Including the opening hand we have 56 draws. How many cards do we need to draw?
60 - #Merfolks - #Instant/Sorcery + #merfolk drawn + #instant/sorcery drawn + #cards exiled that need to be drawn again.
We seem to have 3 merfolk and 4 instant/sorceries but in the opener we have to draw 2 sorceries and exile 1 card to chrome mox. So just going by that we need all of the 56 draws.
We can probably increase the number of fetchable cards a bit, but even with that it seems hard to get the second and third wheel of fortune cast without increasing the number of cards that need to be drawn. For example I think we need the Changeling to reset the mana crypt long before any merfolk fetching can start.
Edit: If we could give Garza Zol, Plague Queen first strike that would be 19 extra draws, likely making up for the missing ones and then adding some repetitions. I did not find an easy way to do that though.
Yeah, without being able to either draw Changeling Titan or use Chrome Mox on a creature without setting up Bloodbond March triggers first, I can't find a way to get set for the second Wheel of Fortune with just seven cards drawn. I believe I see how to do it if we can draw Changeling Titan and use Chrome Mox, and then we can set up Bloodbond March and Cephalid Shrine for the subsequent Wheel of Fortunes. So, if we were able to fetch two more cards from the library, I believe we could get the combo to work.
Looking at other cards, we can almost get Temple Bell to draw out the deck, except it looks like we need March of the Machines, Dual Nature, and Changeling Titan to continually recycle Temple Bell, and we only have room for two since we have replaced Chaos Warp with Show and Tell. We could do without March of the Machines if there were a creature card with an enter the battlefield effect of "each player draws a card"; something like Noggle Ransacker, except that for that card, we can't afford to keep discarding a card every time we use it.
In order for first strike lifelink to help, we need to have an attacker that both a) has some way of getting bigger proportional to the number of creatures (because the set of attackers is locked in), and b) will never leave combat. If March of the Machines goes away for any amount of time, an animated artifact is excluded by b), as is any creature whose original representative keeps cycling in and out because of Dual Nature's wipeout clause. Whatever the current working list is, do we have a usable candidate for that?
Any green/black creature can do the job. We can pump it by creating lots of paragon tokens. Most of the creatures in the stages should be save from Dual Nature, as we cn always hide the dual nature under the changeling when we are not resolving the changeling layer.
Wow, how did I miss Selvala's Enforcer? That should fit the job quite nicely. So we start with Selvala's Enforcer and Dual Nature, then the two Selvala's Enforcers allow us to draw two cards, which could be Changeling Titan, and I guess Leyline of Anticipation. When we play Changeling Titan, we champion Selvala's Enforcer, then the token copy of Changeling Titan comes into play and champions the original, bringing Selvala's Enforcer back to the battlefield, and it and its token copy allows us to draw two cards (presumably we want to bring Horizon Chimera and the other top leve cards in early.). Then the token copy of Changeling Titan gets destroyed, bringing back Changeling Titan, and we can repeat the process. To stop the loop we can just allow the token copy of Changeling Titan to die.
With Merrow Witsniper, we have four Merfolk, of which we can fetch three, and three sorceries, of which we can mill two. We also have to lose a card through imprinting Chrome Mox from the opening hand, but I think we can get by with just one. So we have a four card advantage on the opponent, and thus we are able to access the full combo from the fifth to last card of the opponent. Even from the seventh to last card though, we are able to access all but one stage (leaving the two ninjas for last, for example) with plenty of +1/+1 counters for Korozda Gorgon, so before the fifth to last card, we should be able to reach 10 -> ... -> 1 -> 4, and then the last five cards bump the second to last number up one at a time, so the final lower bound is 10 -> ... -> 6 -> 4.
Edit: I changed the early sequence again. Earlier, I had to remove a "creatures with morph" stage, because I needed to not have Horobi, Death's Wail around when I flipped a card face down, but the stage was too low to bounce Horobi. Now, though, we can Champion Horobi, so everything should work. Going from red to blue mana early allows Spirits to exit into Vampires, so that we can add Balustrade Spy or Sangromancer.
Adding Consecrated Sphinx gets us yet another layer, and should add quite a bit to the number of repititions. We need to analyze the start a bit more to be sure, but I think we can start as follows:
Start with Consecrated Sphinx and Selvala's Enforcer in the opening hand, cast them both to draw three cards.
Draw Opalescence, Dual Nature, and Changeling Titan.
Cast the first two, getting a Dual Nature token.
Cast Changeling Titan, which puts a Champion trigger and two Dual Nature triggers on the stack.
Use the Champion trigger to exile Dual Nature.
Get a "destroy all Dual Nature tokens" trigger, destroy the one Dual Nature token.
