Ah, having a way to animate enchantments will be really nice. As for overcheap reshuffling cards, I guess we don't even know yet whether we will use Precognition Field for our stage combo (assuming we can come up with one), since Cleansing Nova is going away. Precognition Field is certainly a good card though; it lets us cast instants/sorceries (which are very good with TYS) without having to draw them. But, I guess the advantage of still requiring mana in the presence of Omniscience goes away, since we won't have Omniscience any more. Losing Omniscience is actually pretty painful; if we use mana for our stage resource or higher, we have to make sure that we can get everything else we need without using that color of mana. Stakfish used Unclaimed Territory to help out with that, but we won't have access to that anymore either.

Yeah, we should probably wait for at least the next set to really think about it.

Hmmm... As you say, it's not worth getting Kykar with Concoct, except when we absolutely need it for Sarkhan, I think. So we wouldn't be using red mana for the stage.

When we do actually fetch Kykar with Concoct, I imagine it will be the last Concoct before we activate Sarkhan. So we don't get any more stages, we just use our red mana to cast maybe a couple of Repeated Reverberations (since we get a reshuffle from Concoct), and then activate Sarkhan. We can have some leftover red mana after the Sarkhan activation, I imagine we want to use it as quickly as possible, since generally earlier is better. I don't think we'll be saving any red mana to use during a stage.

2 -> 4 -> 7 -> 12 is approximately 2 -> (2 -> 4 -> 16 -> 11) -> 6 -> 12. (The latter is a little bit greater; for the former, we can start with 2 -> 4 -> 16 -> 11 = 2 -> 4 -> 2 -> 12, and then apply the function X to 2 -> 4 -> X -> 11 five times; for the latter, we can start with 2 ^ (2 -> 4 -> 16 -> 11) = 2 -> (2 -> 4 -> 16 -> 11) -> 1 -> 12, and then apply the function X to 2 -> 4 -> X -> 11 five times. So the latter is a little bit greater since we start with a larger number.)

Switching the initial 2 to a 7 makes almost no difference, so 2 -> 4 -> 7 -> 12 will be just a little bit less than 7 -> (7 -> 4 -> 16 -> 11) -> 6 -> 12 as well. So 2 -> 4 -> 7 -> 12 will be greater than 7 -> (7 -> 3 -> 16 -> 11) -> 6 -> 12, for instance.

The first number doesn't make a whole lot of difference; really the biggest significance of a and b in a -> b -> c -> d is the fact that when you reduce down to a -> b -> 1 -> d, that equals a^b. So it is the value of a^b that is important; in case of a tie, b is the tiebreaker. (As is typical, this rule of thumb does not always hold, for example if d = 1, then we just have a -> b -> c, and we know that b is much more important then a then, if a >= 3.) Since we are dealing with X's that are length 4 Conway chains themselves, generally speaking if X1 is a Conway Chain such that X > 2^X1, then X will in all likelihood will be greater than X1^X1 as well. So we could choose X1 = 2 -> X2 -> 21 -> 11, or X1 = X2 -> X2 -> 21 -> 11, and either will be valid. I've been using 10 as a default number, since 10 is a commonly used "base" number.

Yeah, maybe Connive // Concoct is better - I didn't really look at it carefully before just choosing Blood for Bones. So make both the main combo card and the two extras Connive // Concoct?

Good point about needing Stony Strength - we could also use Leyline of Abundance, but either way we would need to keep another card around. I imagine there is some other way to kill the opponent with just one card needed though. If we find a way to save a card, that would definitely worth looking for. I guess right now it's not so pressing.

So, before the first Sanctum of the Sun we get to more than a -> b -> 21 -> 11 for nongigantic a and b. This will be more than a -> b -> 2 -> 12 = a -> b -> a^b -> 11, so long as a^b <= 21. So for example we have more than 2 -> 4 -> 2 -> 12. Then each Sanctum of the Sun will increase the third number by one, so we wind up with more than 2 -> 4 -> 7 -> 12. But we need the 2 and 4 at the beginning.

Ah, good catch. It does look like cutting Karn is the way to go. We still want [c}Azor's Gateway[/c], since we don't have Spark Double for Nikya of the Old Ways. And I guess Squee, the Immortal will go infinite with the card drawing.

