Hmm I wonder if it’s just difference in style that is the issue. What I mean is this: your decks are designed to work on the acquiring of layers as there definition of power. The more layers the stronger the deck, and that makes sense. I think my issue is that’s not entirely what my set up draws it’s power from. It draws powers more from the addition of abilities rather than just straight math towers. Your deck basically works by going up any given chain and then working it’s way back down the chain making larger and larger entities underneath it ending in final structure that would look like a Christmas tree with the highest layer being the top of the tree. My deck by design is much more like a puddle adding drops of water to it. Each drop is added and the entire system expands that much. This means that it might be possible that my 5 layers output could eclipse someone else’s 5 layer output just because of how it was designed to work in the first place.
It’s just kind an idea but maybe this concept is why I’m finding it hard understand why the deck feels so under powered via the layer = power definition?
You are saying your deck does something fundamentally different that allows it to reach gigantic numbers somehow without obeying the layer structure, I'm looking at your deck and this isn't the case. It looks like you feel like it has great power because "Each drop is added and the entire system expands that much." But that is completely normal, to get more layers you need to update your resources continually. So this isn't some new idea that does something different from previous decks.
I get that you feel that your deck should get more than 5 layers with those 20 cards, it's probably because layers and Knuth arrows are so strong. So enormous, gigantic numbers can be expressed with very few Knuth arrows. For example, 10^100 is more than the number of particles in the observable universe, and 10^10^100 can't even be written within the observable universe. And that's just one Knuth arrow, double arrows pretty much immediately shoot you into realms of numbers beyond anything that we can associate to any physical thing.
The thing is, you can't really say "my intuition tells me that you're wrong, I feel like my deck should get 20+ Knuth arrows." No one's intuition is that good. Without looking at how the numbers are increasing, which is what the layers are for, there's no way to determine how large a number you're going to get. In short, you have to do the math. ALL these numbers are too big to comprehend.
I actually get that the numbers are tough. I understand that. It’s just fundamentally my deck is looking for maximum interaction rather than layer inducing segregation. I guess my question comes from this. If one deck implements a layer x times and another deck can do it at x+1 times isn’t the x+1 deck a more powerful deck? Also if we see gains closer to layer implementation x^x times(or even more) at what point does it stop being the layer being implemented? By your definition x is defined infinitely for layer implementation but these decks are inherently finite so at some point it should be possible for a defined layer implementation to be eclipsed by another deck using the same implementation just more times. I think that is my issue. I get that updates are part of layering but it’s just hard when it’s seems like my inherent update ability in my particular set up scales so smoothly. It also doesn’t help that the interactions you guys mostly talk about are only happening at a stage level(which I’m obvioulsy struggling with understanding). I know it will be very basic for your decks but maybe walk me through some of the set up layers before you even get to the stage end of things. That might help me get an idea of what 4/5/6 layer setup looks like and why I’m not doing anything differently. I guess that’s the hard part is lately we’ve just been comparing my decks and nothing else. Something else might help me have a frame of reference. I actually think I understand what type of scaling we need to see layers(I did make a 40ish card deck with 12+ layers) so I get it to some extent it’s just I’m trying to understand why when my updatabilty seems very easy that that isn’t a power of some variety in and unto itself?
Edit: i’m not claiming I’m at 20+ layers by any means. I’m just looking to rectify what I see with what I understand. At most I’m saying I’m at 7 layers with my current list. Nothing even close to 10+ and certainly not 20+ or stage level.
If one deck implements a layer x times and another deck can do it at x+1 times isn’t the x+1 deck a more powerful deck?
Only imperceptibly, it is much more profitable to implement another layer instead. At these scales x+1 is a tiny difference. Furthermore even 2x or 100x is essentially the same as just x once it gets pushed through another layer.
Take the Polyraptor+Forerunner of the empire combo from standard as an example, if you increase the starting number of polyraptors by 10 then sure, you end up with about 10 times as many dinos, but if you instead increased Forerunner's toughness by 10 you'd have 2^10=1024 as many polyraptors. Similarly up the chain until we reach the final limiting resource IE the last copy of Emergency powers or w/e the limiting factor is. Having more of that resource is far more important than having more of something earlier. Ideally you can remake whatever the last resource is x more times and get another layer.
