I got the extra red back by fizzling Ionize after Omniscience, so everything after stays the same.
Added a tappedout link to the decklist.
Thanks for the explanation, these corner cases with relatively small numbers really help.
Yeah I'm just using 7 because we add 6 storm each top level reshuffle and have X of those so we bring X to 7X, and it'll be easier to follow that than switching the base halfway through.
Edit: hmm, it looks like we can use disdainful stroke to fizzle ionize before the first gaea's blessing too, and get an extra storm.
Edit2: I know this doesn't impact any of the estimations, but someone will probably ask. Do you have any clue about how to optimally make/spend our red mana once we have flash? Other than Kykar its generally better as white mana from mox amber, instead, but we can get Kykar back with a connive, and will have to to cast Repeated Reverberation for Sarkhan. Though we can't save it in hand like we could with blood for bones, so we dont get a ton of mana, it is still more than enough to cast a few extra repeated reverberations. Actually no, we can replicate the elemental tokens, so we can get X red.
I kinda think we want to concoct back kykar as little as possible, as Worldshaper is a better target all the time. but we do want to still repeated reverberate the card draw and the concoct itself. But do we want to use the red in the stage? Do we want to get RR on RR for the next layer card? Do we want to just spend all the red we can ASAP to make the stage combo stronger?
Yeah, its hard to get a picture of how the different estimations are all linked, especially with things like Whispering Snitch and extra TYS.
How big does x2 need to be for 7 -> (7 -> x2 -> 21 -> 11) -> 6 -> 12 to be greater than 2 -> 4 -> 7 -> 12?
My estimate isn't great either,
Because of not factoring in the extra sphinxes each top level wrath actually squares the storm and we get a huge number in the front as well, but actually saying that involves some more fiddling with exponents in an already fiddly section.
So the better estimate would be X1->X1->6->12.
where X1= X2->X2->21->11 (extra sarkhans)
and X2= x3->x3->x3->9 (extra life gain triggers from the snitch)
and so on... with their extra life, our extra life, the extra cards from hand from the setup... and extra TYS triggers the whole way, making everything more powerful.
Edit: sent you the edit link again, good catch on the free stony strength I missed.
Concoct is almost the same exact card as blood for bones here, and either way it doesnt really show in the estimate, but Connive is also a blue instant we can cast in the stage too, which contributes to the leading 7 in my estimate.
Stony Strength is better to keep than Leyline as it can make white mana from an animated key. I actually couldn't find a better card to kill them with, though I didn't look very hard.
Oh I see, the 2 -> 4 -> 2 -> 12 is the base storm before doing any flips and we are increasing that by the 5 flips we get to come to 2 -> 4 -> 7 -> 12. Kind of a tricky way to get the extra number, the first two numbers seem like they really shouldn't matter so much, but when the numbers are small it works out like that.
That a -> b -> 2 -> 12 identity seems odd, but actually checks out a -> b -> 2 -> 12 = a -> b -> (a -> b -> 1 -> 12) -> 11 = a -> b -> (a -> b) -> 11 = a -> b -> a^b -> 11
I guess by that logic we get past 2->2->2->13 (which is just 4), and are one flip shy of getting to 2->3->2->13 (which is much more than 4).
It does seem like these would not be nearly as tight of a bound as the 7 -> (7 -> x2 -> 21 -> 11) -> 6 -> 12 estimate, even though they have bigger ending numbers.
Edit: Well, I refactored Karn out, redid the beginning with an extra stony strength for storm, and updated all of the changed images. I'm gonna give us one more day to find any other errors then post the view only link to r/magictcg.
The Gatebreaker is unfortunately not naturally a creature to replicate.
Edit: i tried a bunch of lines, but cant seem to get to another card for 5 flips. Oh well, will rewrite karn out tomorrow.
Edit2: the start needs an extra untap effect, to have enough blue for Precognition field, TYS, and replicate. Making the last Blood for bones a Stony Strength
Edit3: isn't Connive // Concoct just better than Blood for bones? we get a free reshuffle with each resolution instead of a free guy to hand. If we had an extra creature worth returning (worldshaper#2?), that could be worth it, but we don't.
Also, we are actually 2 cards away from 5 flips, we need to keep a Stony Strength to actually make the guy we Gravitic punch them with giant.
edit4: rereading your estimation and I think I'm missing something?
