Yeah Engineered Plague definitely fixes it, as it can counteract the extra buffs.
I'm not convinced that we need to fix it yet, as the damaged tokens left over would die and match the computation up to one without them before their waterclock would trigger again.
Surprisingly, the game engine (namely, Rule 104.4b) provides the ability to go beyond w_1^CK, more powerful than a usual Turing-complete system.
However, I've seen something like Vedalken Orrery in your decks, which allow you acting in instant timing, so it is possible that:
You play some and get the computing simulation starting. Suppose you starts a computation of non-halting Turing machine (or other computation modals equivalent to that)
If you cannot do anything, by the Rule 104.4b, game ends with zero (or a small number) total damage.
If you can do something, even if you don't, the Rule 104.4b will not stop the game. Now you run into some weird cases...
I don't know much details about the uncomputable decks, but could anyone explain how it goes?
Things have changed quite a bit since then, but the core of how arcbond, coat of arms, dralu's crusade and bishop of wings/xanthrid necromancer interact has stayed pretty consistent. One very important thing to note is that because of APNAP if we control any of the death triggers, we can stack them above/below the arcbond trigger. So that is why we are only kicking off computation by saccing our board to get a goblin boom keg or kaervek's spite for initial damage. (that also means we lose our vedalken orrery, locking us out of interfering with the computation)
That is the mandatory loops draw rule
"104.4b If a game that’s not using the limited range of influence option (including a two-player game) somehow enters a “loop” of mandatory actions, repeating a sequence of events with no way to stop, the game is a draw. Loops that contain an optional action don’t result in a draw."
However because we don't allow for infinites, if the loop has an escape mechanism while it builds up, its either up to us or our opponent (or both) on when to stop. If we get to choose when to stop it (Splinter twin style combos) then we won't, and the deck is DQed for not having an upper bound. If the opponent can stop it (goblin game), they will DQ us by letting us go beyond whatever upper bound we thought we had.
So this rule doesnt actually allow for beyond BB damage in this case.
Theoretically this does allow us to have a halting oracle, and go beyond BB, but since one of the outputs of the oracle is "instantly end the game" we can't actually use it for questions we don't know the answer to. (Edit: I guess unless we Shahrazad?)
Rule 104.4b is interesting - I feel like it's a little ambiguous, as it's not clear what constitutes a "set of actions". For example, would continually exponentiating Doubling Seasons constitute a loop, even though the number of Doubling Seasons we are adding is exploding? I suppose yes, if we are casting the same spells/activating the same abilities to perform the exponentiating. But there are probably more difficult corner cases one could come up with.
I suppose a non-halting Turing machine wouldn't fit most anyone's notion of a "loop", but I imagine a judge would generally rule it as such if it were to happen in a game.
Anyway, I don't think such issues affects this challenge - a non-halting computation that cannot be interrupted will end in a draw, so it won't count for any score. (Our challenge requires that you win the game.) If there is a non-halting computation that can be interrupted, and it keeps increasing the available resources, then we (or the opponent, if they are the only ones who can interrupt) can choose to interrupt the computation at any point, with arbitrarily many resources; if this can lead to dealing an arbitrarily large amount of damage, then the deck is considered invalid for not having a finite maximum.
The way we implement the Busy Beaver function is by implementing the Waterfall Model, a Turing-complete computational model described here:
Basically you have bunch of waterclocks, each if which contains a natural number value, and each tick of time every waterclock decrements by one. When a waterclock hits 0, it adds a specific number of counters to each waterclock, determined by the program. The above page doesn't specify when it should halt, but one can choose a specific waterclock that halts the program when it hits zero.
We implement this using creatures of various types. We have a Coat of Arms, so each additional creature of a given type adds one to the toughness of all creatures of that type. We have a bunch of Rotlung Reanimators or Xathrid Necromancers, hacked by Artificial Evolution, so that they say "when a (creature of type A) dies, create a (creature of type B) 2/2 token". So the waterclocks correspond to the various creature types, and the counter number of the waterclock is the toughness of those creatures, minus damage they've taken. We decrement the waterclocks by using Arcbond, to repeatedly deal damage to each creature. (it also deals damage to each player, so this is something that we have to deal with.) We have recently added Comeuppance, so that the creature that is Arcbonded takes damage as well, preserving the symmetry of the situation. We start the repeated Arcbond triggers by destroying a Goblin Boom Keg. We use a sweeper like Desolation Giant or Kaervek's Spite do destroy the Goblin Boom Keg, so clear out our side of things that can allow us to interrupt the computation, particularly Vedalken Orrery.
