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    posted a message on Most turn 1 damage in a deck with no infinite combos
    Keep in mind that we can only have two Arcbonded creatures in a computation. So the only way I see Mirrorpool being safe is if we have one Arcbond, and we get the second one using Mirrorpool. But, it looks like the plan is to only be able to recycle Mirrorpool in the additional stage, and of course if we do the computation that infrequently, we don't get a Busy Beaver hyperstage.

    Edit: Yeah, Thousand-Year Storm is also unsafe, because it can copy Arcbond. We're relying on Sea Gate Stormcaller to get copies of Artificial Evolution and Mobilize. (and Prosperity from the layer sequence)

    Edit: Okay, if taking out Dual Nature works, the next step is to fill out the ending layers. How can we generate a lot of red mana?

    Edit: Hmm, without Fractured Identity, we can't give the opponent Treasure tokens or Gold tokens, so we can use those in the layer sequence. So, how about:

    That would be 1 hyperstage + 1 stage + 5 layers, it looks like. I'm not sure that the changes don't require extra cards, so that's something we should look out for.
    Posted in: Magic General
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    posted a message on Most turn 1 damage in a deck with no infinite combos
    @JonidCrushfire: So the way we do things is to count by layers. To deal a large amount of damage, generally you build more and more resources, so you have X of something that keeps increasing. We want to do as much recursion on X as possible.

    A basic way to increase X is to double it, or multiply it by some fixed number. This is Layer 0. For example, if we have X creatures and cast Clone Legion, we'll have 2X creatures. The next step up is to double our number X times, which is equivalent to multiplying by 2^X. This is considered Layer 1. Then Layer 2 is performing Layer 1 X times, each time inputting the result from the previous operation into the next. So, if we have X copies of Swarm Intelligence, and cast Clone Legion, then we would get X copies of Clone Legion, multiplying our number of creatures by 2^X, for Layer 1. If we have an Opalescence in play, this will multiply our number of Swarm Intelligences by 2^X, so if we were to cast Clone Legion again, we would get 2^X copies, so we would multiply our number of Swarm Intelligences by 2^2^X. So, if we were able to cast Clone Legion X times for some resource X, we would multiply by 2^2^2^...^X with X 2's; this is basically 2^^X, or tetration (repeated exponentiation), Layer 2.

    Note you have to be careful; if we didn't have Opalescence in play, then casting Clone Legion would multiply our number of creatures by 2^X, but our non-animated Swarm Intelligences would stay at the same number. So casting the next Clone Legion would multiply by 2^X again, not 2^2^X, and we would not get tetration out of casting X Clone Legions. So we always have to make sure that we are "updating" whatever resources are important to the number X that we are increasing, others the actual amount will fall far short of what we are going for.

    In you deck, for example, you have Doubling Season and Opalescence. So, if we have X Doubling Seasons in play, if we create a token copy of Doubling Season, the number of tokens will be multiplied by 2^X. So this is Layer 1, and since the input and output are both the number of Doubling Seasons, we are indeed updating our required resource. So, creating X triggers, each of which can create a token copy of Doubling Season, will exponentiate X times, to get us to tetration, or Layer 2 (2^^X). This is done with Flameshadow Conjuring; if we have X Flameshadow Conjurings, and put a Sakashima of a Thousand Faces into play, then we get X triggers of Flameshadow Conjuring. If we then use the first X-1 triggers of Flameshadow Conjuring to create token copies of Doubling Season, then we will exponentiate the number of Doubling Seasons X-1 times, for something like 2^^(X-1) Doubling Seasons. If we then use the last trigger to create token copies of Flameshadow Conjuring, then we will have around 2^^X copies of Flameshadow Conjuring, so we are read for the next appearance of Sakashima; again it is important to update the number of Flameshadow Conjurings to make the recursion work out.

    Then we add Restoration Angel - no wait, that goes infinite. You can have Sakashima enter the battlefield, copying nothing, then you get many triggers of Flameshadow Conjuring, and each of them can create many copies of Sakashima. We can have those copies become copies of Restoration Angel, and each of them can flicker the original Sakashima, going infinite. So that combo can't be in the deck.

    But, I hope you are getting the basic idea for counting - If we then put in something that will allow us to flicker Sakashima X times (for example Flicker with X copies of Thousand-Year Storm), that will get us to 2^^^X, Layer 3. And next we want to do something that will perform Layer 3 X times to get to Layer 4, and so on.
    Posted in: Magic General
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    posted a message on Most turn 1 damage in a deck with no infinite combos
    Giving the opponent life is probably okay, since FortyTwo decided to change the scoring to the negative of the opponent's final life, as opposed to damage dealt.

