Yeah, looks like we can't get Black Lotus out of the graveyard. So it's back to the last start. It looks like we can get six or seven layers worth of Consecrated Sphinxes on the fourth Words of Wisdom - perhaps a stage or more is possible, I don't know.
Knowing that Thornwood Falls allows us to cut Tropical Island except for the start gives me a little hope that we can find an improvement. But, I guess Tropical Island + Channel is pretty hard to match or beat in terms of number of cards needed.
That said, I like that you brought up the question "What's the highest damage in the first turn of a realistic game without infinite combos?"
Yeah, for this deck we are assuming that you draw a particular set of 7 cards, followed by a particular set of 4 cards, followed by 2 cards getting milled, followed by a particular set of 8 cards being drawn; after that I think you cannot fail if you do things right. That's not the only way the deck can get started, but the probability of this deck actually going off is probably one in quadrillions; a large number, but at least much smaller than the amounts of damage we have been talking about in this thread.
One may ask "What's the highest damage in the first turn of a realistic game without infinite combos?", but for the question to be precise, we have to define what "realistic" means exactly. Does it mean some cutoff in terms of the probability of success? If we set the minimum probability at, say, one in a million, then we could achieve that by getting started with a five card combo or less, or a slightly larger combo for which we have multiples. So, a deck which starts off with Black Lotus / Show and Tell / Omniscience / Enter the Infinite would suffice. Unfortunately, this doesn't work with are current deck, since being able to draw cards with a sorcery is too good. However, perhaps the we could have Enter the Infinite compatible with the megastage if we got rid of the additional stages. At the very least, we should certainly be able to get a hyperstage plus some additional stages, so we can still get an extremely large number with a probability of over one in a million.
Of course, one might argue that one in a million is still not "realistic". If we bump up to minimum probability to, say, 1%, then things become much harder. It seems to me at first glance that even constructing a deck that can draw all the cards with at least a 1% chance is a challenge. If we can't, then we have to fill the deck with much of the same type of cards so that we can guarantee a certain amount of damage, which will probably be quite low. The biggest problem though is actually calculating the chance of success, which will be a near impossible calculation most of the time. For that reason, we likely can't implement the 1% challenge - we won't know if a deck achieves the minimum probability.
With Un-Sets legal in Commander until January 15th, I'd like to point out that the Commander variant of this challenge is "solved" by a Turn 1 Infinity Elemental with Haste. It's Infinite Power, but it's NOT an Infinite Combo. The death glares I'm getting means there's going to be a rule change, don't they?
The official rules for the challenge are stated at http://www.soniccenter.org/sm/mtg/megacombo.html , with the key rule being that there must be a finite upper bound to the damage that can be achieved. As far as I know, this prevents all the loopholes that people have tried. (A good one is using a card that allows you to choose a number, then add cards that allow you to turn that number into damage - no infinite combo, but the damage can be as large as you want.)
But, it's amusing that Un-Sets are legal in Commander - I didn't expect that.
That said, I like that you brought up the question "What's the highest damage in the first turn of a realistic game without infinite combos?"
Yeah, for this deck we are assuming that you draw a particular set of 7 cards, followed by a particular set of 4 cards, followed by 2 cards getting milled, followed by a particular set of 8 cards being drawn; after that I think you cannot fail if you do things right. That's not the only way the deck can get started, but the probability of this deck actually going off is probably one in quadrillions; a large number, but at least much smaller than the amounts of damage we have been talking about in this thread.
One may ask "What's the highest damage in the first turn of a realistic game without infinite combos?", but for the question to be precise, we have to define what "realistic" means exactly. Does it mean some cutoff in terms of the probability of success? If we set the minimum probability at, say, one in a million, then we could achieve that by getting started with a five card combo or less, or a slightly larger combo for which we have multiples. So, a deck which starts off with Black Lotus / Show and Tell / Omniscience / Enter the Infinite would suffice. Unfortunately, this doesn't work with are current deck, since being able to draw cards with a sorcery is too good. However, perhaps the we could have Enter the Infinite compatible with the megastage if we got rid of the additional stages. At the very least, we should certainly be able to get a hyperstage plus some additional stages, so we can still get an extremely large number with a probability of over one in a million.
Of course, one might argue that one in a million is still not "realistic". If we bump up to minimum probability to, say, 1%, then things become much harder. It seems to me at first glance that even constructing a deck that can draw all the cards with at least a 1% chance is a challenge. If we can't, then we have to fill the deck with much of the same type of cards so that we can guarantee a certain amount of damage, which will probably be quite low. The biggest problem though is actually calculating the chance of success, which will be a near impossible calculation most of the time. For that reason, we likely can't implement the 1% challenge - we won't know if a deck achieves the minimum probability.
That's way more complicated and interesting that what I was thinking a realistic game meant. It makes me kind of embarrassed about how simple my idea of a realistic game is. I was thinking a realistic game meant realistic competitive decks that just aim to win instead of going for extreme overkill. Even if it's about a .01% chance for perfect overkill, competitive is played enough that it's likely that it's happened, and no game is more realistic than a game that probobly happened.
With Un-Sets legal in Commander until January 15th, I'd like to point out that the Commander variant of this challenge is "solved" by a Turn 1 Infinity Elemental with Haste. It's Infinite Power, but it's NOT an Infinite Combo. The death glares I'm getting means there's going to be a rule change, don't they?
The official rules for the challenge are stated at http://www.soniccenter.org/sm/mtg/megacombo.html , with the key rule being that there must be a finite upper bound to the damage that can be achieved. As far as I know, this prevents all the loopholes that people have tried. (A good one is using a card that allows you to choose a number, then add cards that allow you to turn that number into damage - no infinite combo, but the damage can be as large as you want.)
But, it's amusing that Un-Sets are legal in Commander - I didn't expect that.
This is why Un-Sets are better without Rules Lawyers...
Edit: After opening a Foil Rules Lawyer at the release draft, I take that back.
@crimhead: This is coming incredibly late, but it looks like your deck deals around 2^N damage where N will be several hundred. Each time you untap Doubling Cube and activate it, you will almost double your mana, and once you put 4 Doubling Cubes and 4 Copy Artifacts copying them into play, you will get 8 doublings for each new card. So you will get several hundred doublings in the end. Tolarian Academy and Candelabra of Tawnos will not be as good as getting more doublings, so they won't improve the deck.
Going back to our deck, I had an idea for saving a card. It's nothing new, it's the old idea with Gerrard's Verdict and Deep Reconnaissance. Previously I said it wouldn't work with Goblin Gardener, but now I think there may be a way to use it by using Rude Awakening to animate the Forest, and then using Goblin Gardener to bring it back to our hand, where we can discard it using Gerrard's Verdict. There is still the problem of getting both blue and black mana for the later stages; one thing we could do is use Merfolk for the second stage, using Tideshaper Mystic to turn our Forest into any possible basic land for mana of any color. The problem is this messes up the Goblin Bushwhacker ending, and we get something like:
and it looks like the ending only gets us F_{w^3 + w12 + 4}(2) or thereabouts. I would like to replace Rude Awakening and Swarm Intelligence with Deconstruct and Precursor Golem, but we need Rude Awakening to animate the land, so that Goblin Gardener will bring it back to our hand. Anyone see a way to get an extra layer here?
Well, almost. I don't see how to get started with just Words of Wisdom. Would be cool if you can do that, but otherwise Minds aglow should give us big initial draws for the start, followed by one at a time Reality Spasm draws after we assembled the combo.
Although I am really uncomfortable with rounding up the damage estimate. I think we get a lower bound of:
F_{w^3 + w12 + 4}(F_{w^3 + w12 + 3}(F_{w^3 + 12 + 2}(N)))
with N being the number of Reality Spasm casts before the first combat after drawing the combo, which doesn't quite reach F_{w^3 + w12 + 5}(2).
So, how many Reality Spasms can we cast before the first combat? We can access instants and sorceries from the graveyard, and nicely enough Goblin Welder can retrieve artifacts from the graveyard. I think that's it. We have 4 instants, 11 sorceries, and 10 artifacts, for a total of 24 cards, not including Reality Spasm. But, we have to draw Black Lotus, Mox Emerald, Channel, and Minds Aglow in the opening hand. Also, we need to draw Allay to buy it back. We need to draw Perpetual Timepiece to mill cards, and Mimic Vat in order to get a hasted Goblin Welder token. So we can avoid drawing at most 17 cards, for a maximum 18 possible castings of Reality Spasm. How close can we get?
I agree that we should use a lower bound; I definitely plan to highlight the lower bound when I write this up. I was just being casual in the previous post.
EDIT: In order to get a full effect Reality Spasm, we must have both Precursor Golem and Vedalken Orrery already on the battlefield. I suppose it is possible that we could recover both artifacts from the graveyard by casting an "early" Reality Spasm - it could get us a hasted Mad Auntie, and then with enough Bloodbond Marches we could get multiple hasted Goblin Welder tokens to fetch multiple artifacts.