So that's the main idea; however there is a detail I haven't mentioned yet. If we naively implement the above, then when X creatures die it will trigger each Necromancer X times, so we add a variable number of creatures depending on how many creatures die, which doesn't follow the Waterfall Model. We're not sure whether or not this version is Turing complete, so until we can prove it we can't use it and claim to perform the Busy Beaver function. So, we do a fix: We have various copies of hacked Dralnu's Crusades, hacked to say things like "Each Ape is an Atog". The idea is that we will be creating copies of Atogs, and that represents our waterclock counter, but we create a single Ape as well, and it is the Ape that triggers the Necromancers/Reanimators. So only one creature that triggers will die each time, and we get the same number of creatures created, which is what we want.
After that, we've been working on recursing the Busy Beaver deck as much as possible. We've dubbed a process that repeats the previous process X times a "layer" (i.e. +1 in a fast-growing hierarchy), a process that creates X layers a "stage" (i.e. +w), and a process that creates X stages a "hyperstage" (i.e. w^2). Right now we looking at decks on the order of BB_{w^2 + w2 + 10}, i.e. a fast-growing hierarchy that starts at the Busy Beaver function and goes up to w^2 + w2 + 10.
Hmm, do turns in Shahrazad count against our turn limit?
Because if not, we can use that extra time to go infinite in the subgame and make casting shahrazad into "consult a halting oracle". though distinguishing the output of "both players lost half their life" vs "only one player lost half their life" might be tricky.
And the most important thing: We are able to put Arcbond trigger and Necromancer triggers in any order, interrupting the calculation, maybe leading to halting/non-halting, then Rule 104.4b won't work when we run a non-halting waterfall. Maybe this can be solved by a forced Donate of the arcbond-ed things?
Well, for the Vintage challenge Shahrazad is banned. But, if you have an idea how to get into super-Busy Beaver numbers with Shahrazad, by all means lets explore it!
Edit: Arcbond and Artificial Evolution need to be cast in order to start the computation. From then on, we have to have no way of getting them back to our hand, unless the only way to do so is to destroy our setup (e.g. Worldfire getting rid of all Arcbonded creatures). So yeah, that's a pretty strict constraint on the deck.
If rule 104.4b isn't applied when we have a game that will never end, we still won't ever get to a point where we kill the opponent and sent them to a large negative amount of life, so that game doesn't register a score. So that is just a game that doesn't matter.
@deedlit:oh right, one of the few cards banned not for power level or ante.
I don't really see a way to use it as we can win/lose the subgame as we wish, only drawing the subgame gives us any real information, and I suppose our opponent could even concede the subgame as that's a legal game action for them to take.
@hyp_cos:The way the opponent orders their necromancer triggers is irrelevant, they all have to resolve before our arcbond does damage again. As we are the active player our arcbond goes on the stack first below any of the necromancer triggers which our opponent as the non active player then places in whatever order they want. then we need to wait for their x^^^x or so necromancer triggers to resolve before the next arcbond.
I suppose we could outlaw the opponent conceding the subgame, as that is pretty much along the lines of conceding the main game, which we can't allow to happen. But yeah, it seems difficult to use both players losing half their lives as a query in a program.
What's interesting is that you could cast Shahrahzad within a subgame, so the oracle machine can also call an oracle - this could potentially get the full power of the arithmetical hierarchy.
Looking at the proposed solution to the diagonal issue, I don't think it works, but not because of the few random leftover creatures sometimes.
Extra dummy creatures of a given type that never die only affect the waterclock that is being remade by its own trigger, having 9 extra dummy crabs doesn't increase the cat-crab's toughness by 9 when an ape dies.
I think we are still stuck with the diagonal entries being 2 greater than the sum of the other entries in their rows.
Unless this restricted model can be shown to be TC, we need engineered plague or similar.
I think you might be right about the damaged creatures that stick around dying before they matter. If we can prove that to be true we can work without an extra card by letting all the tokens have the same base toughness.
We'll need a third creature type per clock in order to adjust the toughness of atogs without also buffing apes. We can do something like
Apes are Allies
Atogs are Allies
And use as many Dralnu's Crusade copies for the second as needed to balance out the toughness.
To create programs where the diagonal is not super large we can use a trick to implement an equivalent program.
example:
3 3 1
1 4 0
3 7 3
Step 0: get rid of 1s in the diagonal by adding 1 to the entire row. (Technically a 1 in the diagonal leads to an infinite loop or 2 clocks emptying at the same time, so we don't care about these programs. But we could fix it like this if we want.)
Step 1: create Necromancers according to the number for non diagonal entries and 1 for each entry on the diagonal.
So for the first example row we have 1 Necromancer creating apes when apes die, 3 Necromancers creating birds when apes die and 1 Necromancer creating crabs when apes die.
Step 2: Figure out the toughness a single diagonal creature token will have with that setup. If it is lower than the entry on the diagonal for all rows we can adjust the toughness up with Dralnu's Crusades to the desired value and we are done.