We are effectively using big O notation (Wiki link) for our approximate damage numbers. As a bit of an oversimplification: Big O notation doesn't care about constants.
As for stages Iijil's post linked in the OP (and here) Does a better job than I could explaining how the limitations of the stack prevent things from going infinite.
I actually get that the numbers are tough. I understand that. It’s just fundamentally my deck is looking for maximum interaction rather than layer inducing segregation.
Actually, your deck gets its power from layer stacking just like all the other layer decks. It doesn't do any "maximum interaction" that other decks don't do, not in any meaningful way anyway.
I guess my question comes from this. If one deck implements a layer x times and another deck can do it at x+1 times isn’t the x+1 deck a more powerful deck? Also if we see gains closer to layer implementation x^x times(or even more) at what point does it stop being the layer being implemented?
Ah, this is a very important point. If the layer being implemented is the very top layer, then the number of times it is being implemented is the next most significant thing after the total number of layers. You see that Knuth arrow notation has three basic numbers to them; there is a number to the left, a number to the right, and the number of arrows. For the most part, you compare two different numbers by looking at which has more arrows, and if they have the same number of arrows, look at the number on the right. (I'm assuming we use the same number on the left; typically we use 2 as the left number.) There are exceptions of course - if the number on the right is less than 4, then the number actually reduces down to a smaller expression. (2^^^^3 = 2^^^4, 2^^^^2 = 4, 2^^^^1 = 2.) Anyway, yeah, the number of times you implement the top layer is important, right after the number of layers.
So the next question is: if I have a lower layer that implements the next lower layer X+1 times rather than X times, won't the effects ripple up into the higher layers, and lead to a larger overall estimate? And the answer is a resounding no! Let's take a more extreme example: let's say deck 1 implements 2^^^X as their layer 3, and deck 2 implements 2^^^(X^X) as their layer 3. How does this look at layer 4? Now 2^^^(X^X) is greater than 2^^^X, so implementing layer 3 in deck 2 is stronger than implementing layer 3 in deck 1. But, 2^^^(X^X) is MUCH less than 2^^^(2^^^X), so implementing layer 3 twice in deck 1 is stronger than implementing layer 3 once in deck 2. Now, what if I implement layer 3 twice in deck 2? First, we apply X^X to 2^^^(X^X) to get (2^^^(X^X))^(2^^^(X^X)). This looks complicated, but exponentiation is such a weak operation compared to triple arrows, so this is actually much less than 2^^^(X^X + 1). So after applying 2^^^X, we get a number that is less than 2^^^(2^^^(X^X + 1)), and therefore much less than 2^^^(2^^^(2^^^X)), which is layer 3 of deck 1 applied 3 times. In general, applying layer 3 in deck 2 X times is weaker than applying layer 3 in deck 1 X+1 times. So the advantage is minimal. Now, you might say there is some advantage - yes, so if everything else in the deck is exactly the same, then deck 2 would nudge out deck 1. But obviously if deck 1 had more layers, or the top layer was applied more times, it would be greater.
What if we take a more extreme example: Let's say deck 1 has Cackling Counterpart, but no Riftsweeper, so each card draw took X to 2^^^^X roughly. Then, deck 2 is your deck with Riftsweeper, so with each card draw we can cast CC twice, and it takes X to 2^^^^(2^^^^X). So this is a much more extreme example, do the effects ripple up all the way to the top? And the answer is no again. Say Layer 5 is YB with IBs attached to it; if deck 1 has X IBs, it will apply 2^^^^X X times, so we will get about 2^^^^^X. However, deck two will apply 2^^^^X 2X times, so we get 2^^^^^(2X). Still a tangible advantage, but now you can see the advantage is much smaller. And, just like I explained above, if we apply 2^^^^^(2X) X times, it will be greater than 2^^^^^^X but less than 2^^^^^^(X+1). So Deck 2 will win if we apply Layer 6 exactly the same number of times as deck 1, but if deck 1 applies Layer 6 even one more time, it wins.