In any case, we will need blue mana for the first Reality Spasm, which means we need to shuffle Black Lotus back into our library, as it is our only source of blue mana. That takes us down to at most 16, possibly 15 Reality Spasms. Also, we will need to exile a Perpetual Timepiece to shuffle the Black Lotus into the library, so if we don't want to lose it we need a token copy, meaning March of the Machines. But, we need to get rid of March of the Machines when we recast Black Lotus, so we need to cast Allay, and we want to buy it back. That means we need to spend an additional five mana, so we can draw at most seven cards with the initial Minds Aglow. To cast another Minds Aglow, we need to cast it via Spellweaver Helix - that requires another 3 life and a green mana, so I think we would need to do this after our first Reality Spasm, and have Reality Spasm get us a hasted Merfolk Sovereign along with the hasted Goblin Welders, so that we could get some life back. Otherwise, we would have to cut the seven card draw down to four, which is probably too little.
No, we can't postpone the second Minds Aglow, because we need it to retrieve the Black Lotus. So it looks like we want to draw an Acorn Harvest and a Spellweaver Helix in order to be able to cast the Minds Aglow. The alternative is that we use the seventh card in our opening hand for Perpetual Timepiece, and use it immmediately to reshuffle the Black Lotus into the library. But then we won't have Perpetual Timepiece available until the second Minds Aglow.
EDIT: Here's my first attempt to get started, but unfortunately it doesn't work.
Play Opalescence, then Dual Nature (1 token copy). Play Copy Enchantment and copy Dual Nature (3 token copies copying Dual Nature). Play Cowardice, Psychic Battle, and March of the Machines (6 token copies of each). Play Spellweaver Helix (6 token copies) and imprint an Acorn Harvest and Minds Aglow on one of them. Cast Black Lotus, then respond to the Dual Nature triggers by casting Allay. Allay triggers 7 Psychic Battles, and 8 Cowardices; use one of the Cowardices to bounce March of the Machines, and the other 7 to bounce Copy Enchantment. This generates 2, 4, 8, 16, 32, 64, and 130 Dual Natures (have the last Copy Enchantment copy Dual Nature). Resolve the Dual Nature copies of Black Lotus, getting six.
Tap the six Black Loti for 15 blue mana and 3 green mana. Spend a blue mana, a green mana and 3 life to flashback Acorn Harvest, which triggers Spellweaver Helix to cast Minds Aglow. Spend up to 13 blue mana to draw up to 13 cards:
Play March of the Machines. We play Vedalken Orrery, Mirror of Fate, and Mimic Vat, getting 131 total copies of each. Next we play Precursor Golem, getting 131 total copies and 262 vanilla Golem tokens. Play Bloodbond March and then Goblin Welder, getting 131 triggers of Bloodbond March. Counter the Goblin Welder spell, and use the first Bloodbond March trigger to return it to the battlefield. Spend two blue mana plus one more mana to cast Reality Spasm, targeting the original Precursor Golem. Psychic Battle triggers, and we can redirect the target to March of the Machines. Both Cowardice and Horobi, Death's Wail trigger, and we resolve Cowardice first to bounce March of the Machines back to our hand. We also use Cowardice to bounce the original Precursor Golem, and replay it, getting 130 more Precursor Golems and 262 more vanilla Golem tokens. Next we resolve the first Precursor Golem trigger for Reality Spasm, getting 785 Reality Spasms, each targeting a different Golem. A whole bunch of Psychic Battles trigger, and we use the first one to change the target of a Reality Spasm from a Golem to Goblin Welder. This time we resolve Horobi, Death's Wail first, and put Goblin Welder in the graveyard. The Mimic Vats trigger, and use one of them to imprint the Goblin Welder, putting it in exile. Spend 3 mana and tap the Mimic Vat to create a Goblin Welder token. Then...
Hmmm, there is a problem. We can use the hasted Goblin Welder token to bring back Black Lotus, but we only get one. If we put March of the Machines into play, we don't have a way to get rid of the March of the Machines before all the token copies of Black Lotus die as well. We can't respond with Reality Spasm, because we need to use Reality Spasm to get the hasted Goblin Welder in the first place. I don't think 3 mana is enough, and we can't reuse Goblin Welder until after the first Reality Spasm cast is exhausted. So, we don't have a working start yet.
Presumably there is some optimization still possible. We didn't even use all of the starting life. But I don't see a way to save more cards over our opponent right now. Out of the artifacts, sorceries and instants we drew 9 (Rebuild doesn't count since we cycle, but we get Minds Aglow twice). We also still need to (re-)draw Mimic Vat, Reality Spasm and Black Lotus, but I think the rest would be accessible with milling and Goblin Welder. So I think we are 12 cards ahead?
Very nice! I count that we are 13 cards ahead, for a potential of 14 Reality Spasms if Mimic Vat, Reality Spasm and Black Lotus are the only instants/sorceries/artifacts that we still need to draw. I guess the idea for getting Vedalken Orrery is to cast Reality Spasm without the Orrery, generate a hasted Goblin Welder, and tap it to put the Vedalken Orrery into play while Precursor Golem triggers for the Reality Spasm are still on the stack. That looks like it should work.
By my previous post it looks like there is a maximum of 16 Reality Spasms we can get, unless I eliminated certain cards too quickly. The difference is that you draw Deconstruct and a second Minds Aglow. The Deconstruct is how you're getting all the mana, so that may not be replaceable. We can avoid drawing a second Minds Aglow by milling two Acorn Harvests, but that requires drawing a Spellweaver Helix. Unless... we might be able to draw enough from the original Minds Aglow to cast the first Reality Spasm? But that requires that we have Black Lotus shuffled back into the library, which requires we use Perpetual Timepiece early. And then Perpetual Timepiece won't be available until the second Minds Aglow. So I don't think we can save a card that way.
That leaves Deconstruct as the only available card savings; if we come up with an idea to postpone it, all the better. But in the meanwhile, 14 Reality Spasms is really good!
EDIT: My last argument wasn't quite right - it's possible to get Black Lotus back by shuffling it into the library and then cycling Rebuild to get it back. But, I don't think we can get everything we need with just 12 cards; I think we will need at least
EDIT: Hmmm, how do we handle Precursor Golem? If we destroy the original, then we need to draw it again, and our number of Reality Spasms goes down to 13. I suppose we could save one by playing Grip of Chaos and redirecting one target onto a Perpetual Timepiece token. (Saving another Precursor Golem would require 7 Perpetual Timepieces, so that doesn't work.) But then we have just one Precursor Golem left with no obvious way to bounce it. And if we cast Reality Spasm with no Vedalken Orrery, the one Precursor Golem won't do anything. So I think it is best to just let it die.
(We could also play Cowardice, but it looks like that hurts more than it helps without Vedalken Orrery.)
So the Deconstruct / Precursor Golem strategy for mana actually costs us two cards; of course, this might still be the best.
EDIT: Well, if we have to give up a card anyway for a second drawing of Precursor Golem, perhaps we can do better by drawing Vedalken Orrery instead. Then we can sacrifice all the Golems but the original Precursor Golem for mana, then play Cowardice and bounce the original Precursor Golem, then use all the mana to cast Allay many times and increase our number of enchantments drastically. Each time we cast Allay we take X Grip of Chaoses to more than 2^X Grip of Chaoses. With 3X mana we can therefore generate more than 2^^X Dual Natures. Thus each time we resolve a Precursor Golem trigger for Deconstruct, take X to more than 2^^X. We start with 60 mana, which gets us more than 2^^20 Dual Natures and 2^^20 Precursor Golems for the next trigger, or more than 2^^^3. So after 7 Precursor Golem triggers, we have more than 2^^^9 Dual Natures. We use the final Grip of Chaos triggers to bounce the original Precursor Golem, which we can play to get more than 2^^^9 Precursor Golems for the first Reality Spasm.
EDIT: Meh, I guess it would be better to just cast the first Reality Spasm without Precursor Golem or Vedalken Orrery. We can still get a hasted copy of Minion of Tevesh Szat, along with all the cards available except a few artifacts, and we can get those via Goblin Welder. So we can generate a lot more Dual Natures before the second Reality Spasm... which I guess is what you intended all along, heh.
I guess we should work it all out at some point though.
Hmm. I didn't think about it too much because I was still trying to draw fewer artifacts/instants/sorceries, but you are right. The first Reality Spasm without Vedalken Orrery or Precursor Golem is pretty bad.
Without Orrery we can only have Bloodbond March triggers for a single creature below it on the stack, so unless we redraw creatures we only get one type of token out of it. If we get a Minion of Tevesh Szat or some other high value token, then we just have the same problem when we activate that, so I think only Goblin Welder tokens are useful here. We would activate that to get Orrery and can actually immediately untap it with the Reality Spasm to get a second artifact.
