavior becomes undefined. This seems trickier to resolve, and I'm not sure how we can fix it...

I didn't make the original rules, but certainly it appears that an uninterruptible infinite won't disqualify a deck, unless you were dealing damage during the infinite. The "no infinite" rule really just means there has to be an upper bound to how much damage the deck can deal, so an uninterruptible infinity during which no damage is dealt wouldn't impact that.


Edit: Oh, but it looks like you are dealing damage in the loop. Hmmm... under the original rules, this would deal an infinite amount of damage, and thus be disqualified? It's up to interpretation I think - under the rules, when you see that you are in an uninterruptible infinite loop, you stop the game and agree to a draw. So perhaps the game would be stopped before to much damage is dealt? I dunno.

Now, we have been tweaking the rules a bit, like requiring that you win the game, or the "score" being the negative of your opponent's final life. For the former the deck would not be disqualified, for the latter, there are cards that would prevent a player from going negative. (like Angel of Grace)

Well I was thinking of using arcbond with Platinum angel and Abyssal persecutor so that neither player can die, letting the angel/demon serves as the HALT condition. If neither ever dies the game is a draw even though both players would get to -infinite life.

Edit:
We might be able to get around it by saying we need to actually win the game instead of letting it be a draw? or use Runed Halo as a less elegant way to keep players alive.

Is there a way to force it so that our opponent has all of the Rotlung reanimators and ensure that we can't have any? That would solve both issues.

edit2: also, thanks to the mtg judgechat for the help even though this scenario is not ever going to actually happen.

If we rule that going to -infinite life is not allowed, then there are alternate creatures that prevent a player from going below 1 life.

Probably though, we can just rule that these uninterruptible infinite loops don't disqualify a deck.

Looking through, I don't see a way to force all of the Rotlungs to our opponent, without letting them get our Hungry lynxes.

Yeah, there aren't many ways to transfer control of a creature over to the opponent, and I can't think of any that are restricted. (say by creature type or color)

it would have to be color, as we can manipulate creature types too much, The closest card appears to be Karrthus, Tyrant of Jund who steals dragons and that does not seem good enough.