In the example row 3 is problematic. A cat token will have toughness 14, but we only want 3.
Step 3: Add more than one of each diagonal creature token. By starting with 2 apes and 2 bats and 2 cats we cause all of the Necromancers to trigger twice every time they die. Effectively we are implementing the equivalent program where every entry is doubled. But we didn't need to add more necromancers for that.
So we check if it works now. We want to implement
6 6 2
2 8 0
6 14 6
In the problematic row 3 the toughness of each of the 2 cat tokens is now 15 since they buff each other. Still too high, but we are getting closer.
Step 4: Find the number of diagonal tokens that work. Since all diagonal entries are 2 or more and adding an additional diagonal token only adds 1 toughness to them we are guaranteed to get there eventually.
In the example we need 7 tokens of each diagonal creature and implement
21 21 7
7 28 0
21 49 21
The 7 cats would initially have a toughness of 20, so we add one Dralnu's Crusade for them and get the 21 that we want.
@Deedlit11:
Oh you remind me about this: if damages were initialized by Goblin Boom Keg and processed by Arcbond,they would be 3 at a time. Opponent loses at 21 damages. More importantly, if this small damage is the only way to damage opponent, how can you get big damage before game ends?
And about the challenge rules. I don't see "You must win the game" in the classic writeup.
And something about this pre-Ackermann deck:
You used Gideon, Ally of Zendikar to prevent small creatures from dying. The easiest-to-die creature is the animated Mana Crypt, requiring at least +4/+4, i.e. 4 emblems from Gideon. So I assume that you need 3 Rings of Brighthearth triggers on the only activation of Gideon, with at least 2 token Rings, so by the time March of the Machines should be presense, meaning that Mana Crypt is already gone.
One possible solution: Mana Crypt can be exiled by Mimic Vat on first play of March of the Machines, and later come back by Mirror of Fate and Muzzio, Visionary Architect.
If that works, why doesn't it work on Builder's Blessing version? If that doesn't work, how to get Gideon version worked?
More about the writeup:
So how much damage is that? If you've been keeping track along with me, you'll see that my count comes to 407 nested layers of recursion. That means we're looking at a number of the form 2^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^?, where the number of arrows is 407, and ? is essentially the number of Rite of Passage copies that trigger on the final burst of damage to the all-powerful Omniscience.
Wrong. Final damage is approximately ? itself. So we lose a layer of 2->()->407... Wait, Garza's Assassin doesn't need to draw (unmentioned in the writeup). So the final value is still right.
I get also 15 card sideboard. However I noticed the initial damaged and also noted it down and thereby searching for the possible solution in this regards. But my query is that most if the suggested solutions are not working at all.
Thanks College Essay
@hyp cos: Indeed, the final damage has to either be dealt in one packet, or we make it so that the opponent doesn't die from being at 0 or less life. (But we still win the game in the end.)
The most common way to kill off the opponent is during combat, either with a lot of creatures or one big creature. If that's not available, we generally have to add some big burst spell.
Yes, there are some changes to the rules in the classic writeup: The score is the negative of the opponent's life, rather than final damage (so loss of life helps, healing and then redealing damage does not); and we have to win the game. FortyTwo thought this was more reasonable, and they make sense. Also, I switched the opponent having 60 Islands to having 60 Wastes, which seemed to be more fitting for a "blank" deck.
Ah, the old decks! I look back at those old decks fondly, but sadly it's been a while since we've done them. So, I don't remember the exact startup we came up with for Gideon, but yeah we can bring back Mana Crypt with Mirror of Fate and Umzzio, Visionary Architect if need be. The problem with Builder's Blessing was a subtle infinite that SadisticMystic found, something to do with the tapping and untapping. I'll try to see if I can find something on this.
Yeah, I noticed that SM would sometimes make an off-by-one error in his damage calculation, I mentioned this to him I believe. But good thing that the final damage turns out to be correct.
Edit: Okay, from the old Wizards.com thread, we have this quote from SadisticMystic:
Edit: YUCK.
As I'm reading back over the some of the early parts that were in place for a while, I see that I never really gave an adequate explanation of Builder's Blessing, and why it ends up being safe...turns out, even as constrained as it is, it isn't actually safe at all.
The way we have to use Mana Crypt here, there is never a time after the bootstrap where it is both a) tapped, and b) a creature, so the +0/+2 bonus may as well be permanent for it. Creature form is only used to get the untap abilities onto the stack; they don't resolve until March of the Machines is gone because that's when we can actually tap it in between each ability. Hence we can use Copy Enchantment to produce at least three copies of Builder's Blessing, and give Mana Crypt only four -1/-1 counters, for a net gain in toughness that can continue forever.