If we had Precursor Golems still around for extra copies of that first Reality Spasm, then we could untap that Welder multiple times to get all the artifacts we want. I think we can save it by spending additional life on the first Minds Aglow to draw Spellweaver Volute. As you said we can save the original Precursor Golem via target redirection, and then we put Volute on Rebuild just before casting the second Minds Aglow.
So we should be getting away with just one setup Reality Spasm. But I don't think we can get any hasty tokens more valuable than Welder out of it. I think drawing that setup Spasm is still better than drawing any of the other artifacts.
Oh good. If I'm not mistaken, bouncing the original Precursor Golem allows the first Reality Spasm to be at full power, since we can get access to all cards I think. That should be enough to get F_{w^3 + w12 + 2}(14) before the first combat phase.
EDIT: Oh right, we won't have Vedalken Orrery before the first Reality Spasm, so we don't get Bloodbond March triggers for multiple creatures. So F_{w^3 + w12 + 2}(13) then.
We should be able to use the first Reality Spasm to destroy Minion of Tevesh Szat, imprint that to a Mimic Vat and untap that Vat multiple times to get hasty minion tokens. Use one of the later spasms to destroy Precursor Golem and replace the Minion under Vat, so that it actually is in the graveyard when the stack clears and Bloodbond March gets it back. Then we can use Minion tokens to create Goblin Welder tokens to access Artifacts.
The problem there is that I don't see a way to get more mana before having a Welder active, so the activation cost for Mimic Vat seems like the bottle neck on Minion token creation. But if we have X Minions left over after getting all artifacts we need we get to roughly F_{w^3 + w12}(2X) Precursor Golems before we cast the next Reality Spasm.
Nice. We can get 60 mana from Deconstruct on the Golems without destroying the original Precursor Golem. I believe we need to draw 40 cards, so if we spend 12 life to get 12 mana from Channel, we end up with 32 mana left. We also need to exile Perpetual Timepiece to reshuffle cards into the library, and cycle Rebuild to get Minds Aglow back, so we have 28 left. We can cast Allay 8 times with buyback, getting our number of Dual Natures up to more than 2^^10. Then we can play Black Lotus, and bounce March of the Machines in response. So that should get us more than 3*2^^10 mana, and we should get more than 2^^10 Minion of Tevesh Szat tokens. Still not quite enough to get up to F_{w^3 + w12 + 2}(14), unfortunately - we wind up with F_{w^3 + w12 + 1}^13 (F_{w^3 + w12}(2^^10)).
Ah, true - so I guess we just take X to 2X each Allay? On the plus side, we can get more mana from Deconstruct by drawing Perpetual Timepiece and Mimic Vat, and destroying token copies of those as well as the Golems. We need one Perpetual Timepiece token to reshuffle cards into our library, but I think we can give up the other eleven, plus 20 Golems. So we can get 93 mana from Deconstruct, allowing us to cast 19 Allays prior to playing Black Lotus, which will generate 2^19 Dual Natures. We can use the original Mimic Vat to imprint Minion of Tevesh Szat, and I think we can use the same Mimic Vat to imprint the first Goblin Welder, at which point we can use Goblin Welder to bounce Mimic Vat, getting more token copies, and also bring Vedalken Orrery into play. So I think it should work out with just one Mimic Vat, and we can get nearly 2^19 Minion of Tevesh Szats.
EDIT: We can add two artifacts, by replacing Kithkin Mourncaller and Militia's Pride with Angelheart Vial and Ballista Charger. Clockwork Hydra would be a bit more convenient, but I don't think we can remove the +1/+1 counters after all the attacking Clockwork Hydras are removed from the battlefield because of Worldpurge, so I think we don't get the damage ability off. Ballista Charger should work just fine though. That should allow us to get two more Reality Spasms in, and take us to F_{w^3 + w12 + 1}^15 (F_{w^3 + w12}(2^20)) or thereabouts.
Are there any other replacements that can get us more Reality Spasms? Maybe a replacement for Cephalid Shrine?
EDIT: Chalice of the Void could fit the bill, but we need the spell counter card on the battlefield when we cast Minion of Tevesh Szat, so I guess we don't save a card this way.
We can't use Ballista Charger because the crew ability would allow Judge of Currents to generate life without any hasty merfolks, going infinite. There are some nonartifact alternatives (e.g. Raging Regisaur) we can use so we at least get the gain from Angelheart Vial.
EDIT: Ouch. I just noticed that Worldpurge allows us to refill the opponents library. So making them draw is not actually a limiter on the combo >_<
We'll have to go back to the Worldfire version or find some other limit to use with Worldpurge. Combat works fine, but doesn't get us started. Some combination of making the opponent draw and forcing a discard maybe?
EDIT2: We can resolve Noggle Ransackers ability 52 times before too many cards are in the opponents graveyard, but the 53rd will deck them. If we use Consecrated Sphinx that gives us a possible start+limiter for the Worldpurge versions:
Opener: Mox Emerald, Forest, Channel, Black Lotus, Omniscience, Consecrated Sphinx, Noggle Ransacker.
Play those cards. Ransacker triggers Sphinx twice, so we draw 6 and discard 1 for a net gain of 5 cards: Vedalken Orrery, Opalescence, Dual Nature, Copy Enchantment, Worldpurge.
Play Orrery, Opalescence and Dual Nature. In respnse to the Dual Nature triggering on itseld play Copy Enchantment as Omniscience. In response to the Dual Nature trigger play Worldpurge. We get 9 permanents back into hand, so we shuffle the Forest and Omniscience into the library. Resolve the stack to get one Omniscience and one Dual Nature token.
Play Opalescence, Dual Nature and Copy Enchantment as Dual Nature, resolving their token triggers for a total of 10 Dual Natures. Then play Orrery, Sphinx, get 10 token copies and finally Ransacker. The Ransacker etb ability draws us (effectively) 1 and gets us 22 Sphinx triggers and we can already respond at instant speed. I'm not sure if we can go through the entire combo before the next Ransacker ability, but we can at least get a ridiculous number of Sphinxes with 50 Ransackers still to come.
So, how big a number can we make if we need Noggle Ransacker and Consecrated Sphinx? We can always go back to the previous version and get F_{w^3 + w12 + 4}(50). Can we do better with the Gerrard's Verdict version? Trying to end with World at War looks like it keeps us below F_{w^3 + w12 + 4}(2); if we try to end with Noggle Ransacker, we have an extra card, but we can't use Goblin Bushwhacker.
EDIT: What about Memory Jar or Wheel of Fortune? I don't think we have a way of putting the opponent's land cards into play, so I think Wheel of Fortune should be okay.
With those discard/exile 7, then draw 7 effects we have the problem that Worldpurge lets the opponent choose up to 7 cards to keep in hand. So they can just shuffle their entire hand in and we can keep using the draw 7 to go infinite because they never actually discard/exile anything.
Ah, that annoying rule where the opponent will cooperate to go infinite.
I guess Whispering Madness will go infinite as well - after some point, we will only draw as many cards as we discard, but we can draw Reality Spasm and discard lower cards, so that goes infinite.
Prosperity shouldn't go infinite, since it can't draw itself without something like Swarm Intelligence. But, I don't see how to get that one blue mana to cast it out of our opening hand. Any other card drawers out there that we would have to draw to reuse?
EDIT: Here are some ideas for saving the Gerrard's Verdict version. One is that we can possibly use Consecrated Sphinx / Noggle Ransacker in the layer sequence, and not necessarily at the end; we could continue with something that recycles cards from the graveyard. I don't know of a good card though.
Another is that we could possibly use the first combat phase to draw enough cards to get enough World at Wars to come out ahead.
Genesis Wave triggers the creation of token copies of all the creatures. Respond by casting Allay with buyback targeting the Copy Enchantment. Grip of Chaos and Cowardice trigger. Resolve the Cowardice trigger, bouncing Copy Enchantment back to our hand. Replay it and get a token copy trigger. Respond by casting Worldpurge, shuffling Omniscience, Vedalken Orrery, and March of the Machines back into the library, along with our starting permanents. The remaining cards go back to our hand. Resolve the Dual Nature trigger, getting a token copy of Dual Enchantment. Resolve the Grip of Chaos trigger, redirecting the target of Allay to Copy Enchantment. Resolve the Allay, destroying the Copy Enchantment and putting Allay back in our hand. The token copies are created; have the Copy Enchantment token copy Dual Nature. Replay Opalescence, Dual Nature (6 Dual Natures) Copy Enchantment (12 Dual Natures), Grip of Chaos, and Cowardice (14 copies of each).
The second Allay will get 14 Grip of Chaos triggers, allowing us to double the number of Dual Natures 12 times, for 49152, and then we create 49167 Grip of Chaoses. We bounce Cowardice and destroy the March of the Machines token.