    I haven't come to grips with your combo yet, but I figured I would mention an important issue: We need to update our resources to the results of the BB computation continually. It looks like you are doing that with Mana Echoes to generate colorless mana, I just wanted to make sure that the colorless mana was filtering to everywhere else.

    Edit: It looks like your explanation got messed up a bit, there is a part which goes "which lets us That gives us a stage", suggesting that something got left out.

    Edit: Hmm, we can switch the hyperstage color over to green, but we would still need Inner Fire to get red mana for the stage. Unless we switch the stage over to green mana? I don't know how that would work with Desolation Giant.

    If Desolation Giant proves troublesome, there are some other cards can destroy/sacrifice all creatures: Mogg Infestation, Death Pit Offering, Hellion Eruption, Soulblast.
    Posted in: Magic General
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    posted a message on Most turn 1 damage in a deck with no infinite combos
    Hi clone103! Always glad to see a new person join the challenge.

    Adding Ionize doesn't go infinite, since in order to counter a spell, you need to take 2 damage, and you only have a finite amount of life. It's a good way to extend the "chain" of resources and effects that lead to big numbers.

    It's true that adding more of the "best possible effects" is a good idea, but only when you run out of ideas that can lead to better possible effects. Before we got to stage combos and beyond, the challenge was all about creating as many "layers" as possible, where a layer is basically a recursion loop over the previous layer. If you can come up with something that can add a layer (like FortyTwo's idea of adding Ionize), it pretty much automatically beats adding a bunch of cards that duplicate the previous layer.

    I will go over your deck and estimate the final damage in a little bit.

    Edit: Okay, let's start by talking about the notation that we mainly use to describe numbers in this challenge: the Knuth arrow notation. This notation technically uses the up-arrow symbol, but we just use the caret symbol "^". (both for convenience, and also because apparently the up-arrow symbol is not allowed on this forum)

    Just as multiplication is repeated addition (6*5 = 6+6+6+6+6) and exponentiation is repeated multiplication (6^5 = 6*6*6*6*6), we can continue this pattern and talk about tetration, which is repeated exponentiation:

    6^^5 = 6^6^6^6^6.

    Note that the operations are executed from right to left; this leads to much bigger numbers than if we executed the operations from left to right.

    Then we have pentation, or triple arrows, which is repeated tetration:

    6^^^5 = 6^^6^^6^^6^^6

    So to compute this number, we would start by computing 6^^6, which is an exponential tower of six 6's (6^6^6^6^6^6). Then to compute 6^^6^^6, we would take the result of the last computation (6^^6) and make an exponential tower with that many 6's (so 6^6^6^6^6^...^6 with 6^^6 6's), and the result of computing that entire tower would be 6^^6^^6. We continue this process until we get to 6^^6^^6^^6^^6.

    So, the process continues forever:

    6^^^^5 = 6^^^6^^^6^^^6^^^6

    7^^^^^6 = 7^^^^7^^^^7^^^^7^^^^7^^^^7

    and so on. Each new operation a^....^b means repeating the previous operation with b copies of a. So each new operation represents an extra recursive layer over the previous operation.

    Similarly, the "layers" of a magic combo refer to the stacking of recursive layers in the combo. "Layer 1" refers to some combo that performs exponentation; "Layer 2" refers to some combo that repeats Layer 1 X times, so it performs tetration; "Layer 3" refers to some combo that repeats Layer 2 X times, so it performs pentation; and so on. Not by accident, the layer numbers match up with the corresponding number of arrows; executing a Layer N combo will perform an N-arrow operation.

    So, let's talk about your deck. Each time we resolve an effect that will create a token of a Doubling Season when there are X Doubling Seasons on the battlefield, we will actually create 2^X tokens. So this is a Layer 1 effect. Each time we resolve a Precursor Golem trigger of a copy spell, we create a copy of the spell for each of the X Doubling Seasons, and each one will exponentiate the number of Doubling Seasons, so we will go from X to approximately 2^2^2^...^2^X Doubling Seasons, with X 2's. This is a little more than 2^^X, so this is Layer 2. Then, each time we cast a copy spell, we will get a Precursor Golem trigger for each of the X Precursor Golem triggers in play, so the number of Doubling Seasons will go from around X to more than 2^^2^^2^^...^^2^^X Doubling Seasons, or a little more than 2^^^X Doubling Seasons. Then, when we get around to copying the Precursor Golems we will get more than 2^^^X Precursor Golems thanks to the more than 2^^^X Doubling Seasons in play. So this is Layer 3.