So that was a pretty big piece of the deck, and now we have to replace it. Going back to Elspeth is an option, naturally, but then we have to reconfigure the deck to be mindful of her, so we lose Coastal Drake and Skyshroud Archer at the very least. Another possibility would exist if we had global effects that set base toughness: Godhead of Awe is the only good one, and its grant of just 1 toughness would require Avacyn as an additional support card. Furthermore, despite the name, Godhead of Awe is not actually a God--instead, it's the one creature type that we really do not want any creatures to have. So that's not an option unless we go for an even bigger overhaul, throwing away Clash of Realities and undoubtedly several other cards as well.
Who's up for lobbying for a reprint of Mana Crypt except with the mana cost changed to nine Phyrexian mana? We could at least deal with it that way.
Start with Mana Crypt, Chrome Mox, Chaos Warp, Opalescence, DN, Berserker, and another red card.
Play Mana crypt, Chrome Mox with the red card exiled, then Warp the Chrome Mox into Omniscience. Play Opalescence, then DN, getting its token.
The card champion Omniscience, then a token champion the card. Firstly let Omniscience come back, then exile the token, the Berserker card coming back. The stack is now:
Now for the Berserkers (card or token), every two can flicker Omniscience, and keep one on board. When the stack clear, you still have unboundedly many Berserkers on.
Now go to combat. Since Changeling Berserkers have haste, you can have them all attack, dealing unboundedly many damage.
Possible solution: Use Changeling Titan or Changeling Hero instead of the haste Berserker. This may cancel the stage or the stage, though.
Second thing: Infinite mana supply (maybe Dual Nature + changeling) + Mindshrieker + Emrakul, the Aeons Torn = infinite powered Mindshrieker. If you have some way translating its power into damage (Bloodshot Cyclops), that would go infinite.
And. About the waterfall model:
There are only 261 creature types. If every waterclock uses 2 creature types, we cannot build a calculation simulator with more than 130 waterclocks. I wonder whether this is still Turing-complete.
@hyp_cos: we keep the opponent alive through the calculation by having their arcbonded creature be a lifelinker like K'rrik, Son of Yawgmoth. We don't care that their life gets really high and could even potentially use that as the 'output' of the calculation, But we mostly reset it to 1 with Worldfire.
Ok I think the diagonalization solution in 4018 works if programs behave the same when every entry multiplied by a constant c.
Which is true as we can just look at the state every c steps and see it is equivalent to applying one step of the original program then multiplying by c.
I think this makes our UTM a little more awkward to reset between calculations as the entries get much larger each iteration, but it should be fine.
That's really nice. Is the old deck looking good right now? I was wondering if, after the blue and white stages, we could add a green stage using Stakfish's land + aura idea.
I haven't found a way to interrupt the computation except for The Three Seasons getting Artificial Evolution back to the hand, which FortyTwo already mentioned. So if you plan to add a stage or rework the layers anyway just keep in mind not to use it.
So far everything I looked at was solid, but I'm still working on fully understanding the deck.
What is the plan to turn the computation output into progress? The computation gives the opponent a lot of life and creatures. We can get a lot of mana from Mana Echoes. What do we do with it? I see a Thousand-Year Elixir that can keep untapping itself, but I don't think that is it
The "we must win" rule only really comes up when we're considering platinum angel or abyssal persecutor, to answer the question of whether it's ok for a game to end in a draw by a non-halting computation while making our opponent's life arbitrarily negative. (with the "we must win" rule that's ok, whereas without it then it isn't).
In decks where we keep the opponent alive using a lifelinker or a damage prevention effect, the "we must win" rule isn't relevant; as non-halting computations always end the game with the opponent on a positive life total and thus don't effect the score of the deck.
@Iijil: Damn, I keep forgetting what I was thinking about with these older decks. I think it was Gravitic Punch dealing a bunch of damage with K'rrik, Son of Yawgmoth.
Yeah converting the output is a bit complicated but galvanic punch to gain a lot of life, which we can turn into storm via Lingering souls (and get a bunch more computations in the meantime). And another thing to note is that because we can cast more artificial evolutions from lingering souls we can setup the computation as we like, using the leftover tokens from the previous computation.
I think making more xanthrid necromancers each computation is a bit more inefficient than what we had had, and requires some stack shenanigans but is still possible. (Though we already need to remake k'rrik with the comeuppance change, so this isn't any worse than what we'd already need to do.)
Cast lingering souls triggering a bunch of Spellweaver Volutes, stack them with all of the instants alternating (stacking a cycle of wrong turn, artifical evolution, arcbond, pull from eternity until we are out of volute triggers), then in response, make a soul separator Stern Proctor, to bounce all of them and our real artifacts, (Harmonic Prodigy+Parallel Lives ensures we have enough triggers)
so down the stack the loop will be something like:
...