The third Allay will get 49167 Grip of Chaos triggers. That will take us to more than 2^49180 Dual Natures and Grip of Chaoses. The fourth Allay will take us to more than 2^2^49180 Grip of Chaoses. We play Sylvan Echoes and Sentry Oak, getting more than 2^2^49180 copies of each.
We declare the combat phase, and get more than 2^2^49180 triggers of Sentry Oak. The first will be enough to draw the rest of our deck, and we should wind up with more than F_{w^3 + w12 + 4} (F_{w^3 + w12 + 3}(2^2^49180) in the end.
To me it looks like that will work. That version of the deck also gets tons of bonus points because neither starting life nor deck size of the opponent matter for the damage result. It always feels just a little bit cheap to say we can't deal more damage because the opponent would die first.
Hmm, we can actually do a little better: The first time we bounce and replay Copy Enchantment, have it copy Dual Nature. We then get two Dual Nature triggers. Allay will destroy one of the tokens, but we wind up with one more Dual Nature token to start. Refiguring the numbers:
After replaying the enchantments, we have 16 Dual Natures and 18 Grip of Chaoses.
After the second Allay, we have 16*2^16 = 1048576 Dual Natures and 1048595 Grip of Chaoses.
After the third Allay, we have 1048576 * 2^1048593 = 2^1048613 Dual Natures and 2^1048613 + 2 Grip of Chaoses.
After the fourth Allay, we have 2^(2^1048613 + 1048616) Dual Natures.
Still, it would be nice to get another exponentiation, if we could postpone the first Allay until we had a few more Grip of Chaoses on the battlefield. Unfortunately, I don't know any other way to avoid having two many cards we need to keep after Worldpurge. We could do it if we could have the initial Copy Enchantment copy Opalescence, since then we could shuffle Opalescence into the library. Unfortunately, it looks like Genesis Wave puts all the permanent cards on the battlefield at the same time. If only it worked like Primal Surge!
The best thing would be to keep the Mox Emerald in hand after Worldpurge. I think that can be done if we shuffle Opalescence back into the library, and rely on a token to provide the effect after Worldpurge.
Most basic method to get that Opalescence token would be to resolve the trigger for a (Copy Enchantment as) Dual Nature token before the first Allay and then replay Copy Enchantment as Opalescence. After the Worldpurge we then get 2 token Opalescence copies and can destroy one to resolve Allay.
This way we get one Dual Nature and one Grip of Chaos token after the Worldpurge before replaying anything. I suspect there is some variation that would get us more of those at this point, but everything I tried so far has run into problems.
Anyway, we then use one buybacked Allay to get more Dual Natures (We get to 2^12), proceed to play Mox Emerald and use the last mana to buyback Allay and destroy the one March of the Machines token in response to the Dual Nature triggers. So we generate a lot more mana that we can use on more Allays before playing the card draw stuff. We get to roughly 2^^1368 Dual Natures.
EDIT: I might have made that more complicated than is actually necessary.
We then get 1 token of each of the Genesis Waved permanents except Opalescence. Copy Encahntment copies Dual Nature.
Play Opalescence. Play Dual Nature, get tokens (6 DN). Play Copy Enchantment as itself, get tokens as Grip of Chaos. We did not keep the original Grip of Chaos, but on the last batch of Copy Enchantment tokens we can still have them copy the token that is hanging around. (7 GoC). Make sure to not copy it with the original Copy Enchantment. Otherwise Dual Nature will destroy all the tokens later, and we don't want that.
Allay with buyback to get more DN/GoC. Resolve the Allay by destroying a Dual Nature token: That should get us to 6*2^5-1 = 191 DN and 6*2^5+7 = 199 GoC.
Another buybacked Allay gets us to more than 2^204 DN. After that Play Mox Emerald and use the last buybacked Allay to destroy the March of the Machines. Get Mana and use for more buybacked Allay stuff.
In the end the last batch of Copy Enchantment tokens could copy the Sylvan Echoes token, but I think it is more efficient to get more Dual Natures and thus more Sentry Oak triggers. Even drawing only a single card for each of the latter it won't take long until we get another opportunity to increase the number of Sylvan Echoes.
We should get to more than 2^^(2^202) triggers upon entering combat.
EDIT2: Huh, I somehow forgot that Mox Emerald dies when March of the Machines first shows up. I don't see a way around that, so forget everything I said about additional mana in this post
It should still be possible to just Worldpurge without hiding Allay on the stack, like I did in the second try here, as we never actually need the original Grip of Chaos, Sylvan Echoes or even Dual Nature afterwards.
Oh good - my first post has accurate numbers then, except we get one more Allay, for 2^2^2^49180 Sentry Oaks.
Now that you've pointed out that we don't need to keep a few cards, we don't need March of the Machines either. So we have a choice of getting another permanent. I don't see anything better though. Wormfang Behemoth can hide Allay, saving a card for Worldpurge, but March of the Machines has the same effect. Deconstruct and Precursor Golem could get us a lot of mana for Allay, but without Worldpurge I don't see how to refresh the number of Sentry Oaks.
At some point we can mill Worldpurge and Acorn Harvest x3. and imprint them on Helixes so that when we flash back an Acorn Harvest we get the Worldpurge cast to put Sentry Oak into our hand. We can save the number of Dual Natures we have through the Worldpurge by leaving triggers for new tokens on the stack before we cast it. I don't quite see how we can take advantage of the possible Helixed Deconstruct though.
EDIT: An alternative starting hand: Black Lotus, Channel, Precursor Golem, Deconstruct, Genesis Wave, Allay, Mox Emerald.
Lotus into Channel, Golem for 5 life, Deconstruct for 2 life and the last green, we destroy golems and get 9 green.
Genesis Wave for X up to 14 leaves us with enough stuff to flash back an Acorn Harvest later and the Mox is not yet dead. But the way I went about this right now doesn't seem to get us any progress before we play it, so I'm not sure about this.
Start with Allay and Deconstruct. Cast Genesis Wave with X=13. Reveal the ten cards mentioned before, along with Precursor Golem, Spellweaver Helix, and Perpetual Timepiece. We get a bunch of Dual Nature created tokens; have the Copy Enchantment token copy Grip of Chaos, so we have two Dual Natures and three Grip of Chaoses. Cast the first Allay with buyback, first increasing the number of Dual Natures to 4, then the number of Grip of Chaoses to 8. Bounce Cowardice and destroy the March of the Machines token. Replay Cowardice. Cast Deconstruct, getting two Precursor Golem triggers, 8 Grip of Chaos triggers, and some Cowardice triggers. With the 8 Grip of Chaos triggers and the Cowardice triggers we can bounce the original Precursor Golem 9 times; after each time we replay it, we generate another 10 standard Golem tokens. So after 8 replayings we have 84 standard Golem tokens. Play the second Allay; We can bounce Copy Enchantment 7 times, increasing the number of Dual Natures to 511, and adding another Grip of Chaos token. (I think we need to have at least two Grip of Choases, or we can't make progress with a buyback Allay.) Replay the original Precursor Golem, creating 511 Precursor Golem tokens and 1024 standard Golem tokens, for 1620 Golems in total. Resolve the first Precursor Golem trigger, getting 1620 copies of Deconstruct; we can destroy 1620 artifacts, generating 4860 mana, and incidentally bouncing the original Precursor Golem an inordinate number of times. (Any replayings of Precursor Golem before the final Allay won't have too much effect though.) We can cast 1620 buyback Allays, generating more than 2^^1622 Dual Natures and Grip of Chaoses. Play Precursor Golem again, and get more than 2^^1622 copies. Resolve the second Precursor Golem trigger, getting more than 2^^1622 copies of Deconstruct, allowing us to go to 2^^2^^1622. In the meantime we can bounce and replay Spellweaver Helix and Perpetual Timepiece, getting many copies; then we can bounce March of the Machines so we can use the Timepieces to mill Worldpurge and three Acorn Harvests. Two Spellweaver Helixes come onto the battlefield, and we imprint Acorn Harvest + Worldpurge and Acorn Harvest + Deconstruct.
Hmm, I'm not seeing how we can take advantage of the second Deconstruct either. If we try to resolve Deconstruct first, then Worldpurge will be waiting on the stack; the only thing we will be left with after Worldpurge our triggers below that were created before Acorn Harvest, and those can't take advantage of the second Deconstruct. If we resolve Worldpurge first, Deconstruct will come up next before our restore progress triggers, so we won't get that far with the Deconstruct.
But, we still wind up with more than 2^^2^^1622 Sentry Oaks. Can we do better with the alternative starting hand?