    Of course, we will also have the effects of Kiki-Jiki, Mirror Breaker and Thousand-Year Storm. If we have X Kiki-Jikis, we can create X token creation abilities, enough to take X to 2^^X; but this is the same effect as a single Precursor Golem trigger, so the benefit of all the Kiki-Jikis is roughly equivalent to having one more Precursor Golem. Since we have a gajillion Precursor Golems, the effect of the Kiki-Jikis won't show up in our estimates.

    Similarly, Thousand-Year Storm gets us a bunch of token creation abilities from a copy spell. This time, if we have around X Thousand-Year Storms, and the number of instants/sorceries cast is around X, then we will get around X^2 copies rather than X, so the Thousand-Year Storms have the effect of taking X to 2^^(X^2). This is better than 2^^X, but only by a little bit; it will certainly be worse than the effect of two Precursor Golem triggers, which will take X to 2^^(2^^X). So the effect of the Thousand-Year Storms is more than one Precursor Golem trigger but less than two; again, since we have a gajillion Precursor Golems, the effect won't show up in the estimate.

    Next up, we have Echo of Eons. Each time we cast this, we get many copies from our Thousand-Year Storms; if we have more than X Thousand-Year Storms and a storm count of more than X, then we will be able to retrieve more than 7X^2 copy spells, taking X to more than 2^^^2^^^2^^^...^^^2^^^X with more than 7X^2 2's which is more than 2^^^^(7X^2), so this is Layer 4. Note that there isn't a big difference between 7X^2 and X here; if we had a different ability that only took X to 2^^^^X, getting N+1 copies of that ability would still be better than N copies of Echo of Eons, so it's not as big a difference as it might seem at first.

    Finally, we have our exile spells. Each time we cast Time Reversal or something similar, we get X^2 copies thanks to the Thousand-Year Storms. So for each of these spells, we get to redraw Echo of Eons X^2 times, taking X to approximately 2^^^^^(X^2). So this is Layer 5.

    Okay, now for the precise estimate. We have 26 spells that can copy creatures (Saheeli's Artistry is not as good, since it won't copy our Doubling Seasons, which is the main source of growth here). After the first copy spell, we will have more than 2^^^^3 Doubling Seasons, since 2^^^^3 = 2^^^4 = 2^^2^^4 = 2^^65536, and we can pass that; but, we will have much fewer than 2^^^^4 = 2^^^(2^^65536) Doubling Seasons, since that would require about 2^^65536 Precursor Golem triggers off a copy spell, and we only have 1 to 3. Each copy spell after the first will increase the second number by one, since it takes X to 2^^^X, and 2^^^(2^^^^N) = 2^^^^(N+1). So after 26 copy creature spells, we have between 2^^^^28 and 2^^^^29 Doubling Seasons.

    We then cast Echo of Eons, which takes us to between 2^^^^2^^^^28 and 2^^^^2^^^^29 Doubling Seasons. This is between 2^^^^^4 and 2^^^^^5, and therefore between 2^^^^^^3 and 2^^^^^^4. Then, each of our 16 exile cards will increase the rightmost number by one, so we will end up between 2^^^^^^19 and 2^^^^^^20 creatures by the end.

    So the final damage is between 2^^^^^^19 and 2^^^^^^20.
    Posted in: Magic General
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    posted a message on Most turn 1 damage in a deck with no infinite combos
    Good to hear from you Stakfish!

    Yeah, that seems to be a problem with Perpetual Timepiece. We can get by without losing any cards by replacing Cephalid Shrine with Broken Ambitions to keep our ability to mill, and then replace Perpetual Timepiece with some card that can shuffle cards in our graveyard into our library, like Canal Dredger.

    With Soul Foundry, we don't need to actually bounce or kill Godtoucher! It is enough to bring it from the graveyard/library into our hand, so that we can imprint it onto Soul Foundry. So Wirewood Herald will do the trick. I just noticed, though, that if we use the Herald to bring back Godtoucher, we won't be able to bring back the Herald as well. So I guess we can go back to using Verdant Succession, which will require rejuggling the end stage sequence. Using double Heralds plus Assembly Hall is another possibility.

    So how about:

    I'm certainly interested in what we can do in Standard, although I'm not quite familiar with exactly which cards are in Standard, and it's something of a pain to keep checking which cards are in Standard and which aren't. So I'll let you take the lead Stakfish, and I'll contribute what I can.
    Posted in: Magic General
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    posted a message on Most turn 1 damage in a deck with no infinite combos
    I have updated the OP with links to a few of the explanatory posts.