Computation ends
Resolve Dual Nature triggers for our artifacts/enchantments
Pull from Eternity our creatures into the yard.
Soul separator K'rrik, and necromancer
Resolve an arcbond on a K'rrik token
Resolve artificial evolution on the necromancers, and setup the next BB program
Wrong turn them all to the opponent
Cast+resolve the real artifacts/enchantments getting Dual nature triggers
In response Soul separator Stern proctor to bounce all of our real artifacts/enchantments
Still in response to the Dual Nature triggers Soul separator Desolation giant to kill the boom keg damage their k'rrik and trigger computation.
Locked in computation
...
Edit: Actually with a UTM we don't need to make more necromancers and change the programming each time as only the token input changes.
I think there is an infinite with the hyperstage transition. It can produce too much red mana:
- Start with X Thousand-Year Storm copies and X copies of Spellweaver Volute, all enchanting Pull from Eternity.
- Cast a Gravitic Punch to start a transition. Spellweaver Helix triggers.
- While resolving the Helix we cast Worldfire and Restore. Both of them trigger all the TYS and Volutes.
- When done resolving we put the triggers on the stack. Order them so that we will resolve a repeating sequence of TYS on Wildfire -> Volute on Pull from Eternity -> TYS on Restore
- create a Stern Proctor token to bounce all the Volutes. That makes it so the last known information for them is that they enchanted a Pull from Eternity and all of the triggers can create and cast a copy when they resolve
- Resolve the TYS and Volute triggers to cycle Cragcrown Pathway between battlefield, exile and graveyard, tapping it for a red each time
Private Mod Note
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We can just add Engineered Plague then.
I'm not convinced that we need to fix it yet, as the damaged tokens left over would die and match the computation up to one without them before their waterclock would trigger again.
However, I've seen something like Vedalken Orrery in your decks, which allow you acting in instant timing, so it is possible that:
You play some and get the computing simulation starting. Suppose you starts a computation of non-halting Turing machine (or other computation modals equivalent to that)
If you cannot do anything, by the Rule 104.4b, game ends with zero (or a small number) total damage.
If you can do something, even if you don't, the Rule 104.4b will not stop the game. Now you run into some weird cases...
I don't know much details about the uncomputable decks, but could anyone explain how it goes?
post #2434 (link) explains the initial setup of implementing the Waterfall Model (https://esolangs.org/wiki/The_Waterfall_Model)
Things have changed quite a bit since then, but the core of how arcbond, coat of arms, dralu's crusade and bishop of wings/xanthrid necromancer interact has stayed pretty consistent. One very important thing to note is that because of APNAP if we control any of the death triggers, we can stack them above/below the arcbond trigger. So that is why we are only kicking off computation by saccing our board to get a goblin boom keg or kaervek's spite for initial damage. (that also means we lose our vedalken orrery, locking us out of interfering with the computation)
That is the mandatory loops draw rule
"104.4b If a game that’s not using the limited range of influence option (including a two-player game) somehow enters a “loop” of mandatory actions, repeating a sequence of events with no way to stop, the game is a draw. Loops that contain an optional action don’t result in a draw."
However because we don't allow for infinites, if the loop has an escape mechanism while it builds up, its either up to us or our opponent (or both) on when to stop. If we get to choose when to stop it (Splinter twin style combos) then we won't, and the deck is DQed for not having an upper bound. If the opponent can stop it (goblin game), they will DQ us by letting us go beyond whatever upper bound we thought we had.
So this rule doesnt actually allow for beyond BB damage in this case.
Theoretically this does allow us to have a halting oracle, and go beyond BB, but since one of the outputs of the oracle is "instantly end the game" we can't actually use it for questions we don't know the answer to. (Edit: I guess unless we Shahrazad?)
Rule 104.4b is interesting - I feel like it's a little ambiguous, as it's not clear what constitutes a "set of actions". For example, would continually exponentiating Doubling Seasons constitute a loop, even though the number of Doubling Seasons we are adding is exploding? I suppose yes, if we are casting the same spells/activating the same abilities to perform the exponentiating. But there are probably more difficult corner cases one could come up with.
I suppose a non-halting Turing machine wouldn't fit most anyone's notion of a "loop", but I imagine a judge would generally rule it as such if it were to happen in a game.
Anyway, I don't think such issues affects this challenge - a non-halting computation that cannot be interrupted will end in a draw, so it won't count for any score. (Our challenge requires that you win the game.) If there is a non-halting computation that can be interrupted, and it keeps increasing the available resources, then we (or the opponent, if they are the only ones who can interrupt) can choose to interrupt the computation at any point, with arbitrarily many resources; if this can lead to dealing an arbitrarily large amount of damage, then the deck is considered invalid for not having a finite maximum.