EDIT: Whoops, I used up all my life on those first two Allays. Okay, so we don't get a starting Allay, and we have 2 Dual Natures and 3 Grip of Chaoses when we cast Deconstruct. (I think that's the better configuration.) We get four bounces, and for the first three replayings we get six standard Golems each time, so we have 22 before the final replaying. Then we cast our first Allay, getting us to eight Dual Natures. Replay Precursor Golem, and get 1 original Precursor Golem, 8 Precursor Golem tokens, and 22+18 standard Golem tokens, for 49 Golems total. So we can get 49 copies of Deconstruct from the first Precursor Golem trigger, and we can cast Allay 49 times, getting us to more than 2^^51 Dual Natures. So we wind up with more than 2^^2^^51 Sentry Oaks in the end.
Knowing that Thornwood Falls allows us to cut Tropical Island except for the start gives me a little hope that we can find an improvement. But, I guess Tropical Island + Channel is pretty hard to match or beat in terms of number of cards needed.
Yeah, for this deck we are assuming that you draw a particular set of 7 cards, followed by a particular set of 4 cards, followed by 2 cards getting milled, followed by a particular set of 8 cards being drawn; after that I think you cannot fail if you do things right. That's not the only way the deck can get started, but the probability of this deck actually going off is probably one in quadrillions; a large number, but at least much smaller than the amounts of damage we have been talking about in this thread.
One may ask "What's the highest damage in the first turn of a realistic game without infinite combos?", but for the question to be precise, we have to define what "realistic" means exactly. Does it mean some cutoff in terms of the probability of success? If we set the minimum probability at, say, one in a million, then we could achieve that by getting started with a five card combo or less, or a slightly larger combo for which we have multiples. So, a deck which starts off with Black Lotus / Show and Tell / Omniscience / Enter the Infinite would suffice. Unfortunately, this doesn't work with are current deck, since being able to draw cards with a sorcery is too good. However, perhaps the we could have Enter the Infinite compatible with the megastage if we got rid of the additional stages. At the very least, we should certainly be able to get a hyperstage plus some additional stages, so we can still get an extremely large number with a probability of over one in a million.
Of course, one might argue that one in a million is still not "realistic". If we bump up to minimum probability to, say, 1%, then things become much harder. It seems to me at first glance that even constructing a deck that can draw all the cards with at least a 1% chance is a challenge. If we can't, then we have to fill the deck with much of the same type of cards so that we can guarantee a certain amount of damage, which will probably be quite low. The biggest problem though is actually calculating the chance of success, which will be a near impossible calculation most of the time. For that reason, we likely can't implement the 1% challenge - we won't know if a deck achieves the minimum probability.
The official rules for the challenge are stated at http://www.soniccenter.org/sm/mtg/megacombo.html , with the key rule being that there must be a finite upper bound to the damage that can be achieved. As far as I know, this prevents all the loopholes that people have tried. (A good one is using a card that allows you to choose a number, then add cards that allow you to turn that number into damage - no infinite combo, but the damage can be as large as you want.)
But, it's amusing that Un-Sets are legal in Commander - I didn't expect that.
That's way more complicated and interesting that what I was thinking a realistic game meant. It makes me kind of embarrassed about how simple my idea of a realistic game is. I was thinking a realistic game meant realistic competitive decks that just aim to win instead of going for extreme overkill. Even if it's about a .01% chance for perfect overkill, competitive is played enough that it's likely that it's happened, and no game is more realistic than a game that probobly happened.
This is why Un-Sets are better without Rules Lawyers...Edit: After opening a Foil Rules Lawyer at the release draft, I take that back.
The
Necromancer (or Noob)
Cat.
Don't ask, I don't know why ether...
This is a finite combo.
Opening:
Casting the Portal untaps the artifacts which generate mana to activate it (and cast the card it finds)...
The rest of the deck should probably be mana rocks (including Doubling Cube and Copy Artifact), a Furnace Of Wrath, and a Fireball. Can improve it with a Crop Rotation, Tolarian Academy, and Candelabra of Tawnos (and surely dozens of other tricks). I'm not going to try to think of how to optimize this idea - and absolutely not going to attempt to count the damage!
https://fieldmarshalshandbook.wordpress.com/
RUGLegacy Lands.dec
RUGBLegacy Lands.dec
RGLegacy Lands.dec
WUBRG EDH Lands.dec
UBR EDH Artificer Prodigy
B EDH Relentless Rats
Going back to our deck, I had an idea for saving a card. It's nothing new, it's the old idea with Gerrard's Verdict and Deep Reconnaissance. Previously I said it wouldn't work with Goblin Gardener, but now I think there may be a way to use it by using Rude Awakening to animate the Forest, and then using Goblin Gardener to bring it back to our hand, where we can discard it using Gerrard's Verdict. There is still the problem of getting both blue and black mana for the later stages; one thing we could do is use Merfolk for the second stage, using Tideshaper Mystic to turn our Forest into any possible basic land for mana of any color. The problem is this messes up the Goblin Bushwhacker ending, and we get something like:
2 Psychic Battle
3 Cowardice
4 Horobi, Death's Wail
5 Bloodbond March
6 Cephalid Shrine
7 Mimic Vat
8 Omniscience
9 Vedalken Orrery
10 Mirror of Fate
11 March of the Machines
12 Perpetual Timepiece
13 Dual Nature
14 Copy Enchantment
15 Allay
16 Su-Chi
17 Farrelite Priest
18 Metallurgeon
19 Deep Reconnaissance
20 Battle Cry
21 Rebuild
22 Spellweaver Volute
23 Mox Emerald
25 Vile Redeemer
26 Rude Awakening
27 Swarm Intelligence
28 Worldpurge
29 Acorn Harvest
30 Acorn Harvest
31 Acorn Harvest
32 Acorn Harvest
33 Spellweaver Helix
34 Gerrard's Verdict
35 Forest
36 Goblin Gardener
37 Mad Auntie
38 Goblin Wizard
39 Tideshaper Mystic
40 Merfolk Sovereign
41 Godtoucher
42 Everglove Courier
43 Nectar Faerie
45 Possessed Aven
46 Centaur Archer
47 Maze Glider
48 Possessed Centaur
49 Eastern Paladin
50 Frightshroud Courier
51 Dwarven Warriors
52 Possessed Barbarian
53 Minion of Tevesh Szat
54 Reality Spasm
55 Kithkin Mourncaller
56 Militia's Pride
57 World at War
58 Words of Wisdom
59 Channel
60 Black Lotus
and it looks like the ending only gets us F_{w^3 + w12 + 4}(2) or thereabouts. I would like to replace Rude Awakening and Swarm Intelligence with Deconstruct and Precursor Golem, but we need Rude Awakening to animate the land, so that Goblin Gardener will bring it back to our hand. Anyone see a way to get an extra layer here?
EDIT: Ah, I think I have it:
2 Psychic Battle
3 Cowardice
4 Horobi, Death's Wail
5 Bloodbond March
6 Cephalid Shrine
7 Mimic Vat
8 Omniscience
9 Vedalken Orrery
10 Mirror of Fate
11 March of the Machines
12 Perpetual Timepiece
13 Dual Nature
14 Copy Enchantment
15 Allay
16 Su-Chi
17 Farrelite Priest
18 Metallurgeon
19 Deep Reconnaissance
20 Battle Cry
21 Rebuild
22 Spellweaver Volute
23 Mox Emerald
25 Vile Redeemer
26 Deconstruct
27 Precursor Golem
28 Worldpurge
29 Acorn Harvest
30 Acorn Harvest
31 Acorn Harvest
32 Acorn Harvest
33 Spellweaver Helix
34 Gerrard's Verdict
35 Forest
36 Judge of Currents
37 Merfolk Sovereign
38 Aquatic Incursion
39 Goblin Welder
40 Mad Auntie
41 Godtoucher
42 Everglove Courier
43 Nectar Faerie
45 Possessed Aven
46 Centaur Archer
47 Maze Glider
48 Possessed Centaur
49 Eastern Paladin
50 Frightshroud Courier
51 Dwarven Warriors
52 Possessed Barbarian
53 Minion of Tevesh Szat
54 Reality Spasm
55 Kithkin Mourncaller
56 Militia's Pride
57 World at War
58 Words of Wisdom
59 Channel
60 Black Lotus
This should get us F_{w^3 + w12 + 5}(2).
Iijil, are there any problems with the above deck?
Well, almost. I don't see how to get started with just Words of Wisdom. Would be cool if you can do that, but otherwise Minds aglow should give us big initial draws for the start, followed by one at a time Reality Spasm draws after we assembled the combo.
Although I am really uncomfortable with rounding up the damage estimate. I think we get a lower bound of:
F_{w^3 + w12 + 4}(F_{w^3 + w12 + 3}(F_{w^3 + 12 + 2}(N)))
with N being the number of Reality Spasm casts before the first combat after drawing the combo, which doesn't quite reach F_{w^3 + w12 + 5}(2).