    EDIT: I've been wondering whether the "target artifact" combos like Arcum Dagsson or Goblin Trashmaster could be made to work after all. They would certainly go infinite in the old version of the combo, but in this new version we have a lot of new moving parts, and maybe those can't be refreshed as easily as the artifacts. But I'm not sure.

    If it still goes infinite, then I think we can still make it work by getting rid of Mirrorworks. Just replace Mirror of Fate and Mirrorworks with Izzet Guildmage and Pull from Eternity, I think. That resolves the problem of requiring more Psychic Battle triggers of our stage artifact, since we will need lots of mana for the stage transition and one copy of Mana Vault and a Keyrune won't be enough. However, we may have the Muzzio problem of being able to bring a copy of whatever we are using to target/sacrifice an artifact below the hyperstage transition, and getting an extra use out of them. Stakfish, do you know an artifact combo that would be safe from this happening?

    EDIT: It just occurred to me that getting rid of Mirrorworks can also solve the problem we had with the Soul Foundry deck. That deck also used Muzzio, so we have to switch that out as well, but perhaps we can squeeze out an extra stage or two with that deck.
    Posted in: Magic General
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    posted a message on Most turn 1 damage in a deck with no infinite combos
    Child of Alara can be retrieved with Goryo's Vengeance. For Muzzio, the idea was to have Scattershot Archer deal damage to it while it was dealing damage to Moggcatcher. But, either way.
    Posted in: Magic General
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    posted a message on Most turn 1 damage in a deck with no infinite combos
    Reality Spasm is very nice, because it allows us to create a hasted Disciple of Tevesh Szat token, which we need, and also contributes a layer. In our last deck Goblin Bushwhacker was ridiculous - it created hasted tokens, and managed to create three layers per card draw, with the aid of Black Lotus and Dual Nature; unfortunately, we don't have either of those. With a creature stage at the end, it looks like we need at least a token creator and an initial card drawer to get started, and probably more. Hopefully we can optimize the main combo list to allow for whatever cards we need to get started.

    One problem with generating mana is that we have to watch for infinities in each of the stage transitions. For the hyperstage transition, for instance, we have to watch out for being able to restart the hyperstage without any Metallurgeon tokens, just with mana and the artifacts that we can use, and generate more mana each time we repeat. Mana Echoes and Mana Reflection look very dangerous to me, since if the deck works we would be able to have gajillions of those, and could get a lot of mana without any Metallurgeons. Thran Dynamo / Mana Vault may be safe, since then there is a limit to how much mana we can get starting from no artifacts.

    When the Wizards forum was going to be shut down, I took the time to save all the pages on archive.org: http://web.archive.org/web/20150917153327/http://community.wizards.com/forum/cards-and-combos/threads/2230096

    Have fun!

    Edit: Hmm, since you have switched to Thorn Lieutenant, is Shrewd Negotation really necessary? You just need to copy Onward // Victory prior to copying Switcheroo to give Raging Swordtooth to the opponent.
    Posted in: Magic General
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    posted a message on Most turn 1 damage in a deck with no infinite combos
    Nice deck, CTNC!

    I don't see how you can tap the Mimic Vats, since they will be creatures with March of the Machines on the battlefield. We can't destroy the March of the Machines cards using Righteous Fury since we can't tap March of the Machines.

    I think Jace, Architect of Thought goes infinite. You can cast it with one Doubling Season on the battlefield, so that it gets 8 counters. Then, activate the ultimate ability, destroying it, and copy the ability many times with Rings of Brighthearth. Use Archangel's Light to shuffle Jace into the library, and use one of the ability copies to redraw Jace, along with many other cards like Kheru Spellsnatcher

    Similarly, Jace, the Mind Scupltor goes infinite; cast it with two Doubling Seasons on the battlefield, then use the +0 and +12 loyalty abilities.