The way we implement the Busy Beaver function is by implementing the Waterfall Model, a Turing-complete computational model described here:
The Waterfall Model
Basically you have bunch of waterclocks, each if which contains a natural number value, and each tick of time every waterclock decrements by one. When a waterclock hits 0, it adds a specific number of counters to each waterclock, determined by the program. The above page doesn't specify when it should halt, but one can choose a specific waterclock that halts the program when it hits zero.
We implement this using creatures of various types. We have a Coat of Arms, so each additional creature of a given type adds one to the toughness of all creatures of that type. We have a bunch of Rotlung Reanimators or Xathrid Necromancers, hacked by Artificial Evolution, so that they say "when a (creature of type A) dies, create a (creature of type B) 2/2 token". So the waterclocks correspond to the various creature types, and the counter number of the waterclock is the toughness of those creatures, minus damage they've taken. We decrement the waterclocks by using Arcbond, to repeatedly deal damage to each creature. (it also deals damage to each player, so this is something that we have to deal with.) We have recently added Comeuppance, so that the creature that is Arcbonded takes damage as well, preserving the symmetry of the situation. We start the repeated Arcbond triggers by destroying a Goblin Boom Keg. We use a sweeper like Desolation Giant or Kaervek's Spite do destroy the Goblin Boom Keg, so clear out our side of things that can allow us to interrupt the computation, particularly Vedalken Orrery.
So that's the main idea; however there is a detail I haven't mentioned yet. If we naively implement the above, then when X creatures die it will trigger each Necromancer X times, so we add a variable number of creatures depending on how many creatures die, which doesn't follow the Waterfall Model. We're not sure whether or not this version is Turing complete, so until we can prove it we can't use it and claim to perform the Busy Beaver function. So, we do a fix: We have various copies of hacked Dralnu's Crusades, hacked to say things like "Each Ape is an Atog". The idea is that we will be creating copies of Atogs, and that represents our waterclock counter, but we create a single Ape as well, and it is the Ape that triggers the Necromancers/Reanimators. So only one creature that triggers will die each time, and we get the same number of creatures created, which is what we want.
After that, we've been working on recursing the Busy Beaver deck as much as possible. We've dubbed a process that repeats the previous process X times a "layer" (i.e. +1 in a fast-growing hierarchy), a process that creates X layers a "stage" (i.e. +w), and a process that creates X stages a "hyperstage" (i.e. w^2). Right now we looking at decks on the order of BB_{w^2 + w2 + 10}, i.e. a fast-growing hierarchy that starts at the Busy Beaver function and goes up to w^2 + w2 + 10.
Hope that helps!
(P.S. what have you been up to googologically?)
Because if not, we can use that extra time to go infinite in the subgame and make casting shahrazad into "consult a halting oracle". though distinguishing the output of "both players lost half their life" vs "only one player lost half their life" might be tricky.
But there are still instant cards like Arcbond, Artificial Evolution and maybe Pull from Eternity, so how to force them leaving your hand when the calculation starts?
And the most important thing: We are able to put Arcbond trigger and Necromancer triggers in any order, interrupting the calculation, maybe leading to halting/non-halting, then Rule 104.4b won't work when we run a non-halting waterfall. Maybe this can be solved by a forced Donate of the arcbond-ed things?
Edit: Arcbond and Artificial Evolution need to be cast in order to start the computation. From then on, we have to have no way of getting them back to our hand, unless the only way to do so is to destroy our setup (e.g. Worldfire getting rid of all Arcbonded creatures). So yeah, that's a pretty strict constraint on the deck.
If rule 104.4b isn't applied when we have a game that will never end, we still won't ever get to a point where we kill the opponent and sent them to a large negative amount of life, so that game doesn't register a score. So that is just a game that doesn't matter.
I don't really see a way to use it as we can win/lose the subgame as we wish, only drawing the subgame gives us any real information, and I suppose our opponent could even concede the subgame as that's a legal game action for them to take.
@hyp_cos:The way the opponent orders their necromancer triggers is irrelevant, they all have to resolve before our arcbond does damage again. As we are the active player our arcbond goes on the stack first below any of the necromancer triggers which our opponent as the non active player then places in whatever order they want. then we need to wait for their x^^^x or so necromancer triggers to resolve before the next arcbond.
What's interesting is that you could cast Shahrahzad within a subgame, so the oracle machine can also call an oracle - this could potentially get the full power of the arithmetical hierarchy.
Extra dummy creatures of a given type that never die only affect the waterclock that is being remade by its own trigger, having 9 extra dummy crabs doesn't increase the cat-crab's toughness by 9 when an ape dies.
I think we are still stuck with the diagonal entries being 2 greater than the sum of the other entries in their rows.
Unless this restricted model can be shown to be TC, we need engineered plague or similar.