Without the artifact retrieval, it looks like we have 25 exilable cards without Gravitic Punch, or 24 with. That means that if we are required to send the opponent to a low negative life total, adding Saheeli, Sublime Artificer won't add another Sanctum of the Sun. It won't lose one either though, so we might as well keep it in, since we can still have Dowsing Daggers and Hadana's Climb.

We can exile 24 cards, so we can get 4 Sanctum of the Suns that way, and we can get one more by using the Saheeli trick. That takes us to more than 10 -> X1 -> 6 -> 12 final damage.

X1 is how much life we can get before we tap the first Sanctum of the Sun. The main component of this is the number of times we can activate Sarkhan, Dragonsoul. We can activate it once when we play it, then we can recycle it once using Raging Regisaur, then another time for each black mana that we can produce prior to activating the forst SotS. We can use Nikya so that each of the four Dowsing Daggers can add four black mana each, then Hadana's Climb can add two more. So we can activate Sarkhan 20 times, so that X1 > 10 -> X2 -> 21 -> 11.

In turn, X2 is how great a TYS count we can get prior to the first Sarkhan activation. THe biggest component of that comes from using Whispering Snitch to gain the opponent a lot of life. We can Switcheroo a Citywatch Sphinx to the opponent, then destroy it (with Cleansing Nova, say). Then in response to the surveil trigger, we can Switcheroo a lot of Whispering Snitches to the opponent, and the surveil will trigger a lot of life gains from the Whispering Snitches. So that gives us X2 > 10 -> 10 -> X3 -> 9, where X3 is how many Whispering Snitches we can transfer over to the enemy.

The main component of X3 comes from the fact that we can resolve 19 copies of Vicious Rumors, making use of the opponent's initial 20 health. So X3 > 10 -> X4 -> 19 -> 8, where X4 is how high we can pump our TYS count before the first Vicious Rumors.

The main component of X4 comes using our 16 remaining life after our initial start to cast Gaea's Blessing followed by Ionize. We can do this 7 times, and each time we can get many Repeated Reverberation triggers, and four Thousand-Year Storm triggers, so we get many copies of Gaea's Blessing 35 times. So X4 > 10 -> X5 -> 36 -> 7.

The main component of X5 comes from the Bankrupt in Blood that we can draw and cast during the initial start, for 5 big batches of copies. So X5 > 10 -> X6 -> 6 -> 6.

The main component of X6 comes from the four Blood for Bones, which each get 5 big batches of copies, so X6 > 10 -> X7 -> 21 -> 5.

The biggest component of X7 copies from putting many copies of World Shaper into play, and destroying them, each of which creates a trigger to refetch [c/]Lotus Field[/c]. So X7 > 10 -> 10 -> X8 -> 3.

Before we put World Shaper into play, we can use Wayward Swordtooth to allow us to play Emergence Zone with more than 2^700,000 Evolution Sages in play, so X8 > 10 -> 10 -> 2^700,000 -> 2.

Note that X1 > 10 -> X2 -> 21 -> 11 > 2 -> 4 -> 2 -> 12. So after 5 Sanctum of the Suns, we get a final damage of more than 2 -> 4 -> 7 -> 12. So that's a simpler lower bound, but it is harder to expand like we did above.

I have accounts on Googles sites (where I currently have my unfinished writeup of the megastage Vintage deck) and Wordpress, so we could stick it on one of those, if you don't want to get your own account. Perhaps we could convert it into a nice HTML document, with card images?

Are you satisfied with the writeup? Should we publicize it?

Yeah, we should probably wait for at least the next set to really think about it.

When we do actually fetch Kykar with Concoct, I imagine it will be the last Concoct before we activate Sarkhan. So we don't get any more stages, we just use our red mana to cast maybe a couple of Repeated Reverberations (since we get a reshuffle from Concoct), and then activate Sarkhan. We can have some leftover red mana after the Sarkhan activation, I imagine we want to use it as quickly as possible, since generally earlier is better. I don't think we'll be saving any red mana to use during a stage.