Note that, in my analyses, I haven't just been giving the number of layers; I've been giving precise estimates, like "your deck deals a final damage between 2^^^^^17 and 2^^^^^18." If a different deck was determined to be more than 2^^^^^18, then that's that; if it happened to also be between 2^^^^^17 and 2^^^^^18, then we would have to analyze further to determine exactly which deck won. I don't recall two totally completely different decks winding up being this close, but it can happen in the same deck where we want to determine which final cards to put in, and it often can be hard to decide which cards lead to the greatest advantage.
By your definition x is defined infinitely for layer implementation but these decks are inherently finite so at some point it should be possible for a defined layer implementation to be eclipsed by another deck using the same implementation just more times. I think that is my issue.
As I said above, if the total number of layers are the same, then we do indeed compare the number of implementations of the top layer to decide which deck is better. (More precisely, we determine which Knuth arrow numbers the decks lie between; a deck could have fewer implementations of the top layer but maybe it starts off from a higher base. So we do want to determine exact Knuth arrow bounds to determine how much damage a deck deals.) Now, you may be wondering, "Can't a deck with a smaller number of layers beat out a deck with a higher number of layers if the number of implementations of the former is large enough?" And the answer is yes, in a technical sense it can. But the number of implmentations is itself a number with the higher number of Knuth arrows. For example, there are certainly numbers X so that 2^^^^X is greater than 2^^^^^17, for example. But that only happens when X is greater than 2^^^^^16! So how are you generating that X in the first place? You need some recursive structure that gets you to five arrows anyway.
I get that updates are part of layering but it’s just hard when it’s seems like my inherent update ability in my particular set up scales so smoothly.
The proliferate thing is nice, it's very convenient. But convenience in and of itself doesn't lead to more powerful recursion; at best, it makes it easier to implement the processes that do lead to more powerful recursion. It doesn't generate anything by itself, it's a means to an end.
It also doesn’t help that the interactions you guys mostly talk about are only happening at a stage level(which I’m obvioulsy struggling with understanding). I know it will be very basic for your decks but maybe walk me through some of the set up layers before you even get to the stage end of things. That might help me get an idea of what 4/5/6 layer setup looks like and why I’m not doing anything differently. I guess that’s the hard part is lately we’ve just been comparing my decks and nothing else. Something else might help me have a frame of reference. I actually think I understand what type of scaling we need to see layers(I did make a 40ish card deck with 12+ layers) so I get it to some extent it’s just I’m trying to understand why when my updatabilty seems very easy that that isn’t a power of some variety in and unto itself?
If you read some of the earlier pages in this thread (I think most are in the first 10 pages, so you don't have to read too far), you will see decks contributed by various people that I analyze. So you can take a look at those. I think the most layers from a deck that someone posted on this thead was 22?
In addition, there is a sequence of five writeups detailing our earlier deck champions. The first two were written by metroidcomposite, take a look at
I hope those help - although I can already see you protesting that the updates aren't as "smooth" as your deck
As for why the ease of updating isn't worth more layers - I don't know what to say, it's obvious to me that ease isn't going to make for more powerful recursion, it can only facilitate it. It's also possible that your deck could have stuff like 2^^^(2^X) rather than 2^^^X, but as I explained above, that advantage disappears at the higher levels.
thanks to both of you! lot to look into. as i said i'm just saying what i see at this point and i do welcome corrections(however much humble pie it is lol). i just want to be able to grasp what is going on so that at some point i'll be able to maybe be able to help with some of the higher concept stuff.
i guess smooth is a bad way to describe it. it's more how the updates are immediate(even if they are happening via lower layer structures). i don't need to drop down through my stack to do get to the updates, but it looks like that isn't a source of power, just of convince.