Get "Destroy all tokens created by Dual Nature" triggers, destroy nothing.
Get a Changeling Titan token, use the Champion trigger to exile Consecrated Sphinx.
Get a Changeling Titan token, use the Champion trigger to exile the original Changeling Titan.
The Changeling Titan leaves the battlefield, triggering "destroy all token copies" and "return Dual Nature to the battlefield".
Return Dual Nature to the battlefield, getting a Dual Nature token.
Destroy the token copies, triggering "return Changeling Titan to the battlefield" and "return Consecrated Sphinx to the battlefield" triggers.
Return Consecrated Sphinx to the battlefield, getting two token copies.
return the original Changeling Titan, placing a Champion trigger and two Dual Nature triggers on the stack.
Resolve a Dual Nature trigger, getting a Changeling Titan token and a Champion trigger.
Use the Champion trigger to exile Selvala's Enforcer.
Resolve a Dual Nature trigger, getting a Changeling Titan token and a Champion trigger.
Use the Champion trigger to exile the original Changeling Titan.
The original Changeling Titan leaves the battlefield, triggering "destroy all Changeling Titan tokens".
Destroy the tokens, getting return triggers.
Return Selvala's Enforcer, getting two tokens and a total of three Parley triggers.
The Parley triggers resolve, and we draw 7*3 = 21 cards, as well as some +1/+1 counters.
Hmm, I was hoping to do something fancy so that we could get three Consecrated Sphinxes but just one Selvala's Enforcer, so that we could get one draw of 7 cards, and use those 7 cards to get more Sphinxes before we recycle Selvala's Enforcer again. Otherwise, we can either draw 21 cards with three Enforcers, or we can draw Leyline of Anticipation instead of Opalescence, and draw just five cards with the first Enforcer, but then we can play those cards to perhaps increase the number of Sphinxes before we resolve the next Enforcer.
Certainly with those 21 draws we should be able to get 15+ Sphinxes to draw out the rest of the deck, we should have the full combo going from the fifth Selvala's Enforcer at the latest.
Merrow Witsniper or Balustrade Spy don't work out as the millcard in this version. In the rust tick stage we need to mill the rust tick everytime just after we created a token. Specifically between all the triggers in the lowest layer we need a mill. So we need about X mills lined up and they can't rely on the stack. But the cheapest thing that sticks around and can trigger a mill are the assembly-worker tokens that we are just creating in this stage. So for the purpose of the rust tick stage the mill is to expensive.
Well, we can still use Sangromancer in the transitional Vampire spot, so we can still get a five-card ending sequence provided we use Sangromancer. I guess we could go Korozda Gorgon / Archangel of Thune / Sangromancer / Wheel of Fortune / Yawgmoth's Bargain. We can start by activating Yawgmoth's Bargain 19 times, which should be more than enough to produce a large number of Sangromancers, and even two would be enough to draw out the deck after the first Wheel of Fortune.
I don't think Lore Broker works since there is no way to get a hasty token of it. To target it requires the use of Korozda Gorgon which requires +1/+1 counters, which require gaining life, which require the opponent discarding, which requires a hasty Lore Broker.
Noggle Ransacker might be able to top off that sequence if we have save discards (sorceries?). But it doesn't feel good to essentially waste a card slot just to get enough card draw. Consecrated Sphinx or Yawgmoth's Bargain would work. The Sphinx gets more draw per Ransacker, but the Bargain allows for a more explosive start. So I'd guess the Bargain would produce a better result.
Noggle Ransacker is okay, although it only gets 26 uses as opposed to 53.
It would be nice to use Horizon Chimera and Floating-Dream Zubera, if only the trigger was "creature leaves the battlefield" rather than "creature dies", which seems to hard to handle.
Something like Pain Magnification would be nice, but we need a way to recycle the graveyard. Is there some card that shuffles the opponent's graveyard into their library on a limited basis, perhaps using opponent life or combat?
If we don't manage to add another layer we can use Selvala's Enforcer to draw our deck and Ravenous Rats to trigger the discard at will. Limited by the opponent having only 59 cards to discard (Show and Tell working against us).
Apologies for the sidenote here, but I'm considering writing an article about this challenge, and am wondering a couple of things:
Whats the highest damage someone has noted thus far?
(Conway notation is fine)
Has anyone managed to make the C value in Conway's notation quadratic?
My example solution has a damage of 2 -> 11 -> 45067 upon its first iteration (10 cards in), and then proceeds to make the C value quadratic (the second iteration should be 2 -> 11 -> 2,031,079,556). I'm wondering if this remains a solid example, or if it's outclassed? I haven't noticed anyone who's given a solution with that much damage, but many examples haven't actually calculated damage.