So, how many Reality Spasms can we cast before the first combat? We can access instants and sorceries from the graveyard, and nicely enough Goblin Welder can retrieve artifacts from the graveyard. I think that's it. We have 4 instants, 11 sorceries, and 10 artifacts, for a total of 24 cards, not including Reality Spasm. But, we have to draw Black Lotus, Mox Emerald, Channel, and Minds Aglow in the opening hand. Also, we need to draw Allay to buy it back. We need to draw Perpetual Timepiece to mill cards, and Mimic Vat in order to get a hasted Goblin Welder token. So we can avoid drawing at most 17 cards, for a maximum 18 possible castings of Reality Spasm. How close can we get?
I agree that we should use a lower bound; I definitely plan to highlight the lower bound when I write this up. I was just being casual in the previous post.
EDIT: In order to get a full effect Reality Spasm, we must have both Precursor Golem and Vedalken Orrery already on the battlefield. I suppose it is possible that we could recover both artifacts from the graveyard by casting an "early" Reality Spasm - it could get us a hasted Mad Auntie, and then with enough Bloodbond Marches we could get multiple hasted Goblin Welder tokens to fetch multiple artifacts.
In any case, we will need blue mana for the first Reality Spasm, which means we need to shuffle Black Lotus back into our library, as it is our only source of blue mana. That takes us down to at most 16, possibly 15 Reality Spasms. Also, we will need to exile a Perpetual Timepiece to shuffle the Black Lotus into the library, so if we don't want to lose it we need a token copy, meaning March of the Machines. But, we need to get rid of March of the Machines when we recast Black Lotus, so we need to cast Allay, and we want to buy it back. That means we need to spend an additional five mana, so we can draw at most seven cards with the initial Minds Aglow. To cast another Minds Aglow, we need to cast it via Spellweaver Helix - that requires another 3 life and a green mana, so I think we would need to do this after our first Reality Spasm, and have Reality Spasm get us a hasted Merfolk Sovereign along with the hasted Goblin Welders, so that we could get some life back. Otherwise, we would have to cut the seven card draw down to four, which is probably too little.
No, we can't postpone the second Minds Aglow, because we need it to retrieve the Black Lotus. So it looks like we want to draw an Acorn Harvest and a Spellweaver Helix in order to be able to cast the Minds Aglow. The alternative is that we use the seventh card in our opening hand for Perpetual Timepiece, and use it immmediately to reshuffle the Black Lotus into the library. But then we won't have Perpetual Timepiece available until the second Minds Aglow.
EDIT: Here's my first attempt to get started, but unfortunately it doesn't work.
Opening hand:
Black Lotus
Mox Emerald
Forest
Channel
Omniscience
Minds Aglow
Perpetual Timepiece
Play Perpetual Timepiece, tap it to mill two Acorn Harvests, and pay 2 mana and exile it to shuffle Black Lotus back into the library.
Cast Minds Aglow, draw 9 cards:
Black Lotus
Spellweaver Helix
Dual Nature
Opalescence
March of the Machines
Allay
Cowardice
Psychic Battle
Copy Enchantment
Play Opalescence, then Dual Nature (1 token copy). Play Copy Enchantment and copy Dual Nature (3 token copies copying Dual Nature). Play Cowardice, Psychic Battle, and March of the Machines (6 token copies of each). Play Spellweaver Helix (6 token copies) and imprint an Acorn Harvest and Minds Aglow on one of them. Cast Black Lotus, then respond to the Dual Nature triggers by casting Allay. Allay triggers 7 Psychic Battles, and 8 Cowardices; use one of the Cowardices to bounce March of the Machines, and the other 7 to bounce Copy Enchantment. This generates 2, 4, 8, 16, 32, 64, and 130 Dual Natures (have the last Copy Enchantment copy Dual Nature). Resolve the Dual Nature copies of Black Lotus, getting six.
Tap the six Black Loti for 15 blue mana and 3 green mana. Spend a blue mana, a green mana and 3 life to flashback Acorn Harvest, which triggers Spellweaver Helix to cast Minds Aglow. Spend up to 13 blue mana to draw up to 13 cards:
Reality Spasm
Precursor Golem
Vedalken Orrery
Mimic Vat
Horobi, Death's Wail
Goblin Welder
Bloodbond March
Cephalid Shrine
Mirror of Fate
some other cards perhaps
Play March of the Machines. We play Vedalken Orrery, Mirror of Fate, and Mimic Vat, getting 131 total copies of each. Next we play Precursor Golem, getting 131 total copies and 262 vanilla Golem tokens. Play Bloodbond March and then Goblin Welder, getting 131 triggers of Bloodbond March. Counter the Goblin Welder spell, and use the first Bloodbond March trigger to return it to the battlefield. Spend two blue mana plus one more mana to cast Reality Spasm, targeting the original Precursor Golem. Psychic Battle triggers, and we can redirect the target to March of the Machines. Both Cowardice and Horobi, Death's Wail trigger, and we resolve Cowardice first to bounce March of the Machines back to our hand. We also use Cowardice to bounce the original Precursor Golem, and replay it, getting 130 more Precursor Golems and 262 more vanilla Golem tokens. Next we resolve the first Precursor Golem trigger for Reality Spasm, getting 785 Reality Spasms, each targeting a different Golem. A whole bunch of Psychic Battles trigger, and we use the first one to change the target of a Reality Spasm from a Golem to Goblin Welder. This time we resolve Horobi, Death's Wail first, and put Goblin Welder in the graveyard. The Mimic Vats trigger, and use one of them to imprint the Goblin Welder, putting it in exile. Spend 3 mana and tap the Mimic Vat to create a Goblin Welder token. Then...
Hmmm, there is a problem. We can use the hasted Goblin Welder token to bring back Black Lotus, but we only get one. If we put March of the Machines into play, we don't have a way to get rid of the March of the Machines before all the token copies of Black Lotus die as well. We can't respond with Reality Spasm, because we need to use Reality Spasm to get the hasted Goblin Welder in the first place. I don't think 3 mana is enough, and we can't reuse Goblin Welder until after the first Reality Spasm cast is exhausted. So, we don't have a working start yet.
Opener: Mox Emerald, Forest, Channel, Black Lotus, Omniscience, Minds Aglow, Opalescence.
Play stuff, draw 10 cards with Minds Aglow, by going to 3 life.
Draw 10: Dual Nature, Copy Enchantment, Precursor Golem, Deconstruct, Perpetual Timepiece, Rebuild, Allay, Grip of Chaos, Cowardice, March of the Machines.
Play stuff, get 6 Dual Natures, then 21 Golems, then 63 mana by destroying those golems. After playing all the enchantmens, play Timepiece and get token copies, then cast Allay with Buyback to bounce most of the enchantments. use Timepiece tokens to mill stuff we want milled and exile a token to put Minds Aglow and Lotus back into the library. Cycle into it with Rebuild and then cast Minds Aglow to draw the rest of the cards we want to draw.
Presumably there is some optimization still possible. We didn't even use all of the starting life. But I don't see a way to save more cards over our opponent right now. Out of the artifacts, sorceries and instants we drew 9 (Rebuild doesn't count since we cycle, but we get Minds Aglow twice). We also still need to (re-)draw Mimic Vat, Reality Spasm and Black Lotus, but I think the rest would be accessible with milling and Goblin Welder. So I think we are 12 cards ahead?
By my previous post it looks like there is a maximum of 16 Reality Spasms we can get, unless I eliminated certain cards too quickly. The difference is that you draw Deconstruct and a second Minds Aglow. The Deconstruct is how you're getting all the mana, so that may not be replaceable. We can avoid drawing a second Minds Aglow by milling two Acorn Harvests, but that requires drawing a Spellweaver Helix. Unless... we might be able to draw enough from the original Minds Aglow to cast the first Reality Spasm? But that requires that we have Black Lotus shuffled back into the library, which requires we use Perpetual Timepiece early. And then Perpetual Timepiece won't be available until the second Minds Aglow. So I don't think we can save a card that way.
That leaves Deconstruct as the only available card savings; if we come up with an idea to postpone it, all the better. But in the meanwhile, 14 Reality Spasms is really good!
EDIT: My last argument wasn't quite right - it's possible to get Black Lotus back by shuffling it into the library and then cycling Rebuild to get it back. But, I don't think we can get everything we need with just 12 cards; I think we will need at least
Reality Spasm
Goblin Welder
Bloodbond March
Cephalid Shrine
Horobi, Death's Wail
Precursor Golem
Perpetual Timepiece
Allay
March of the Machines
Mimic Vat
Rebuild
Dual Nature
Deconstruct
which is 13 cards already.
EDIT: Hmmm, how do we handle Precursor Golem? If we destroy the original, then we need to draw it again, and our number of Reality Spasms goes down to 13. I suppose we could save one by playing Grip of Chaos and redirecting one target onto a Perpetual Timepiece token. (Saving another Precursor Golem would require 7 Perpetual Timepieces, so that doesn't work.) But then we have just one Precursor Golem left with no obvious way to bounce it. And if we cast Reality Spasm with no Vedalken Orrery, the one Precursor Golem won't do anything. So I think it is best to just let it die.