Are you sure we get to ...->7->12?
I agree that we get to 7->X1->6->12 where X1 is 7->x2->21->11 but I don't see how that can possibly be big enough to give us something like 7->c->7->12? where c is some small non chained arrow constant like 3x10^18 or 4.
By definition, 7->c->7->12 = 7->c->(7->c->6->12)->11 which seems difficult to compare to 7->(7->x2->21->11)->6->12
Yeah, I checked for that infinite before but that was before sarkhan+repeated reverberation was a layer. Oh well, its still ->12.
We cant use karn for an early animation so there's no ministage before the Emergence Zone. So we make more like 10^13 Evolution sages.
Our exileable cards are a bit clogged at 4, with 2x leyline 3x blood for bones, kykar, and raging regisaur. Good thing connive // concoct is basically the same card for this challenge.
Being one card short of 5 flips is kind of frustrating, but I don't see any way to squeeze an extra slot, and still kill them.
I think we can cut Militia bugler, Kaya's Ghostform, and one The Antiquities War for Mystic Forge and Tezzeret's Gatebreaker. Hmm, no this is still short a way to recycle Teshar.
Hmm with 1 black from Hadana's climb and the 3 mana from dowsing dagger, is Nikya of the old ways better than a connive // concoct? Just for the 2 extra black before the first real azor's gateway flip?
EDIT: ABORT, UGH
I found an infinite:
Activate Azor's Gateway, draw bankrupt in blood, exile an artifact (like dowsing dagger)
use Karn to return the artifact
Repeated reverberation Sarkhan, dragonsoul kills both karn and himself
cast bankrupt in blood
combo off.
use excess draws to redraw the walkers.
I don't see any sort of simple fix.
Cut repeated reverberation? loses the Sarkhan layer, Also makes the start much less explosive.
Cut Azor's gateway? Can't make much black then.
Cut Karn? This seems the best, we can still exile enough for a few flips, but more like 4 than 20
Yeah definitely, this was hard enough. Its kind of fun to learn more about how these notations work, but explaining it is a bit of a chore, and the vintage deck is a whole 'nother beast. I tried to puzzle it out on my own, and its just incredible how fast these things get completely intractable.
You might want to improve my estimates a bit, and currently its at 6->2^(700,000)->20->12 but it should really probably be something like 6->(6->2^(700,000)->X->6)->20->12. Or some further nested chain nonsense.
Edit: Hmm, just double checking the combat triggers, which seem like they need to be really good to be worth it. I think maybe Hadana's Climb is the closest? It looks like it would definitely be better than a Concoct if we didn't already use Sarkhan precombat to let Raging Regisaur kill him. It is an extra black mana from combat though, so it is probably still good.
Another thought is using gideon6 and Role reversal to kill sarkhan in combat by attacking him, without using Raging Regisaur at all. One bonus to this is that we can equip gideon and then wrath in combat, though we still can't Purify, so it's probably not worth it. (Edit2: oops gideon doesnt become indestructible himself, so this is definitely a no go)
Feel free to comment or edit if you notice anything amiss. I'd like to get it finalized before we get too many Eldrane spoilers.
You are right, there are 20. I double counted Saheeli.
Edit: oops the decklist was 61 cards, I cut a connive//concoct.
Edit2: changed the 'small' example to a full resolution of 2 storm 6 mana.
I'm not exactly sure how to post the writeup? I don't have a blog to throw this on, and its pretty long to just cut up across several reddit posts. It's probably too niche to get put on any of the main sites. (though Frank Karsten does so some wacky magic math articles...)
Oh I see, hmm, yeah blue mana is a bit tighter at the start, and its not worth switching to add another Stony strength they way some of our earlier lines were able to use.
Edit: I have the updated pre-landfall line in the google doc if you want to look over it and see if there are any errors or to make any of the estimates more exact. The Repeated Reverberations get pretty damn strong! and I have storm at around 3 trillion, but with 2^630000 landfall triggers, so we aren't starting nearly as far behind the ministage starts as I had initially thought.
Key improvements over the line in your post: Getting the whole deck into hand with the TYS trigger (except for Gaea's Blessing). Making more initial red when Kykar is still in play. Sneaking a couple more Repeated reverberations in for value. Increasing the sphinx:gyre engineer ratio to more heavily use Stony strength for storm (might not actually be better?). And the Teshar/Militia Bugler swap to allow the line to actually continue into the main combo.