But, I'd be very interested to see your example; if your damage is correct, it would beat everything that had been done up until we discovered the Ackermann combo a few months ago. Too be honest, I'm somewhat suspicious though - I can't imagine how the third value in a Conway chain would grow quadratically.
Let's start with the easiest way to get things going. Someone can probably find another way to cast it all, perhaps with less cards, but I'm going for an easy setup.
We draw everything and can cast everything. Simple.
Lets start off with the basic permanents:
Cast Conspiracy (Name "Golem").
Cast Oplescence.
Cast Dual Nature (Get a token copy from itself).
Cast Doubling Season
.. Two Dual Nature triggest make 2 copies
.. First copy gets doubled by original (3 total)
.. Second copy gets 2^3 copies (+6).
.. 11 Total Doubling Seasons.
Cast Precursor Golem
.. 2 x 2^11 copies
.. +4096 Golems
.. 4097 total Golems in play.
Cast Heat Shimmer targetting a 3/3 golem token.
We get 4097 triggers from the Precursor Golems. Each trigger will resolve and make Heat Shimmer target everything on the board. The triggers resolve one at a time, meaning that we'll get all of the Heat Shimmers, they'll resolve, and then the next Golem trigger will resolve to do more copying. This means that each Precursor trigger will make Heat Shimmer target the tokens that the previous iteration made.
Copy Doubling Season 11 times:
Each one adds a ^ to the calculation.
That's adding 2^^^^^^^^^11 (11 ^s) DS's the final time.
I'll Conway-Expression that to 2->11->11
(A->B->C : A with C ^s to B)
Adding in the previous ones, we end up with:
The original 11 + ( 2->11->12 - 2)
Lets just ignore the +11 and -2 for ease.
So we'll round to 2->11->12
Now, we put 3 * 2->11->12 Precursor Golems on the battlefield.
Now do this 4096 more times.
(For the 4096 remaining Golem Triggers)
..and the math gets a little fuzzy here.
At first, I calculated just adding 11 to the C value for each of the 4096 copies.
This would be copying each of the original 11 doubling seasons.
That would give us 2->9->45067 total Doubling Seasons.
However, I believe I messed this up and it's actually much larger.
Because there are now 2->9->45067 total doubling seasons, the next trigger should hit each of these, thus adding "2->9->45067" to the C value - each doubling season adds 1 the the C value for the doubles.
Also, there might actually only be 2->9->45,066 actual seasons, with the 45067 being total number of doublings - I need to recheck this.
Even if my original +11 was somehow correct, the next iteration of Heat Shimmer will definitely make the C value quadratic, as it will target 2->9->45067 doubling seasons 2->9->45067 times. Thus, as the number of targets and number of copies both become quadratic, the C value has become quadratic.
When the Precursor Golems trigger (and don't forget that you also have 16,781,312 vanilla Golem tokens), the first trigger to resolve creates some copies. If the copies targeting DS resolve first, then you go to 2059, then 2^2059, and so on, ending at 2^^4099. This is not the same as 2 -> 2 -> 4099, but rather 2 -> 4099 -> 2. (In this case, the latter expression is larger because the first one is just 4, but when numbers bigger than 2 are involved, small -> small -> big is for greater than small -> big -> small.
The second Precursor trigger now sees about 2^^4099 creatures to distribute copies too, and at the end of that, you go to 2^^(2^^4099). Each subsequent trigger merely adds a 2^^( in front of that expression, but since each set of ^^ is in a separate parenthetical expression, you can't just merge all the arrows together; they're simply racking up iterations one by one at a certain level of recursion. When the stack finally clears, that puts you at about 2^^^4098, which is 2 -> 4098 -> 3, a far cry from anything involving 45,000 up arrows.
A second Heat Shimmer would put you around 2^^^^4 (2->4->4), and if you devote any more slots to token-making effects, they each increase the second number in that expression by just one, and don't affect the third number at all. Going higher than that requires a way to dynamically produce some number of Heat Shimmer plays that's commensurate with everything you've already done. One way of doing this would involve playing Gaea's Cradle once you've used up all your other resources to lock in a particular amount of mana, and then Tasigur, the Golden Fang to repeatedly get the card back from your graveyard. But then you'd be hard pressed to extend anything beyond that.
Each time we add a token copy of an animated Doubling Season with Opalescence in play along with X Doubling Seasons, we get 2^X additional Doubling Seasons. So If we start with 11 Doubling Seasons, and resolve 11 copies of Heat Shimmer, we'll get a little more than 2^2^2^2^2^2^2^2^2^2^2^11 Doubling Seasons.