(We could also play Cowardice, but it looks like that hurts more than it helps without Vedalken Orrery.)
So the Deconstruct / Precursor Golem strategy for mana actually costs us two cards; of course, this might still be the best.
EDIT: Well, if we have to give up a card anyway for a second drawing of Precursor Golem, perhaps we can do better by drawing Vedalken Orrery instead. Then we can sacrifice all the Golems but the original Precursor Golem for mana, then play Cowardice and bounce the original Precursor Golem, then use all the mana to cast Allay many times and increase our number of enchantments drastically. Each time we cast Allay we take X Grip of Chaoses to more than 2^X Grip of Chaoses. With 3X mana we can therefore generate more than 2^^X Dual Natures. Thus each time we resolve a Precursor Golem trigger for Deconstruct, take X to more than 2^^X. We start with 60 mana, which gets us more than 2^^20 Dual Natures and 2^^20 Precursor Golems for the next trigger, or more than 2^^^3. So after 7 Precursor Golem triggers, we have more than 2^^^9 Dual Natures. We use the final Grip of Chaos triggers to bounce the original Precursor Golem, which we can play to get more than 2^^^9 Precursor Golems for the first Reality Spasm.
EDIT: Meh, I guess it would be better to just cast the first Reality Spasm without Precursor Golem or Vedalken Orrery. We can still get a hasted copy of Minion of Tevesh Szat, along with all the cards available except a few artifacts, and we can get those via Goblin Welder. So we can generate a lot more Dual Natures before the second Reality Spasm... which I guess is what you intended all along, heh.
I guess we should work it all out at some point though.
Without Orrery we can only have Bloodbond March triggers for a single creature below it on the stack, so unless we redraw creatures we only get one type of token out of it. If we get a Minion of Tevesh Szat or some other high value token, then we just have the same problem when we activate that, so I think only Goblin Welder tokens are useful here. We would activate that to get Orrery and can actually immediately untap it with the Reality Spasm to get a second artifact.
If we had Precursor Golems still around for extra copies of that first Reality Spasm, then we could untap that Welder multiple times to get all the artifacts we want. I think we can save it by spending additional life on the first Minds Aglow to draw Spellweaver Volute. As you said we can save the original Precursor Golem via target redirection, and then we put Volute on Rebuild just before casting the second Minds Aglow.
So we should be getting away with just one setup Reality Spasm. But I don't think we can get any hasty tokens more valuable than Welder out of it. I think drawing that setup Spasm is still better than drawing any of the other artifacts.
EDIT: Oh right, we won't have Vedalken Orrery before the first Reality Spasm, so we don't get Bloodbond March triggers for multiple creatures. So F_{w^3 + w12 + 2}(13) then.
The problem there is that I don't see a way to get more mana before having a Welder active, so the activation cost for Mimic Vat seems like the bottle neck on Minion token creation. But if we have X Minions left over after getting all artifacts we need we get to roughly F_{w^3 + w12}(2X) Precursor Golems before we cast the next Reality Spasm.
We don't get near 2^^10 though: without Vedalken Orrery we don't get a recursion layer from Grip of Chaos on buybacked Allay.
EDIT: We can add two artifacts, by replacing Kithkin Mourncaller and Militia's Pride with Angelheart Vial and Ballista Charger. Clockwork Hydra would be a bit more convenient, but I don't think we can remove the +1/+1 counters after all the attacking Clockwork Hydras are removed from the battlefield because of Worldpurge, so I think we don't get the damage ability off. Ballista Charger should work just fine though. That should allow us to get two more Reality Spasms in, and take us to F_{w^3 + w12 + 1}^15 (F_{w^3 + w12}(2^20)) or thereabouts.
Are there any other replacements that can get us more Reality Spasms? Maybe a replacement for Cephalid Shrine?
EDIT: Chalice of the Void could fit the bill, but we need the spell counter card on the battlefield when we cast Minion of Tevesh Szat, so I guess we don't save a card this way.
EDIT: Ouch. I just noticed that Worldpurge allows us to refill the opponents library. So making them draw is not actually a limiter on the combo >_<
We'll have to go back to the Worldfire version or find some other limit to use with Worldpurge. Combat works fine, but doesn't get us started. Some combination of making the opponent draw and forcing a discard maybe?
EDIT2: We can resolve Noggle Ransackers ability 52 times before too many cards are in the opponents graveyard, but the 53rd will deck them. If we use Consecrated Sphinx that gives us a possible start+limiter for the Worldpurge versions:
Opener: Mox Emerald, Forest, Channel, Black Lotus, Omniscience, Consecrated Sphinx, Noggle Ransacker.
Play those cards. Ransacker triggers Sphinx twice, so we draw 6 and discard 1 for a net gain of 5 cards:
Vedalken Orrery, Opalescence, Dual Nature, Copy Enchantment, Worldpurge.
Play Orrery, Opalescence and Dual Nature. In respnse to the Dual Nature triggering on itseld play Copy Enchantment as Omniscience. In response to the Dual Nature trigger play Worldpurge. We get 9 permanents back into hand, so we shuffle the Forest and Omniscience into the library. Resolve the stack to get one Omniscience and one Dual Nature token.
Play Opalescence, Dual Nature and Copy Enchantment as Dual Nature, resolving their token triggers for a total of 10 Dual Natures. Then play Orrery, Sphinx, get 10 token copies and finally Ransacker. The Ransacker etb ability draws us (effectively) 1 and gets us 22 Sphinx triggers and we can already respond at instant speed. I'm not sure if we can go through the entire combo before the next Ransacker ability, but we can at least get a ridiculous number of Sphinxes with 50 Ransackers still to come.
So, how big a number can we make if we need Noggle Ransacker and Consecrated Sphinx? We can always go back to the previous version and get F_{w^3 + w12 + 4}(50). Can we do better with the Gerrard's Verdict version? Trying to end with World at War looks like it keeps us below F_{w^3 + w12 + 4}(2); if we try to end with Noggle Ransacker, we have an extra card, but we can't use Goblin Bushwhacker.
EDIT: What about Memory Jar or Wheel of Fortune? I don't think we have a way of putting the opponent's land cards into play, so I think Wheel of Fortune should be okay.
I guess Whispering Madness will go infinite as well - after some point, we will only draw as many cards as we discard, but we can draw Reality Spasm and discard lower cards, so that goes infinite.
Prosperity shouldn't go infinite, since it can't draw itself without something like Swarm Intelligence. But, I don't see how to get that one blue mana to cast it out of our opening hand. Any other card drawers out there that we would have to draw to reuse?
EDIT: Here are some ideas for saving the Gerrard's Verdict version. One is that we can possibly use Consecrated Sphinx / Noggle Ransacker in the layer sequence, and not necessarily at the end; we could continue with something that recycles cards from the graveyard. I don't know of a good card though.
Another is that we could possibly use the first combat phase to draw enough cards to get enough World at Wars to come out ahead.
How about:
Black Lotus
Mox Emerald
Forest
Channel
Genesis Wave for up to 19 cards.
Then we have 19 permanents plus two other cards to get started with. That should be enough I think. What would be the best two other cards to use?
EDIT: So, we draw those five cards, plus Allay and Worldpurge. Cast Genesis Wave with X=10, revealing Opalescence, Dual Nature, March of the Machines, Vedalken Orrery, Omniscience, Copy Enchantment, Grip of Chaos, Cowardice, Sylvan Echoes, and Sentry Oak.
Genesis Wave triggers the creation of token copies of all the creatures. Respond by casting Allay with buyback targeting the Copy Enchantment. Grip of Chaos and Cowardice trigger. Resolve the Cowardice trigger, bouncing Copy Enchantment back to our hand. Replay it and get a token copy trigger. Respond by casting Worldpurge, shuffling Omniscience, Vedalken Orrery, and March of the Machines back into the library, along with our starting permanents. The remaining cards go back to our hand. Resolve the Dual Nature trigger, getting a token copy of Dual Enchantment. Resolve the Grip of Chaos trigger, redirecting the target of Allay to Copy Enchantment. Resolve the Allay, destroying the Copy Enchantment and putting Allay back in our hand. The token copies are created; have the Copy Enchantment token copy Dual Nature. Replay Opalescence, Dual Nature (6 Dual Natures) Copy Enchantment (12 Dual Natures), Grip of Chaos, and Cowardice (14 copies of each).
The second Allay will get 14 Grip of Chaos triggers, allowing us to double the number of Dual Natures 12 times, for 49152, and then we create 49167 Grip of Chaoses. We bounce Cowardice and destroy the March of the Machines token.
The third Allay will get 49167 Grip of Chaos triggers. That will take us to more than 2^49180 Dual Natures and Grip of Chaoses. The fourth Allay will take us to more than 2^2^49180 Grip of Chaoses. We play Sylvan Echoes and Sentry Oak, getting more than 2^2^49180 copies of each.