We'll need a third creature type per clock in order to adjust the toughness of atogs without also buffing apes. We can do something like
Apes are Allies
Atogs are Allies
And use as many Dralnu's Crusade copies for the second as needed to balance out the toughness.
To create programs where the diagonal is not super large we can use a trick to implement an equivalent program.
example:
3 3 1
1 4 0
3 7 3
Step 0: get rid of 1s in the diagonal by adding 1 to the entire row. (Technically a 1 in the diagonal leads to an infinite loop or 2 clocks emptying at the same time, so we don't care about these programs. But we could fix it like this if we want.)
Step 1: create Necromancers according to the number for non diagonal entries and 1 for each entry on the diagonal.
So for the first example row we have 1 Necromancer creating apes when apes die, 3 Necromancers creating birds when apes die and 1 Necromancer creating crabs when apes die.
Step 2: Figure out the toughness a single diagonal creature token will have with that setup. If it is lower than the entry on the diagonal for all rows we can adjust the toughness up with Dralnu's Crusades to the desired value and we are done.
In the example row 3 is problematic. A cat token will have toughness 14, but we only want 3.
Step 3: Add more than one of each diagonal creature token. By starting with 2 apes and 2 bats and 2 cats we cause all of the Necromancers to trigger twice every time they die. Effectively we are implementing the equivalent program where every entry is doubled. But we didn't need to add more necromancers for that.
So we check if it works now. We want to implement
6 6 2
2 8 0
6 14 6
In the problematic row 3 the toughness of each of the 2 cat tokens is now 15 since they buff each other. Still too high, but we are getting closer.
Step 4: Find the number of diagonal tokens that work. Since all diagonal entries are 2 or more and adding an additional diagonal token only adds 1 toughness to them we are guaranteed to get there eventually.
In the example we need 7 tokens of each diagonal creature and implement
21 21 7
7 28 0
21 49 21
The 7 cats would initially have a toughness of 20, so we add one Dralnu's Crusade for them and get the 21 that we want.
Oh you remind me about this: if damages were initialized by Goblin Boom Keg and processed by Arcbond,they would be 3 at a time. Opponent loses at 21 damages. More importantly, if this small damage is the only way to damage opponent, how can you get big damage before game ends?
And about the challenge rules. I don't see "You must win the game" in the classic writeup.
And something about this pre-Ackermann deck:
You used Gideon, Ally of Zendikar to prevent small creatures from dying. The easiest-to-die creature is the animated Mana Crypt, requiring at least +4/+4, i.e. 4 emblems from Gideon. So I assume that you need 3 Rings of Brighthearth triggers on the only activation of Gideon, with at least 2 token Rings, so by the time March of the Machines should be presense, meaning that Mana Crypt is already gone.
One possible solution: Mana Crypt can be exiled by Mimic Vat on first play of March of the Machines, and later come back by Mirror of Fate and Muzzio, Visionary Architect.
If that works, why doesn't it work on Builder's Blessing version? If that doesn't work, how to get Gideon version worked?
More about the writeup:
Wrong. Final damage is approximately ? itself. So we lose a layer of 2->()->407... Wait, Garza's Assassin doesn't need to draw (unmentioned in the writeup). So the final value is still right.
Thanks
College Essay
The most common way to kill off the opponent is during combat, either with a lot of creatures or one big creature. If that's not available, we generally have to add some big burst spell.
Yes, there are some changes to the rules in the classic writeup: The score is the negative of the opponent's life, rather than final damage (so loss of life helps, healing and then redealing damage does not); and we have to win the game. FortyTwo thought this was more reasonable, and they make sense. Also, I switched the opponent having 60 Islands to having 60 Wastes, which seemed to be more fitting for a "blank" deck.
Ah, the old decks! I look back at those old decks fondly, but sadly it's been a while since we've done them. So, I don't remember the exact startup we came up with for Gideon, but yeah we can bring back Mana Crypt with Mirror of Fate and Umzzio, Visionary Architect if need be. The problem with Builder's Blessing was a subtle infinite that SadisticMystic found, something to do with the tapping and untapping. I'll try to see if I can find something on this.
Yeah, I noticed that SM would sometimes make an off-by-one error in his damage calculation, I mentioned this to him I believe. But good thing that the final damage turns out to be correct.
Edit: Okay, from the old Wizards.com thread, we have this quote from SadisticMystic:
First thing, Dual Nature + Changeling Berserker = infinite damage
Start with Mana Crypt, Chrome Mox, Chaos Warp, Opalescence, DN, Berserker, and another red card.
Play Mana crypt, Chrome Mox with the red card exiled, then Warp the Chrome Mox into Omniscience. Play Opalescence, then DN, getting its token.