Note that this is not 2^^^^^^^^^^^11. Rather, it is between 2^^13 and 2^^14. The way Knuth arrows are defined is as follows:
a^^b = a^a^a...^a (with b a's)
a^^^b = a^^a^^a...^^a (with b a's)
a^^^^b = a^^^a^^^a...^^^a (with b a's)
and so on. So adding tokens of Doubling Season X times will get you about 2^^X = 2^2^2...^2 Doubling Seasons.
That happens for every trigger of Precursor Golem, so casting Heat Shimmer with X Precursor Golems on the battlefield will get you about 2^^^X Doubling Seasons after all the triggers have been resolved.
Basically, if you have a procedure that takes X to 2 -> X -> N, and you create a new procedure that repeats that previous procedure X times, the new procedure will take X to 2 -> X -> N+1. We call each new such procedure a "recursion layer", and having N recursion layers gets you N Knuth arrows.
For examples of how we count recursion layers, please look at this and this.
Quick question for the folks who actually fully understand this math. When doing multiple Ackermann stages, do you get maximum output by climbing up and down the stages repeatedly, or do you resolve one stage completely before beginning the next? For example, if you had a green stage leading into a red one, that would mean the green stage is building up a reservoir of whatever resource is cycled in the red stage. Do you start acting in the red level as soon as you have some of whatever that resource is, or do you use up all the green resource to have one big quantity before doing anything with the red stage. I ask because intuitively, my brain thinks climbing up and down the ladder is better, but remembering back to the discovery of the Ackermann combo, it was having a big pot of green in the first place that let Elvish Spirit Guide do anything.
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Zedruu: "This deck is not only able to go crazy - it also needs to do so."
If you have a source that will get you, say, 100 green mana but no more, it's best to get all of the mana at once. Then the layers stack on top of each other as (green stage with 99 mana floating) under (green stage with 98 mana floating) under (green stage with 97 mana floating) ... under (green stage with 0 mana floating), for 100 separate layers. And in most cases, the numbers being dealt with will be far greater than 100 anyway.
So, unlike something like a bunch of entering Hamletback Goliaths where the optimal solution is a zigzagging method, these Ackermann stages are more of a batch process.
So, if we could theoretically resolve an Ackermann stage of a large quantity of some mana using it to make some larger quantity of permanents, and then use those permanents to make the same type of mana proportional to the output, but only after the full resolution of the previous stage and only a discreet number of cycles, we could functionally have the equivalent of one Ackermann stage for each time we could do that and then blow the current damage output out of the water, provided the number of cycles is greater than 25?
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Zedruu: "This deck is not only able to go crazy - it also needs to do so."
Not quite. The Ackermann stages are set up in a way that they produce that large amout of some mana a lot of times. Count your progress as X. Every time you get to the lowest layer of the stage, say (triggers with 0 blue mana floating), you resolve just that layer to get, say X red mana. Then, with the rest of the blue mana stage still on the stack you go through the red mana stage to ultimately increase X. After you have resolved the entire red stage you get back to the partially resolved blue stage and continue there to get a new (triggers with 0 blue mana floting) layer. This time with the newly increased amount of X triggers to generate the increased amount of red mana.
Essentially it is still the up and down process that you are used to from the layer setups, just with the entire lowest layer of a stage treated as a single event. But that one layer is only a small part of that stage.
Step 4: Mana Reflection, Battle Hymn for a ton of mana, Vernal Equinox. 34.
Step 5: Summon Grimgrin, Corpse-Born. Sacrifice one original Copy Enchantment to Grimgrin. Summon Monk Idealist, respond to each ETB trigger with Copy Enchantment. Repeat for next 3 Monk Idealists, 4 Auramancers and 4 Griffin Dreamfinders. 25.
Step 6: Sac one Copy Enchantment, kicked Rite of Replication , 4x Increasing Vengeance on Rite of Replication, Flashback Vengeance, respond to each enchantment reanimation trigger with Copy Enchantment. 19.
Step 7: 4x Deja Vu, 4x Mystic Retreival and flashback and 4x Call to Mind on Rite of Replication. Then sac all the spent enchantment reanimators, Mana Reflection, all four Copy Enchantments and Opalescence to Grimgrin. 8.
Step 8: 4x Praetor's Council, replaying Opalescence and then everything from steps 4-8 each time. 4.
Step 9: 3x Cranial Archive, each drawing Enter the Infinite putting Lotus on top. 1.
Step 10: Use all red mana to cast Unwilling Recruit. Attack with everything. Savage Beating (Only the sentiment)
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Standard: 5-color Eldrazi
Modern: Delver
Legacy: OmniTell
Commander: Too many
Everywhere it works: Storm.