Actually, in the stage deck all the groups are getting updated at the optimal time. Sure, you update the Nth group of triggers right after you've resolved the entire group, but that's precisely when you want to update it. It's just like activating Vitu-Ghazi Guildmage with a bunch of Illusionist Bracers on it; you don't update the Bracers until you've used up all the IB triggers and need to activate the VGG again. For everything before then, you populate Doubling Season.
ok. so after reading through the old season of doubling articles and watching a few of them play out and explain the layers and their updating at levels closer to mine, i'm seeing more how things do work and need to work to go up(also both of your explanations have helped). so, think i'm getting a wrap on what a layer is in the first place and what isn't. i still am struggling with the updating of YB draw power between activation's. in most instances of updating we are going down in layers when we do our updating but in my current list we are updating our highest layer with lower ones. so normally we would make x resource, use 1 to do many thing underneath it before we use another of our highest resource. while this is true with YB in regards to raw number of activation's we have access to, the ability to update YB power before using those activation's doesn't seem to fit the updating protocol by going up the chain rather than down it. it's probably just an oddity within the updating mechanic but it still seems a bit odd.
edit: also reading through the stage explanation is starting to make sense, sort of ... lol i'll prob still have to read through a bunch more because the specifics get really messy and they unfortunately are a required messiness to really comprehend everything going on.
Hmm, I would answer you, but to be honest I don't quite understand what you are saying with regard to YB. When we activate a layer, it keys off a certain resource; after resolving the combo, and just before activating the layer again, we update that resource using a lower resource. So, when we activate a Yawgmoth's Bargain, it keys off the number of Illusionist's Bracers that are attached to it. We then resolve the combo, and just before we need to activate YB again, we populate IB, which updates the number of IBs thanks to all the Doubling Seasons. So it seems to me that it operates quite normally.
Getting back to the gigastage deck - last time, I mentioned that the loss of Simian Spirit Guide meant that we needed to add another card, like Mana Crypt, to get started. Well, I just noticed that with Mana Crypt + Salvaging Station + Karn, Silver Golem can give us as much colorless mana as we want. This doesn't lead to unlimited damage, since colorless mana is just a facilitator - we need untapped artifacts like Mimic Vat to create more enchantments, and colorless mana won't get us more of those. So it is legal for this challenge, and it allows us to keep World at War, as well as probably keep Words of Wisdom.
@Stakfish - so, what do you think about our deck having an infinite mana combo in it? If we want to avoid it, we would lose World at War, and have to switch from Words of Wisdom back to Reforge the Soul. Which is not much in the grand scheme of things, the question is whether we dislike this enough to not pick the actual maximum damage deck?
I think infinite colorless mana is fair game as long as it doesn't translate into more damage. We can already generate more colorless than we use. This just makes some of the setup easier and closes off cards that turn colorless into damage or creatures or life etc.
So I think my confusion with YB was that I was thinking of the activations as a resource(which in a way they are) when those activations where using my life and that my life was the resource. If we had a process that updated my life between the activations we would quickly go infinite as we would just be going down 1 layer to get many resources to reuse that same ability again for a boundless loop. I knew my loop didn’t go infinite but it felt like it was going higher up the chain than it should. I think the hardest part was seeing a series of events not going infinite and reaching farther up the chain than what i thought it should to just be a layer. After doing a bit of learning about how this stuff all works it was just doing exactly what it should to get me my layer in the first place. Basically I was just defining my resources incorrectly and that was causing all sorts of weird perceptions issues on my part.
All that being said I think I have a much better idea of the layer system which will hopefully lead to understanding the full blown stage stuff as i get more and more comfortable with some of the more complex end of this stuff.
So a quick question about layers in general: do we want events that potentially could start multiple chains or is it generally better to stick with one chain and more narrow additions to it?
And a stage question: so with the PB and BM stage(and I think most of them) that it starts with a series of triggered events that try to enter the stack at the same time which allows us to stack them all however we want. I’m guessing this structure of events is pretty required to set these things up? Again I’m still pretty much in the dark with stages but I’m just tying to pick up a few of the bare minimum set up requirements.
Ah, good to hear that you are getting the hang of things. In general, we want to have only one chain. If we have multiple chains that don't rely on each other, than basically whichever one is longest measures the strength of our deck; two chains of the same length don't get any stronger, except possibly you could activate the final layer more times.