Edit: ok I've gone through to the end, but haven't included all of the optimizations, like the Saheeli making Azor's gateway a Dowsing dagger trick, or the effects of the extra creature fetchers. I currently count a total of 21 Sanctum of the sun taps which brings us to 5->X->21->12. Where that X is gonna be something like 5->Z->3->12.
There is a bit of a tradeoff, I think actually optimally we slot the TYS trigger for Gaea's blessing on top of 2 or so of the Repeated reverberations, so we don't have to slow down to not deck. But I haven't worked it out yet, it looks like +4 or so red can be saved like that.
Edit: without Nexus of fate, red mana is more expensive than blue. one of the Act of treason should maybe go back to Replicate?
Oh, with the storm count this low at the start, we can stack the RR draws from Gaea's blessing first to increase the storm for the TYS trigger for Gaea's Blessing, and not worry much about decking.
Edit:
We have 14 cards that are in play, in exile, or otherwise not drawable, they are:
Leyline
Leyline
Leyline
Llanowar Elf
Breeding Pool
Plains
Emergency powers (exiled)
Kykar
Samut
Mox amber
Gyre engineer
Precognition field
Thousand-year storm
Gaea’s Blessing (can’t draw)
Thus we should get the storm count to make 46 copies of Gaea’s Blessing but no more.
Looks like we can get to ~ 19389RRs with 1287G,327U,21R floating, 47 storm, and an empty graveyard and 1 card deck with that line.
Hmm, yeah the timing is not good, we only want to have Teshar in play with a reshuffle looming.
What if we played Teshar instead of militia bugler first? That way we have the bugler in hand to fetch Teshar with later. We can save playing Karn until after Teshar as the historic spell.
10^10^5 or so is certainly a lot smaller than we were entering the stage with when we had Nexus of fate, but we catch up before we spend any more life.
I am going to miss having all of the turns stored up though.
One other thing to possibly consider for combat is having an innately indestructible creature like drudge sentinels or Zetalpa, primal dawn wear the equipment, freeing us up to wrath mid-combat. (We still can't Purify though, so no full combat stage. Which means this probably isn't worth it)
It's really too bad that treasure tokens aren't safe. The current loop is that a creature treasure can be copied a bunch and live through a wrath, and then pay for the black card draw spell to get enough resources to animate again and make more copies. If something forced us to purify in the first few layers, they probably would be safe, but I don't see a way to force that. (if only the antiquities war stuck around doing nothing...)
Added a tappedout link to the decklist.
Thanks for the explanation, these corner cases with relatively small numbers really help.
Yeah I'm just using 7 because we add 6 storm each top level reshuffle and have X of those so we bring X to 7X, and it'll be easier to follow that than switching the base halfway through.
Edit: hmm, it looks like we can use disdainful stroke to fizzle ionize before the first gaea's blessing too, and get an extra storm.
Edit2: I know this doesn't impact any of the estimations, but someone will probably ask. Do you have any clue about how to optimally make/spend our red mana once we have flash? Other than Kykar its generally better as white mana from mox amber, instead, but we can get Kykar back with a connive, and will have to to cast Repeated Reverberation for Sarkhan. Though we can't save it in hand like we could with blood for bones, so we dont get a ton of mana, it is still more than enough to cast a few extra repeated reverberations. Actually no, we can replicate the elemental tokens, so we can get X red.
I kinda think we want to concoct back kykar as little as possible, as Worldshaper is a better target all the time. but we do want to still repeated reverberate the card draw and the concoct itself. But do we want to use the red in the stage? Do we want to get RR on RR for the next layer card? Do we want to just spend all the red we can ASAP to make the stage combo stronger?
How big does x2 need to be for 7 -> (7 -> x2 -> 21 -> 11) -> 6 -> 12 to be greater than 2 -> 4 -> 7 -> 12?
My estimate isn't great either,
Because of not factoring in the extra sphinxes each top level wrath actually squares the storm and we get a huge number in the front as well, but actually saying that involves some more fiddling with exponents in an already fiddly section.
So the better estimate would be X1->X1->6->12.
where X1= X2->X2->21->11 (extra sarkhans)
and X2= x3->x3->x3->9 (extra life gain triggers from the snitch)
and so on... with their extra life, our extra life, the extra cards from hand from the setup... and extra TYS triggers the whole way, making everything more powerful.