That is infinite. Praetor's Counsel, respond with Increasing Vengeance for free, respond with Battle Hymn for free. Get some mana, make a copy of the spell, and now Battle Hymn and Increasing Vengeance are in the graveyard. The copy of Praetor's Counsel will return both cards to your hand (and exile itself, which is pretty meaningless because it's a copy). Then you can replay both again, for as much red mana as you want.
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60 - #Merfolks - #Instant/Sorcery + #merfolk drawn + #instant/sorcery drawn + #cards exiled that need to be drawn again.
We seem to have 3 merfolk and 4 instant/sorceries but in the opener we have to draw 2 sorceries and exile 1 card to chrome mox. So just going by that we need all of the 56 draws.
We can probably increase the number of fetchable cards a bit, but even with that it seems hard to get the second and third wheel of fortune cast without increasing the number of cards that need to be drawn. For example I think we need the Changeling to reset the mana crypt long before any merfolk fetching can start.
Edit: If we could give Garza Zol, Plague Queen first strike that would be 19 extra draws, likely making up for the missing ones and then adding some repetitions. I did not find an easy way to do that though.
Looking at other cards, we can almost get Temple Bell to draw out the deck, except it looks like we need March of the Machines, Dual Nature, and Changeling Titan to continually recycle Temple Bell, and we only have room for two since we have replaced Chaos Warp with Show and Tell. We could do without March of the Machines if there were a creature card with an enter the battlefield effect of "each player draws a card"; something like Noggle Ransacker, except that for that card, we can't afford to keep discarding a card every time we use it.
Merrow Witsniper could serve as a fetchable replacement for Shriekhorn.
Edit: There's Selvala's Enforcer as a creature to draw the library.
With Merrow Witsniper, we have four Merfolk, of which we can fetch three, and three sorceries, of which we can mill two. We also have to lose a card through imprinting Chrome Mox from the opening hand, but I think we can get by with just one. So we have a four card advantage on the opponent, and thus we are able to access the full combo from the fifth to last card of the opponent. Even from the seventh to last card though, we are able to access all but one stage (leaving the two ninjas for last, for example) with plenty of +1/+1 counters for Korozda Gorgon, so before the fifth to last card, we should be able to reach 10 -> ... -> 1 -> 4, and then the last five cards bump the second to last number up one at a time, so the final lower bound is 10 -> ... -> 6 -> 4.
Edit: I changed the early sequence again. Earlier, I had to remove a "creatures with morph" stage, because I needed to not have Horobi, Death's Wail around when I flipped a card face down, but the stage was too low to bounce Horobi. Now, though, we can Champion Horobi, so everything should work. Going from red to blue mana early allows Spirits to exit into Vampires, so that we can add Balustrade Spy or Sangromancer.
2 Changeling Titan
3 Assembly-Worker
4 Rust Tick
5 Archetype of Aggression
6 Hull Breach
7 Imperial Hellkite
8 Master of the Veil
9 Labyrinth Minotaur
10 Anaba Ancestor
11 Horobi, Death's Wail
12 Rend Spirit
13 Balustrade Spy
14 Baron Sengir
15 Empress Galina
16 Merfolk Sovereign
17 Seahunter
18 Mercenary Informer
19 Boreal Griffin
20 Boreal Druid
21 Ohran Yeti
23 Nectar Faerie
24 Ghosthelm Courier
25 Possessed Aven
26 Grassland Crusader
27 Possessed Nomad
28 Shauku's Minion
29 Centaur Archer
30 Maze Glider
31 Paragon of Eternal Wilds
32 Devout Chaplain
33 Royal Assassin
34 Goblin Tunneler
35 Flamestick Courier
36 Dralnu's Crusade
37 Frightshroud Courier
38 Paragon of Open Graves
39 Viashino Fangtail
40 Korozda Gorgon
41 Archangel of Thune
42 Horizon Chimera
43 Consecrated Sphinx
44 Selvala's Enforcer
46 Chrome Mox
47 Mirror Gallery
48 Bloodbond March
49 Cephalid Shrine
50 Cowardice
51 Mimic Vat
52 Psychic Battle
53 Omniscience
54 Leyline of Anticipation
55 Opalescence
56 March of the Machines
57 Mirror of Fate
58 Mana Crypt
59 Snapcaster Mage
60 Gideon, Ally of Zendikar
Adding Consecrated Sphinx gets us yet another layer, and should add quite a bit to the number of repititions. We need to analyze the start a bit more to be sure, but I think we can start as follows:
Start with Consecrated Sphinx and Selvala's Enforcer in the opening hand, cast them both to draw three cards.
Draw Opalescence, Dual Nature, and Changeling Titan.