Play Berserker, now the stack looks like this:
card Champion
create Berserker token
create Berserker token
The card champion Omniscience, then a token champion the card. Firstly let Omniscience come back, then exile the token, the Berserker card coming back. The stack is now:
card Champion
create Berserker token
create Berserker token
exile all Berserker token
create Berserker token
The card champion DN, then a token champion the card, DN coming back; another token sacrificed. Current stack:
exile all Berserker token
create Berserker token
Exile the token, Berserker card coming back. The stack is now:
card Champion
create Berserker token
create Berserker token
create Berserker token
This can loop unboundedly, so generally you can get
card Champion
create Berserker token
create Berserker token
...
create Berserker token
create Berserker token
Now for the Berserkers (card or token), every two can flicker Omniscience, and keep one on board. When the stack clear, you still have unboundedly many Berserkers on.
Now go to combat. Since Changeling Berserkers have haste, you can have them all attack, dealing unboundedly many damage.
Possible solution: Use Changeling Titan or Changeling Hero instead of the haste Berserker. This may cancel the
Second thing: Infinite mana supply (maybe Dual Nature + changeling) + Mindshrieker + Emrakul, the Aeons Torn = infinite powered Mindshrieker. If you have some way translating its power into damage (Bloodshot Cyclops), that would go infinite.
And. About the waterfall model:
There are only 261 creature types. If every waterclock uses 2 creature types, we cannot build a calculation simulator with more than 130 waterclocks. I wonder whether this is still Turing-complete.
Yes, in fact jfb proved that 6 waterclocks (plus an output clock I believe) is enough, so 13 creature types are enough.
jfb wrote the proof here:
Ok I think the diagonalization solution in 4018 works if programs behave the same when every entry multiplied by a constant c.
Which is true as we can just look at the state every c steps and see it is equivalent to applying one step of the original program then multiplying by c.
I think this makes our UTM a little more awkward to reset between calculations as the entries get much larger each iteration, but it should be fine.
So far everything I looked at was solid, but I'm still working on fully understanding the deck.
What is the plan to turn the computation output into progress? The computation gives the opponent a lot of life and creatures. We can get a lot of mana from Mana Echoes. What do we do with it? I see a Thousand-Year Elixir that can keep untapping itself, but I don't think that is it
In decks where we keep the opponent alive using a lifelinker or a damage prevention effect, the "we must win" rule isn't relevant; as non-halting computations always end the game with the opponent on a positive life total and thus don't effect the score of the deck.
@Iijil: Damn, I keep forgetting what I was thinking about with these older decks. I think it was Gravitic Punch dealing a bunch of damage with K'rrik, Son of Yawgmoth.
I think making more xanthrid necromancers each computation is a bit more inefficient than what we had had, and requires some stack shenanigans but is still possible. (Though we already need to remake k'rrik with the comeuppance change, so this isn't any worse than what we'd already need to do.)
Cast lingering souls triggering a bunch of Spellweaver Volutes, stack them with all of the instants alternating (stacking a cycle of wrong turn, artifical evolution, arcbond, pull from eternity until we are out of volute triggers), then in response, make a soul separator Stern Proctor, to bounce all of them and our real artifacts, (Harmonic Prodigy+Parallel Lives ensures we have enough triggers)
so down the stack the loop will be something like:
...
Computation ends
Resolve Dual Nature triggers for our artifacts/enchantments
Pull from Eternity our creatures into the yard.
Soul separator K'rrik, and necromancer
Resolve an arcbond on a K'rrik token
Resolve artificial evolution on the necromancers, and setup the next BB program
Wrong turn them all to the opponent
Cast+resolve the real artifacts/enchantments getting Dual nature triggers
In response Soul separator Stern proctor to bounce all of our real artifacts/enchantments
Still in response to the Dual Nature triggers Soul separator Desolation giant to kill the boom keg damage their k'rrik and trigger computation.
Locked in computation
...
Edit: Actually with a UTM we don't need to make more necromancers and change the programming each time as only the token input changes.
I think there is an infinite with the hyperstage transition. It can produce too much red mana:
- Start with X Thousand-Year Storm copies and X copies of Spellweaver Volute, all enchanting Pull from Eternity.
- Cast a Gravitic Punch to start a transition. Spellweaver Helix triggers.
- While resolving the Helix we cast Worldfire and Restore. Both of them trigger all the TYS and Volutes.
- When done resolving we put the triggers on the stack. Order them so that we will resolve a repeating sequence of TYS on Wildfire -> Volute on Pull from Eternity -> TYS on Restore
- create a Stern Proctor token to bounce all the Volutes. That makes it so the last known information for them is that they enchanted a Pull from Eternity and all of the triggers can create and cast a copy when they resolve
- Resolve the TYS and Volute triggers to cycle Cragcrown Pathway between battlefield, exile and graveyard, tapping it for a red each time