Edit: sent you the edit link again, good catch on the free stony strength I missed.
Stony Strength is better to keep than Leyline as it can make white mana from an animated key. I actually couldn't find a better card to kill them with, though I didn't look very hard.
Oh I see, the 2 -> 4 -> 2 -> 12 is the base storm before doing any flips and we are increasing that by the 5 flips we get to come to 2 -> 4 -> 7 -> 12. Kind of a tricky way to get the extra number, the first two numbers seem like they really shouldn't matter so much, but when the numbers are small it works out like that.
That a -> b -> 2 -> 12 identity seems odd, but actually checks out a -> b -> 2 -> 12 = a -> b -> (a -> b -> 1 -> 12) -> 11 = a -> b -> (a -> b) -> 11 = a -> b -> a^b -> 11
I guess by that logic we get past 2->2->2->13 (which is just 4), and are one flip shy of getting to 2->3->2->13 (which is much more than 4).
It does seem like these would not be nearly as tight of a bound as the 7 -> (7 -> x2 -> 21 -> 11) -> 6 -> 12 estimate, even though they have bigger ending numbers.
Edit: Well, I refactored Karn out, redid the beginning with an extra stony strength for storm, and updated all of the changed images. I'm gonna give us one more day to find any other errors then post the view only link to r/magictcg.
Edit: i tried a bunch of lines, but cant seem to get to another card for 5 flips. Oh well, will rewrite karn out tomorrow.
Edit2: the start needs an extra untap effect, to have enough blue for Precognition field, TYS, and replicate. Making the last Blood for bones a Stony Strength
Edit3: isn't Connive // Concoct just better than Blood for bones? we get a free reshuffle with each resolution instead of a free guy to hand. If we had an extra creature worth returning (worldshaper#2?), that could be worth it, but we don't.
Also, we are actually 2 cards away from 5 flips, we need to keep a Stony Strength to actually make the guy we Gravitic punch them with giant.
edit4: rereading your estimation and I think I'm missing something?
Are you sure we get to ...->7->12?
I agree that we get to 7->X1->6->12 where X1 is 7->x2->21->11 but I don't see how that can possibly be big enough to give us something like 7->c->7->12? where c is some small non chained arrow constant like 3x10^18 or 4.
By definition, 7->c->7->12 = 7->c->(7->c->6->12)->11 which seems difficult to compare to 7->(7->x2->21->11)->6->12
We cant use karn for an early animation so there's no ministage before the Emergence Zone. So we make more like 10^13 Evolution sages.
Our exileable cards are a bit clogged at 4, with 2x leyline 3x blood for bones, kykar, and raging regisaur. Good thing connive // concoct is basically the same card for this challenge.
Being one card short of 5 flips is kind of frustrating, but I don't see any way to squeeze an extra slot, and still kill them.
It looks like the rebuild section is the most likely to have a cuttable card, but we need to have a way to get Gyre engineer, Citywatch sphinx, tragic poet and evolution sage, without getting World shaper. Oh, and still have a white legend
I think we can cut Militia bugler, Kaya's Ghostform, and one The Antiquities War for Mystic Forge and Tezzeret's Gatebreaker. Hmm, no this is still short a way to recycle Teshar.
Hmm with 1 black from Hadana's climb and the 3 mana from dowsing dagger, is Nikya of the old ways better than a connive // concoct? Just for the 2 extra black before the first real azor's gateway flip?
EDIT: ABORT, UGH
I found an infinite:
Activate Azor's Gateway, draw bankrupt in blood, exile an artifact (like dowsing dagger)
use Karn to return the artifact
Repeated reverberation
Sarkhan, dragonsoul kills both karn and himself
cast bankrupt in blood
combo off.
use excess draws to redraw the walkers.
I don't see any sort of simple fix.
Cut repeated reverberation? loses the Sarkhan layer, Also makes the start much less explosive.
Cut Azor's gateway? Can't make much black then.
Cut Karn? This seems the best, we can still exile enough for a few flips, but more like 4 than 20
This sucks, but at least I caught it.
You might want to improve my estimates a bit, and currently its at 6->2^(700,000)->20->12 but it should really probably be something like 6->(6->2^(700,000)->X->6)->20->12. Or some further nested chain nonsense.