Cast the first two, getting a Dual Nature token.
Cast Changeling Titan, which puts a Champion trigger and two Dual Nature triggers on the stack.
Use the Champion trigger to exile Dual Nature.
Get a "destroy all Dual Nature tokens" trigger, destroy the one Dual Nature token.
Get "Destroy all tokens created by Dual Nature" triggers, destroy nothing.
Get a Changeling Titan token, use the Champion trigger to exile Consecrated Sphinx.
Get a Changeling Titan token, use the Champion trigger to exile the original Changeling Titan.
The Changeling Titan leaves the battlefield, triggering "destroy all token copies" and "return Dual Nature to the battlefield".
Return Dual Nature to the battlefield, getting a Dual Nature token.
Destroy the token copies, triggering "return Changeling Titan to the battlefield" and "return Consecrated Sphinx to the battlefield" triggers.
Return Consecrated Sphinx to the battlefield, getting two token copies.
return the original Changeling Titan, placing a Champion trigger and two Dual Nature triggers on the stack.
Resolve a Dual Nature trigger, getting a Changeling Titan token and a Champion trigger.
Use the Champion trigger to exile Selvala's Enforcer.
Resolve a Dual Nature trigger, getting a Changeling Titan token and a Champion trigger.
Use the Champion trigger to exile the original Changeling Titan.
The original Changeling Titan leaves the battlefield, triggering "destroy all Changeling Titan tokens".
Destroy the tokens, getting return triggers.
Return Selvala's Enforcer, getting two tokens and a total of three Parley triggers.
The Parley triggers resolve, and we draw 7*3 = 21 cards, as well as some +1/+1 counters.
Hmm, I was hoping to do something fancy so that we could get three Consecrated Sphinxes but just one Selvala's Enforcer, so that we could get one draw of 7 cards, and use those 7 cards to get more Sphinxes before we recycle Selvala's Enforcer again. Otherwise, we can either draw 21 cards with three Enforcers, or we can draw Leyline of Anticipation instead of Opalescence, and draw just five cards with the first Enforcer, but then we can play those cards to perhaps increase the number of Sphinxes before we resolve the next Enforcer.
Certainly with those 21 draws we should be able to get 15+ Sphinxes to draw out the rest of the deck, we should have the full combo going from the fifth Selvala's Enforcer at the latest.
Well, we can still use Sangromancer in the transitional Vampire spot, so we can still get a five-card ending sequence provided we use Sangromancer. I guess we could go Korozda Gorgon / Archangel of Thune / Sangromancer / Wheel of Fortune / Yawgmoth's Bargain. We can start by activating Yawgmoth's Bargain 19 times, which should be more than enough to produce a large number of Sangromancers, and even two would be enough to draw out the deck after the first Wheel of Fortune.
Edit: Lore Broker can be used 53 times compared to 7 for Wheel of Fortune.
Noggle Ransacker might be able to top off that sequence if we have save discards (sorceries?). But it doesn't feel good to essentially waste a card slot just to get enough card draw. Consecrated Sphinx or Yawgmoth's Bargain would work. The Sphinx gets more draw per Ransacker, but the Bargain allows for a more explosive start. So I'd guess the Bargain would produce a better result.
It would be nice to use Horizon Chimera and Floating-Dream Zubera, if only the trigger was "creature leaves the battlefield" rather than "creature dies", which seems to hard to handle.
Night Dealings / Ion Storm /Archangle of Thune / Sangromancer / Wheel of Fortune would get another layer, if there was some way to give opponent life.
Something like Pain Magnification would be nice, but we need a way to recycle the graveyard. Is there some card that shuffles the opponent's graveyard into their library on a limited basis, perhaps using opponent life or combat?
Whats the highest damage someone has noted thus far?
(Conway notation is fine)
Has anyone managed to make the C value in Conway's notation quadratic?
My example solution has a damage of 2 -> 11 -> 45067 upon its first iteration (10 cards in), and then proceeds to make the C value quadratic (the second iteration should be 2 -> 11 -> 2,031,079,556). I'm wondering if this remains a solid example, or if it's outclassed? I haven't noticed anyone who's given a solution with that much damage, but many examples haven't actually calculated damage.
No longer staff here.
10 -> 10 -> 10 -> 10 -> 10 -> 10 -> 10 -> 10 -> 10 -> 10 -> 10 -> 10 -> 10 -> 10 -> 10 -> 10 -> 10 -> 10 -> 10 -> 10 -> 10 -> 10 -> 10 -> 10 -> 10 -> 10 -> 60 -> 4 in Conway chained arrow notation. (That's 26 10's)
But, I'd be very interested to see your example; if your damage is correct, it would beat everything that had been done up until we discovered the Ackermann combo a few months ago. Too be honest, I'm somewhat suspicious though - I can't imagine how the third value in a Conway chain would grow quadratically.