We declare the combat phase, and get more than 2^2^49180 triggers of Sentry Oak. The first will be enough to draw the rest of our deck, and we should wind up with more than F_{w^3 + w12 + 4} (F_{w^3 + w12 + 3}(2^2^49180) in the end.
To me it looks like that will work. That version of the deck also gets tons of bonus points because neither starting life nor deck size of the opponent matter for the damage result. It always feels just a little bit cheap to say we can't deal more damage because the opponent would die first.
After replaying the enchantments, we have 16 Dual Natures and 18 Grip of Chaoses.
After the second Allay, we have 16*2^16 = 1048576 Dual Natures and 1048595 Grip of Chaoses.
After the third Allay, we have 1048576 * 2^1048593 = 2^1048613 Dual Natures and 2^1048613 + 2 Grip of Chaoses.
After the fourth Allay, we have 2^(2^1048613 + 1048616) Dual Natures.
Still, it would be nice to get another exponentiation, if we could postpone the first Allay until we had a few more Grip of Chaoses on the battlefield. Unfortunately, I don't know any other way to avoid having two many cards we need to keep after Worldpurge. We could do it if we could have the initial Copy Enchantment copy Opalescence, since then we could shuffle Opalescence into the library. Unfortunately, it looks like Genesis Wave puts all the permanent cards on the battlefield at the same time. If only it worked like Primal Surge!
Most basic method to get that Opalescence token would be to resolve the trigger for a (Copy Enchantment as) Dual Nature token before the first Allay and then replay Copy Enchantment as Opalescence. After the Worldpurge we then get 2 token Opalescence copies and can destroy one to resolve Allay.
This way we get one Dual Nature and one Grip of Chaos token after the Worldpurge before replaying anything. I suspect there is some variation that would get us more of those at this point, but everything I tried so far has run into problems.
Anyway, we then use one buybacked Allay to get more Dual Natures (We get to 2^12), proceed to play Mox Emerald and use the last mana to buyback Allay and destroy the one March of the Machines token in response to the Dual Nature triggers. So we generate a lot more mana that we can use on more Allays before playing the card draw stuff. We get to roughly 2^^1368 Dual Natures.
EDIT: I might have made that more complicated than is actually necessary.
After the Genesis Wave, with all token triggers still on the stack we can immideatly Worldpurge. We keep in hand:
Opalescence, Copy Enchantment, Cowardice, Allay, Mox Emerald, Sentry Oak and Dual Nature.
We then get 1 token of each of the Genesis Waved permanents except Opalescence. Copy Encahntment copies Dual Nature.
Play Opalescence. Play Dual Nature, get tokens (6 DN). Play Copy Enchantment as itself, get tokens as Grip of Chaos. We did not keep the original Grip of Chaos, but on the last batch of Copy Enchantment tokens we can still have them copy the token that is hanging around. (7 GoC). Make sure to not copy it with the original Copy Enchantment. Otherwise Dual Nature will destroy all the tokens later, and we don't want that.
Allay with buyback to get more DN/GoC. Resolve the Allay by destroying a Dual Nature token: That should get us to 6*2^5-1 = 191 DN and 6*2^5+7 = 199 GoC.
Another buybacked Allay gets us to more than 2^204 DN. After that Play Mox Emerald and use the last buybacked Allay to destroy the March of the Machines. Get Mana and use for more buybacked Allay stuff.
In the end the last batch of Copy Enchantment tokens could copy the Sylvan Echoes token, but I think it is more efficient to get more Dual Natures and thus more Sentry Oak triggers. Even drawing only a single card for each of the latter it won't take long until we get another opportunity to increase the number of Sylvan Echoes.
We should get to more than 2^^(2^202) triggers upon entering combat.
EDIT2: Huh, I somehow forgot that Mox Emerald dies when March of the Machines first shows up. I don't see a way around that, so forget everything I said about additional mana in this post
It should still be possible to just Worldpurge without hiding Allay on the stack, like I did in the second try here, as we never actually need the original Grip of Chaos, Sylvan Echoes or even Dual Nature afterwards.
Now that you've pointed out that we don't need to keep a few cards, we don't need March of the Machines either. So we have a choice of getting another permanent. I don't see anything better though. Wormfang Behemoth can hide Allay, saving a card for Worldpurge, but March of the Machines has the same effect. Deconstruct and Precursor Golem could get us a lot of mana for Allay, but without Worldpurge I don't see how to refresh the number of Sentry Oaks.
We can now get up to unspecified shenanigans with Precursor Golem, Deconstruct, Cowardice, Allay,... all the good stuff.
At some point we can mill Worldpurge and Acorn Harvest x3. and imprint them on Helixes so that when we flash back an Acorn Harvest we get the Worldpurge cast to put Sentry Oak into our hand. We can save the number of Dual Natures we have through the Worldpurge by leaving triggers for new tokens on the stack before we cast it. I don't quite see how we can take advantage of the possible Helixed Deconstruct though.
EDIT: An alternative starting hand: Black Lotus, Channel, Precursor Golem, Deconstruct, Genesis Wave, Allay, Mox Emerald.
Lotus into Channel, Golem for 5 life, Deconstruct for 2 life and the last green, we destroy golems and get 9 green.
Genesis Wave for X up to 14 leaves us with enough stuff to flash back an Acorn Harvest later and the Mox is not yet dead. But the way I went about this right now doesn't seem to get us any progress before we play it, so I'm not sure about this.
Start with Allay and Deconstruct. Cast Genesis Wave with X=13. Reveal the ten cards mentioned before, along with Precursor Golem, Spellweaver Helix, and Perpetual Timepiece. We get a bunch of Dual Nature created tokens; have the Copy Enchantment token copy Grip of Chaos, so we have two Dual Natures and three Grip of Chaoses. Cast the first Allay with buyback, first increasing the number of Dual Natures to 4, then the number of Grip of Chaoses to 8. Bounce Cowardice and destroy the March of the Machines token. Replay Cowardice. Cast Deconstruct, getting two Precursor Golem triggers, 8 Grip of Chaos triggers, and some Cowardice triggers. With the 8 Grip of Chaos triggers and the Cowardice triggers we can bounce the original Precursor Golem 9 times; after each time we replay it, we generate another 10 standard Golem tokens. So after 8 replayings we have 84 standard Golem tokens. Play the second Allay; We can bounce Copy Enchantment 7 times, increasing the number of Dual Natures to 511, and adding another Grip of Chaos token. (I think we need to have at least two Grip of Choases, or we can't make progress with a buyback Allay.) Replay the original Precursor Golem, creating 511 Precursor Golem tokens and 1024 standard Golem tokens, for 1620 Golems in total. Resolve the first Precursor Golem trigger, getting 1620 copies of Deconstruct; we can destroy 1620 artifacts, generating 4860 mana, and incidentally bouncing the original Precursor Golem an inordinate number of times. (Any replayings of Precursor Golem before the final Allay won't have too much effect though.) We can cast 1620 buyback Allays, generating more than 2^^1622 Dual Natures and Grip of Chaoses. Play Precursor Golem again, and get more than 2^^1622 copies. Resolve the second Precursor Golem trigger, getting more than 2^^1622 copies of Deconstruct, allowing us to go to 2^^2^^1622. In the meantime we can bounce and replay Spellweaver Helix and Perpetual Timepiece, getting many copies; then we can bounce March of the Machines so we can use the Timepieces to mill Worldpurge and three Acorn Harvests. Two Spellweaver Helixes come onto the battlefield, and we imprint Acorn Harvest + Worldpurge and Acorn Harvest + Deconstruct.
Hmm, I'm not seeing how we can take advantage of the second Deconstruct either. If we try to resolve Deconstruct first, then Worldpurge will be waiting on the stack; the only thing we will be left with after Worldpurge our triggers below that were created before Acorn Harvest, and those can't take advantage of the second Deconstruct. If we resolve Worldpurge first, Deconstruct will come up next before our restore progress triggers, so we won't get that far with the Deconstruct.
But, we still wind up with more than 2^^2^^1622 Sentry Oaks. Can we do better with the alternative starting hand?
EDIT: Whoops, I used up all my life on those first two Allays. Okay, so we don't get a starting Allay, and we have 2 Dual Natures and 3 Grip of Chaoses when we cast Deconstruct. (I think that's the better configuration.) We get four bounces, and for the first three replayings we get six standard Golems each time, so we have 22 before the final replaying. Then we cast our first Allay, getting us to eight Dual Natures. Replay Precursor Golem, and get 1 original Precursor Golem, 8 Precursor Golem tokens, and 22+18 standard Golem tokens, for 49 Golems total. So we can get 49 copies of Deconstruct from the first Precursor Golem trigger, and we can cast Allay 49 times, getting us to more than 2^^51 Dual Natures. So we wind up with more than 2^^2^^51 Sentry Oaks in the end.