    Assuming these problems are fixed, I get the following for the numbers:

    Each Kiki-Jiki, Mirror Breaker abiilty can copy a Doubling Season, taking X Doubling Seasons to 2^X Doubling Seasons.
    Each time you tap Kiki-Jiki with X Rings of Brighthearth, we get X copies of the ability, taking X to 2^^X.
    Each time we create a copy of Kiki-Jiki with X Doubling Seasons, we get 2^X Kiki-Jikis, taking X to 2^^^(2^X).
    Each time we tap a Mimic Vat imprinted with Kiki-Jiki with X Rings, we take X to 2^^^^X.
    Each time we cast a spell with X Paradox Engines, we can untap the Mimic Vats X times, taking X to 2^^^^^X.
    Each time we gain X life, we can do the Wydwen dance X times, taking X to 2^^^^^^X.
    Each time we cast Righteous Fury, with X Rikus/Meleks, we get X copies, taking X to 2^^^^^^^X.
    Each time we cast Archangel's Light with X Rikus, we can reshuffle in Righteous Fury X times, taking X to 2^^^^^^^^X.
    Each time we activate a Lesser Walker with X Rings, we can retrieve Kheru Spellsnatcher X times, taking X to 2^^^^^^^^^X.
    Each time we activate a Greater Walker with X Rings, we can draw a Lesser Walker X times, taking X to 2^^^^^^^^^^X.
    Each time we activate Garruk, Apex Predator with X Rings, we can destroy a Greater Walker X times and retrieve it, taking X to 2^^^^^^^^^^^X.
    Each time we have a combat phase, we can attack with X Bragos, flickering Garruk X times and taking X to 2^^^^^^^^^^^^X.

    So, first you attack with Brago 9 times, allowing 18 activations of Garruk, Apex Predator and generating about 2^^^^^^^^^^^^20. Then, we attack with 2^^^^^^^^^^^^20 Scourge of the Thrones, getting that many combat phases. So the final damage will be about 2^^^^^^^^^^^^^(2^^^^^^^^^^^^20) (13 and 12 arrows respectively).

    Concerning your loophole - is a Vintage game modifiable by a previously played Unglued game? If that were to be allowable, then I suppose one could further argue that we don't even need the modifying game to be an official M:tG game - we could just make up a game that says that in your next Magic game you start out with Rayo's number of life. Perhaps I should add another rule saying we are just playing a standard game starting fresh, unmodified by anything happening prior (This would eliminate someone's idea to use one of the Karns to restart the game with cards already in play.).
    Posted in: Magic General
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    posted a message on Most turn 1 damage in a deck with no infinite combos
    This thread may be of interest to you guys.

    [EDIT] I just had a thought. We previously rejected Argivian Find and one Fountain of Youth, because we couldn't find a way to get back three life after the Worldfire resolved, so we were bleeding a life each stage. But, that was before we realized that we could use a Retract in the higher hyperstage to bring Fountain of Youth back to our hand.

    So I think the hyperstage transition could go something like this:

    We are at 4 life and have a black mana. Cast Acorn Harvest, bringing us to one life, and get Spellweaver Volute triggers for both Battle Cry and Argivian Find. Resolve Battle Cry, and get lots of hasted untapped Metallurgeons. Put Argivian Find on the stack, but do not resolve it. Set up a stage with the Metallurgeon tokens, and use those tokens to transition to the higher hyperstage a bunch of times using Lingering Souls. When the Metallurgeon stage is exhausted, we are down to Argivian Find next on the stack. We make sure to bring back Fountain of Youth to our hand in the higher hyperstage, so we play it and gain a life. Then we play March of the Machines to put the Fountain of Youth in the graveyard, exile it with Mimic Vat, bounce March of the Machines, and use the created token to get another life. Then we resolve Argivian Find, bring Fountain of Youth back to our hand, play it, and use it to gain a third life. We then resolve some Psychic Battle triggers for Metallurgeon so that we can get some hasted tokens again, and then recast Acorn Harvest.

    So it looks like we don't actually have to bleed a life. The question is whether we can go infinite if we throw a Retract in there. But, as Iijil noted in the previous analysis, if we resolve Retract, whether before or after Battle Cry, prior to Argivian Find, then all the hasted Metallurgeon tokens will be destroyed, and we can't continue the combo when we go to the higher hyperstage. So this doesn't seem to be a problem.

    What does seem to be a problem: When we go to lower stages in the lower hyperstage, if we set them up the same way, we will have an Argivian Find on the stack, and if we resolve it that gives us the ability to gain 2 life. But we need three life in order to recast Acorn Harvest. So we will bleed a life each stage again if we do it this way. So, how about the following: for all the stages below the top stage, we will put the triggers in the order Battle Cry, Argivian Find, and the Retract. We spend 3 life to cast Acorn Harvest, and gain 2 life back when we resolve Argivian Find, so we lose a net 1 life and add one Retract to the stack each time we go up a stage. For the topmost stage we do as described in the beginning.

    Does this make sense?
    Posted in: Magic General
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