Black Lotus
Show and Tell
Omniscience
Enter the Infinite
We draw everything and can cast everything. Simple.
Lets start off with the basic permanents:
Cast Conspiracy (Name "Golem").
Cast Oplescence.
Cast Dual Nature (Get a token copy from itself).
Cast Doubling Season
.. Two Dual Nature triggest make 2 copies
.. First copy gets doubled by original (3 total)
.. Second copy gets 2^3 copies (+6).
.. 11 Total Doubling Seasons.
Cast Precursor Golem
.. 2 x 2^11 copies
.. +4096 Golems
.. 4097 total Golems in play.
Cast Heat Shimmer targetting a 3/3 golem token.
We get 4097 triggers from the Precursor Golems. Each trigger will resolve and make Heat Shimmer target everything on the board. The triggers resolve one at a time, meaning that we'll get all of the Heat Shimmers, they'll resolve, and then the next Golem trigger will resolve to do more copying. This means that each Precursor trigger will make Heat Shimmer target the tokens that the previous iteration made.
Copy Doubling Season 11 times:
Each one adds a ^ to the calculation.
That's adding 2^^^^^^^^^11 (11 ^s) DS's the final time.
I'll Conway-Expression that to 2->11->11
(A->B->C : A with C ^s to B)
Adding in the previous ones, we end up with:
The original 11 + ( 2->11->12 - 2)
Lets just ignore the +11 and -2 for ease.
So we'll round to 2->11->12
Now, we put 3 * 2->11->12 Precursor Golems on the battlefield.
Now do this 4096 more times.
(For the 4096 remaining Golem Triggers)
..and the math gets a little fuzzy here.
At first, I calculated just adding 11 to the C value for each of the 4096 copies.
This would be copying each of the original 11 doubling seasons.
That would give us 2->9->45067 total Doubling Seasons.
However, I believe I messed this up and it's actually much larger.
Because there are now 2->9->45067 total doubling seasons, the next trigger should hit each of these, thus adding "2->9->45067" to the C value - each doubling season adds 1 the the C value for the doubles.
Also, there might actually only be 2->9->45,066 actual seasons, with the 45067 being total number of doublings - I need to recheck this.
Even if my original +11 was somehow correct, the next iteration of Heat Shimmer will definitely make the C value quadratic, as it will target 2->9->45067 doubling seasons 2->9->45067 times. Thus, as the number of targets and number of copies both become quadratic, the C value has become quadratic.
Corrections welcome.
No longer staff here.
The second Precursor trigger now sees about 2^^4099 creatures to distribute copies too, and at the end of that, you go to 2^^(2^^4099). Each subsequent trigger merely adds a 2^^( in front of that expression, but since each set of ^^ is in a separate parenthetical expression, you can't just merge all the arrows together; they're simply racking up iterations one by one at a certain level of recursion. When the stack finally clears, that puts you at about 2^^^4098, which is 2 -> 4098 -> 3, a far cry from anything involving 45,000 up arrows.
A second Heat Shimmer would put you around 2^^^^4 (2->4->4), and if you devote any more slots to token-making effects, they each increase the second number in that expression by just one, and don't affect the third number at all. Going higher than that requires a way to dynamically produce some number of Heat Shimmer plays that's commensurate with everything you've already done. One way of doing this would involve playing Gaea's Cradle once you've used up all your other resources to lock in a particular amount of mana, and then Tasigur, the Golden Fang to repeatedly get the card back from your graveyard. But then you'd be hard pressed to extend anything beyond that.
Note that this is not 2^^^^^^^^^^^11. Rather, it is between 2^^13 and 2^^14. The way Knuth arrows are defined is as follows:
a^^b = a^a^a...^a (with b a's)
a^^^b = a^^a^^a...^^a (with b a's)
a^^^^b = a^^^a^^^a...^^^a (with b a's)
and so on. So adding tokens of Doubling Season X times will get you about 2^^X = 2^2^2...^2 Doubling Seasons.
That happens for every trigger of Precursor Golem, so casting Heat Shimmer with X Precursor Golems on the battlefield will get you about 2^^^X Doubling Seasons after all the triggers have been resolved.
Basically, if you have a procedure that takes X to 2 -> X -> N, and you create a new procedure that repeats that previous procedure X times, the new procedure will take X to 2 -> X -> N+1. We call each new such procedure a "recursion layer", and having N recursion layers gets you N Knuth arrows.
For examples of how we count recursion layers, please look at this and this.
This is what I messed up on; my understanding of the notation.
