Hmm, with [c}Darkbore Pathway[/c] generating black mana, I think we don't need [c}Gravitic Punch[/c] to generate life for ourselves. So, perhaps we could remove the copies of Gravitic Punch, and add a second Recoup? That would equalize the number of card slots. But, I guess it's possible there's an infinite with Recoup.
With green mana freed up, I'd like to look for a green mana stage. Unfortunately, the requirement for our land to be a nonbasic land means we can't replace [c}Restore[/c] with Journey for the Elixir to fetch it. So, if we need lands to be sacrificed and not come back cheaply in the green mana stage, that doesn't seem to work out with Restore bringing lands back. But maybe there's a different buy similar stage we could implement.
Hmm, it would be nice if we could make our hand indispensable, and thus avoid having to sacrifice green mana. It seemed like this happened with the newer deck, where we had to protect our lifelands from Worldfire. But, I suppose even then we could just not cast Worldfire, as we don't need computations to go infinite.
But, maybe there's something similar that could make multiple Worldfires a nono.
@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.
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.
@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.
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.
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.
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.
Hmmm, that's an interesting idea. So, in FortyTwo's example, he has 11 Necromancers that are cats making a cat, three atogs, and seven birds, pumping up the number of cats by 11. That's 9 more than we want, and is the most that any type is being pumped up. So, we could have various creatures with two types, one of which will be Wizards that don't die, and the other types can be various types that pump all the other creature types, so that everything gets pumped up by the same amount. So, instead of
3 3 1
1 4 0
3 7 3
we would have
12 12 10
10 13 9
9 16 12
This pumps everything up by an additional 9 whenever something dies, so that we will simply wait another 9 ticks to get to where the normal waterfall would go to immediately. Yeah, I don't see why this wouldn't work!
What would be really nice is if we could prove that this restricted version of the Waterfall model still was Turing-complete. I thought about maybe using groups of waterclocks to represent a single waterclock, but I'm not sure if that would help.
But, Engineered Plague looks reasonable? I don't see anything wrong with using that at the moment.
Edit: Oh, bleah. Actually, it should be 3 blue creatures with the same mana value; to produce N mana, we need to bounce 2N-1 creatures. We can have one creature be the one we have Bloodbond March layers underneath, and that can produce a blue mana each time we bounce it. The other creatures require two bounces to cycle: One can bounce it to our hand, and the next time we can cast it to get Bloodbond March triggers before casting our Stolen By the Fae or whatever, and we can bounce and then imprint it on a Chrome Mox; it then winds up on the battlefield. So with 2 mana needed for Stolen by the Fae, we need 3 blue creatures. So we can replace Marchesa's Smuggler with Break Through the Line if we wind up using both Floating-Dream Zubera and Thrummingbird, or just use Marchesa's Smuggler if we only use one of the two.
With green mana freed up, I'd like to look for a green mana stage. Unfortunately, the requirement for our land to be a nonbasic land means we can't replace [c}Restore[/c] with Journey for the Elixir to fetch it. So, if we need lands to be sacrificed and not come back cheaply in the green mana stage, that doesn't seem to work out with Restore bringing lands back. But maybe there's a different buy similar stage we could implement.
@hyp_cos: I'll go into more detail about the computational decks later, busy weekend.
But, maybe there's something similar that could make multiple Worldfires a nono.
@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.
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:
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:
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.
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.
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?)
We can just add Engineered Plague then.
3 3 1
1 4 0
3 7 3
we would have
12 12 10
10 13 9
9 16 12
This pumps everything up by an additional 9 whenever something dies, so that we will simply wait another 9 ticks to get to where the normal waterfall would go to immediately. Yeah, I don't see why this wouldn't work!
But, Engineered Plague looks reasonable? I don't see anything wrong with using that at the moment.
Edit: Oh, bleah. Actually, it should be 3 blue creatures with the same mana value; to produce N mana, we need to bounce 2N-1 creatures. We can have one creature be the one we have Bloodbond March layers underneath, and that can produce a blue mana each time we bounce it. The other creatures require two bounces to cycle: One can bounce it to our hand, and the next time we can cast it to get Bloodbond March triggers before casting our Stolen By the Fae or whatever, and we can bounce and then imprint it on a Chrome Mox; it then winds up on the battlefield. So with 2 mana needed for Stolen by the Fae, we need 3 blue creatures. So we can replace Marchesa's Smuggler with Break Through the Line if we wind up using both Floating-Dream Zubera and Thrummingbird, or just use Marchesa's Smuggler if we only use one of the two.
4000 posts.