Edit: Hmm, just double checking the combat triggers, which seem like they need to be really good to be worth it. I think maybe Hadana's Climb is the closest? It looks like it would definitely be better than a Concoct if we didn't already use Sarkhan precombat to let Raging Regisaur kill him. It is an extra black mana from combat though, so it is probably still good.
Another thought is using gideon6 and Role reversal to kill sarkhan in combat by attacking him, without using Raging Regisaur at all. One bonus to this is that we can equip gideon and then wrath in combat, though we still can't Purify, so it's probably not worth it. (Edit2: oops gideon doesnt become indestructible himself, so this is definitely a no go)
Good idea putting it on a google sites or wordpress account. I'll look into that.
Edit: I don't want to get stuck reformatting everything again, so I'm currently leaning towards just posting a comment or view only link to the gdoc.
Feel free to comment or edit if you notice anything amiss. I'd like to get it finalized before we get too many Eldrane spoilers.
You are right, there are 20. I double counted Saheeli.
Edit: oops the decklist was 61 cards, I cut a connive//concoct.
Edit2: changed the 'small' example to a full resolution of 2 storm 6 mana.
I'm not exactly sure how to post the writeup? I don't have a blog to throw this on, and its pretty long to just cut up across several reddit posts. It's probably too niche to get put on any of the main sites. (though Frank Karsten does so some wacky magic math articles...)
Edit: I have the updated pre-landfall line in the google doc if you want to look over it and see if there are any errors or to make any of the estimates more exact. The Repeated Reverberations get pretty damn strong! and I have storm at around 3 trillion, but with 2^630000 landfall triggers, so we aren't starting nearly as far behind the ministage starts as I had initially thought.
Key improvements over the line in your post: Getting the whole deck into hand with the TYS trigger (except for Gaea's Blessing). Making more initial red when Kykar is still in play. Sneaking a couple more Repeated reverberations in for value. Increasing the sphinx:gyre engineer ratio to more heavily use Stony strength for storm (might not actually be better?). And the Teshar/Militia Bugler swap to allow the line to actually continue into the main combo.
Edit: ok I've gone through to the end, but haven't included all of the optimizations, like the Saheeli making Azor's gateway a Dowsing dagger trick, or the effects of the extra creature fetchers. I currently count a total of 21 Sanctum of the sun taps which brings us to 5->X->21->12. Where that X is gonna be something like 5->Z->3->12.
Edit: without Nexus of fate, red mana is more expensive than blue. one of the Act of treason should maybe go back to Replicate?
Edit:
We have 14 cards that are in play, in exile, or otherwise not drawable, they are:
Leyline
Leyline
Leyline
Llanowar Elf
Breeding Pool
Plains
Emergency powers (exiled)
Kykar
Samut
Mox amber
Gyre engineer
Precognition field
Thousand-year storm
Gaea’s Blessing (can’t draw)
Thus we should get the storm count to make 46 copies of Gaea’s Blessing but no more.
Looks like we can get to ~ 19389RRs with 1287G,327U,21R floating, 47 storm, and an empty graveyard and 1 card deck with that line.
(I think Red mana is miscounted in your line?)
What if we played Teshar instead of militia bugler first? That way we have the bugler in hand to fetch Teshar with later. We can save playing Karn until after Teshar as the historic spell.
I think that works?
Edit: Teshar not Kykar
10^10^5 or so is certainly a lot smaller than we were entering the stage with when we had Nexus of fate, but we catch up before we spend any more life.
I am going to miss having all of the turns stored up though.
One other thing to possibly consider for combat is having an innately indestructible creature like drudge sentinels or Zetalpa, primal dawn wear the equipment, freeing us up to wrath mid-combat. (We still can't Purify though, so no full combat stage. Which means this probably isn't worth it)
It's really too bad that treasure tokens aren't safe. The current loop is that a creature treasure can be copied a bunch and live through a wrath, and then pay for the black card draw spell to get enough resources to animate again and make more copies. If something forced us to purify in the first few layers, they probably would be safe, but I don't see a way to force that. (if only the antiquities war stuck around doing nothing...)
(maybe wrathing before animating the key is good?)
The red mana on the other hand looks like more of a bottleneck that I'd expected. Losing Nexus of fate really hurts early.