I was wondering how I got so high so fast.
Apologies for the sidetrack.
No longer staff here.
So, if we could theoretically resolve an Ackermann stage of a large quantity of some mana using it to make some larger quantity of permanents, and then use those permanents to make the same type of mana proportional to the output, but only after the full resolution of the previous stage and only a discreet number of cycles, we could functionally have the equivalent of one Ackermann stage for each time we could do that and then blow the current damage output out of the water, provided the number of cycles is greater than 25?
Essentially it is still the up and down process that you are used to from the layer setups, just with the entire lowest layer of a stage treated as a single event. But that one layer is only a small part of that stage.
Prospective deck:
2 Changeling Berserker
3 Assembly-Worker
4 Rust Tick
5 Archetype of Endurance
6 Gleeful Sabotage
7 Krosan Cloudscraper
8 Master of the Veil
9 Labyrinth Minotaur
10 Anaba Ancestor
11 Horobi, Death's Wail
12 Rend Spirit
13 Sangromancer
14 Baron Sengir
15 Empress Galina
16 Merfolk Sovereign
17 Seahunter
18 Mercenary Informer
19 Boreal Griffin
20 Boreal Druid
21 Ohran Yeti
23 Nectar Faerie
24 Ghosthelm Courier
25 Possessed Aven
26 Grassland Crusader
27 Possessed Nomad
28 Shauku's Minion
29 Centaur Archer
30 Maze Glider
31 Paragon of Eternal Wilds
32 Devout Chaplain
33 Royal Assassin
34 Goblin Tunneler
35 Flamestick Courier
36 Dralnu's Crusade
37 Frightshroud Courier
38 Paragon of Open Graves
39 Viashino Fangtail
40 Korozda Gorgon
41 Archangel of Thune
42 Selvala's Enforcer
43 Ravenous Rats
45 Show and Tell
46 Chrome Mox
47 Mirror Gallery
48 Bloodbond March
49 Cephalid Shrine
50 Cowardice
51 Mimic Vat
52 Psychic Battle
53 Omniscience
54 Leyline of Anticipation
55 Starfield of Nyx
56 March of the Machines
57 Mirror of Fate
58 Mana Crypt
59 Snapcaster Mage
60 Gideon, Ally of Zendikar
Modern: Delver
Legacy: OmniTell
Commander: Too many
Everywhere it works: Storm.
1x Show and Tell
1x Omniscience
1x Enter the infinite
1x Opalescence
4x Dual Nature
4x Doubling Season
4x Primal Vigor
4x Copy Enchantment
1x Xenograft
1x Mana Reflection
1x Battle Hymn
1x Vernal Equinox
1x Grimgrin, Corpse-Born
4x Monk Idealist
4x Auramancer
4x Griffin Dreamfinder
4x Increasing Vengeance
4x Deja Vu
4x Call to Mind
4x Mystic Retrieval
4x Praetor's Council
3x Cranial Archive
1x Unwilling Recruit
Step 1: Lotus, Show and Tell, Omniscience, Enter the Infinite putting back Unwilling Recruit. 56 cards left.
Step 2: Opalescence, alternate 4x Dual Nature and 4x Doubling Season. 4x Primal Vigor, 4x Copy Enchantment on nothing, all the tokens alternate Lives and Season. 39 left.
Step 3: Precursor Golem, Xenograft naming Golem. 37 left.
Step 4: Mana Reflection, Battle Hymn for a ton of mana, Vernal Equinox. 34.
Step 5: Summon Grimgrin, Corpse-Born. Sacrifice one original Copy Enchantment to Grimgrin. Summon Monk Idealist, respond to each ETB trigger with Copy Enchantment. Repeat for next 3 Monk Idealists, 4 Auramancers and 4 Griffin Dreamfinders. 25.
Step 6: Sac one Copy Enchantment, kicked Rite of Replication , 4x Increasing Vengeance on Rite of Replication, Flashback Vengeance, respond to each enchantment reanimation trigger with Copy Enchantment. 19.
Step 7: 4x Deja Vu, 4x Mystic Retreival and flashback and 4x Call to Mind on Rite of Replication. Then sac all the spent enchantment reanimators, Mana Reflection, all four Copy Enchantments and Opalescence to Grimgrin. 8.
Step 8: 4x Praetor's Council, replaying Opalescence and then everything from steps 4-8 each time. 4.
Step 9: 3x Cranial Archive, each drawing Enter the Infinite putting Lotus on top. 1.
Step 10: Use all red mana to cast Unwilling Recruit. Attack with everything. Savage Beating (Only the sentiment)
Modern: Delver
Legacy: OmniTell
Commander: Too many
Everywhere it works: Storm.