Switching the initial 2 to a 7 makes almost no difference, so 2 -> 4 -> 7 -> 12 will be just a little bit less than 7 -> (7 -> 4 -> 16 -> 11) -> 6 -> 12 as well. So 2 -> 4 -> 7 -> 12 will be greater than 7 -> (7 -> 3 -> 16 -> 11) -> 6 -> 12, for instance.

The first number doesn't make a whole lot of difference; really the biggest significance of a and b in a -> b -> c -> d is the fact that when you reduce down to a -> b -> 1 -> d, that equals a^b. So it is the value of a^b that is important; in case of a tie, b is the tiebreaker. (As is typical, this rule of thumb does not always hold, for example if d = 1, then we just have a -> b -> c, and we know that b is much more important then a then, if a >= 3.) Since we are dealing with X's that are length 4 Conway chains themselves, generally speaking if X1 is a Conway Chain such that X > 2^X1, then X will in all likelihood will be greater than X1^X1 as well. So we could choose X1 = 2 -> X2 -> 21 -> 11, or X1 = X2 -> X2 -> 21 -> 11, and either will be valid. I've been using 10 as a default number, since 10 is a commonly used "base" number.

2 -> 4 -> 7 -> 12 is actually greater than 7 -> 4000000 -> 6 -> 12, although I suppose 7 -> 4000000 -> 6 -> 12 might LOOK bigger. Of course, 7 -> (7 -> x2 -> 21 -> 11) -> 6 -> 12 is bigger still.

Edit: I currently don't have access to edit the doc, so I will post some comments here:

Are the [ deck ] and [ /deck ] in the deck lists intentional?

After Precognition Field we should have 1G,1R, so that we can cast Stony Strength next. So we have:

Precognition Field - 1G,1R

L - Stony Strength - 3G,2R,1U

L - Stony Strength - 5G,3R,2U

Thousand-Year Storm - 1G,4R,1U

So it looks like everything has one less R from there on.

Yeah, maybe Connive // Concoct is better - I didn't really look at it carefully before just choosing Blood for Bones. So make both the main combo card and the two extras Connive // Concoct?

Good point about needing Stony Strength - we could also use Leyline of Abundance, but either way we would need to keep another card around. I imagine there is some other way to kill the opponent with just one card needed though. If we find a way to save a card, that would definitely worth looking for. I guess right now it's not so pressing.

So, before the first Sanctum of the Sun we get to more than a -> b -> 21 -> 11 for nongigantic a and b. This will be more than a -> b -> 2 -> 12 = a -> b -> a^b -> 11, so long as a^b <= 21. So for example we have more than 2 -> 4 -> 2 -> 12. Then each Sanctum of the Sun will increase the third number by one, so we wind up with more than 2 -> 4 -> 7 -> 12. But we need the 2 and 4 at the beginning.

Without the artifact retrieval, it looks like we have 25 exilable cards without Gravitic Punch, or 24 with. That means that if we are required to send the opponent to a low negative life total, adding Saheeli, Sublime Artificer won't add another Sanctum of the Sun. It won't lose one either though, so we might as well keep it in, since we can still have Dowsing Daggers and Hadana's Climb.

So, perhaps we can go with:

Startup:1 Leyline of Abundance

2 Leyline of Abundance

3 Breeding Pool

4 Llanowar Elves

5 Plains

6 Stony Strength

7 Stony Strength

8 Emergency Powers

9 Kykar, Wind's Fury

10 Samut, Tyrant Smasher

11 Mox Amber

12 Gyre Engineer

13 Precognition Field

14 Thousand-Year Storm

15 Omniscience

16 Emergence Zone

Stage Combo:17 Manifold Key

18 The Antiquities War

19 The Antiquities War

20 Cleansing Nova

21 Cleansing Nova

22 Disdainful Stroke

Rebuild and Reshuffle:23 Teshar, Ancestor's Apostle

24 Militia Bugler

25 Tragic Poet

26 Gaea's Blessing

27 Citywatch Sphinx

28 Kaya's Ghostform

29 Repudiate // Replicate

Proliferation:30 Evolution Sage

Recycling Lands:31 World Shaper

32 Lotus Field

Drawing:33 Blood for Bones

34 Bankrupt in Blood

35 Ionize

Life Gain:36 Sarkhan, Dragonsoul

37 Repeated Reverberation

39 Dreadmalkin

39 Imperial Ceratops

40 Angel of Vitality

41 Vicious Rumors

42 Dowsing Dagger

43 Switcheroo

Black Mana:44 Azor's Gateway

Putting Emergence Zone into play:45 Wayward Swordtooth

The Final Hit:46 Gravitic Punch

Disposable Cards:47 Saheeli, Sublime Artificer

48 Dowsing Dagger

49 Dowsing Dagger

50 Dowsing Dagger

51 Hadana's Climb

52 Nikya of the Old Ways

53 Raging Regisaur

54 Whispering Snitch

55 Thousand-Year Storm

56 Thousand-Year Storm

57 Thousand-Year Storm

58 Blood for Bones

59 Blood for Bones

60 Blood for Bones

We can exile 24 cards, so we can get 4 Sanctum of the Suns that way, and we can get one more by using the Saheeli trick. That takes us to more than 10 -> X1 -> 6 -> 12 final damage.

X1 is how much life we can get before we tap the first Sanctum of the Sun. The main component of this is the number of times we can activate Sarkhan, Dragonsoul. We can activate it once when we play it, then we can recycle it once using Raging Regisaur, then another time for each black mana that we can produce prior to activating the forst SotS. We can use Nikya so that each of the four Dowsing Daggers can add four black mana each, then Hadana's Climb can add two more. So we can activate Sarkhan 20 times, so that X1 > 10 -> X2 -> 21 -> 11.

In turn, X2 is how great a TYS count we can get prior to the first Sarkhan activation. THe biggest component of that comes from using Whispering Snitch to gain the opponent a lot of life. We can Switcheroo a Citywatch Sphinx to the opponent, then destroy it (with Cleansing Nova, say). Then in response to the surveil trigger, we can Switcheroo a lot of Whispering Snitches to the opponent, and the surveil will trigger a lot of life gains from the Whispering Snitches. So that gives us X2 > 10 -> 10 -> X3 -> 9, where X3 is how many Whispering Snitches we can transfer over to the enemy.

The main component of X3 comes from the fact that we can resolve 19 copies of Vicious Rumors, making use of the opponent's initial 20 health. So X3 > 10 -> X4 -> 19 -> 8, where X4 is how high we can pump our TYS count before the first Vicious Rumors.

The main component of X4 comes using our 16 remaining life after our initial start to cast Gaea's Blessing followed by Ionize. We can do this 7 times, and each time we can get many Repeated Reverberation triggers, and four Thousand-Year Storm triggers, so we get many copies of Gaea's Blessing 35 times. So X4 > 10 -> X5 -> 36 -> 7.

The main component of X5 comes from the Bankrupt in Blood that we can draw and cast during the initial start, for 5 big batches of copies. So X5 > 10 -> X6 -> 6 -> 6.

The main component of X6 comes from the four Blood for Bones, which each get 5 big batches of copies, so X6 > 10 -> X7 -> 21 -> 5.

The biggest component of X7 copies from putting many copies of World Shaper into play, and destroying them, each of which creates a trigger to refetch [c/]Lotus Field[/c]. So X7 > 10 -> 10 -> X8 -> 3.

Before we put World Shaper into play, we can use Wayward Swordtooth to allow us to play Emergence Zone with more than 2^700,000 Evolution Sages in play, so X8 > 10 -> 10 -> 2^700,000 -> 2.

Note that X1 > 10 -> X2 -> 21 -> 11 > 2 -> 4 -> 2 -> 12. So after 5 Sanctum of the Suns, we get a final damage of more than 2 -> 4 -> 7 -> 12. So that's a simpler lower bound, but it is harder to expand like we did above.

Edit: Oh, you've added images already.

I'll try to work out more exact numbers later.

Hmm, are there 21 Sanctum of the Suns? I counted 19, leading to 10 -> X -> 20 -> 12. (21 Sanctum of the Suns would get us to 10 -> X -> 22 -> 12.)

Edit: I guess there are 20, which would lead to 10 -> X -> 21 -> 12.