What you definitely don't want to have happen is multiple chains that are dependent on each other. Very often what happens is that we run into timing and stack issues trying to get both chains working. For example, casting a spell could be Layer N, because it gets X copies from TYS, and each copy implements Layer N-1. But, if we have to alternate two spells, then we are in trouble, because if we cast the two spells in succession, then all the copies of one are above all the copies of the other. So we only get one alternation, and it's not Layer N at all. Stuff like that is why you don't want multiple dependent chains.
No, in the PB and BM stage, we don't have different abilities entering the stack at the same time. We first cast the Metallurgeon, getting Bloodbond March triggers; then, after bringing the M back to the battlefield, we tap a token M, putting a bunch of PB triggers on the stack; then, after we bounce M back to our hand, we replay it to get a bunch of BM triggers; and so on. So the groups enter the stack one after the other, not at the same time.
Ah ok, still need to do a bit more digging into the stage stuff I guess.
I got side tracked a bit with fumbling around while I was figuring out some basic layers stuff but I remembered something about an interaction you mentioned when I was wrongly pointing out what I thought where my layers. So in my setup cradle of vitality and boon reflection can interact within the same chain. I think it only works because my mana is derived from +1/+1 counters. So hopefully I will be setting up a life gain entity in my deck that will gain life in multiple connected events and not just in one giant lump. If it’s in a series of life gain events then these 2 cards can amplify each other as the series of life gain events begin to resolve. So BR is just a replacement effect so it doesn’t use the stack anyway, but when a life gain event happens we will get many CoV triggers. We will need to have access to at least 2 mana as this all starts but that’s it. So after our life gain event has happened we pay for our first CoV trigger. We put these counters on a RSK. We then remove the counters to pump back into our DS making IB powered populate engine. We use it the same way we normally would but in this case we are pretty much solely concerned with making DS. So we do that and use our mana to most efficiently make DS. So as before when we get down to our last mana left we save 2 and let our next CoV trigger come and be paid for. This one will be powered up by the last CoV trigger resolving. So we keep repeating this process until we reach the last of our CoV triggers for any given life gain event. This time we still make a lot of DS until we get down to the end of our mana and populate abilities. This time we save our 2 mana but use our last 2 populate abilities to make a wave of CoV and a wave of BR. Both are now updated fully leading into our next life gain event. BR being fully updated will make the raw life gain substantially higher and we will have an updated amount of CoVs to be able to take maximum advantage of that updated life gain amount.
I think it means that if I can somehow covert an event into a +1/+1 counter making event that I can probably manage to get a layer out of it. Most likely this works because I do get my mana from counters and might not work in most set ups.
i mean even within that set of interactions it still allows me to gain more life which in turn makes more +1/+1 counters off each cradle i have(and/or choose to make). then on top of that i get to dump more life back into YB. without BR i can't update my life gain, which i want to be able to do to maximize my YB loops. without it i'm stuck on just gaining whatever amount of life i would normally gain, say 2x(x+x) over a 2 instance event, where w/ BR it's way way way more than that(like x + x^? ... not sure on the actual math here).
in a way YB and CoV kinda compete for who gets to abuse the life gain first but in the end i don't think it matters which one goes first. whoever uses the life gain event first just makes sure at the end of their loop cycle they update whichever looping mechanism is about to start and then at the end of that loop we re-update the first loop to be ready to go again once the next life gain event has occurred. my gut says i would do the YB loop before i do the CoV loop for every iteration except the last one and then on the last one do the YB loop as late as possible.
No, gaining more life via Boon Reflection doesn't make more +1/+1 counters, each Cradle of Vitality triggers once off a life gain event.
Whoops, that's wrong... what I meant was that you don't get a layer for Boon Reflection on top of Cradle of Vitality, since if you gain B life and have C Cradle of Vitalities you will just gain BC life. So it's that multiplicative effect that I was talking about earlier, so it's not multiple layers.
Yes, Boon Reflection does feed into Yawgmoth's Bargain, but that would be a different chain from one with Cradle of Vitality. I was just saying you couldn't have Boon Reflection and Cradle of Vitality as different layers in the same chain, since both feed off of life gain.
the BC thing is sort of right, but more C = even more potent C triggers all off the same life gain event as we can turn 1 C trigger into many DS(between C triggers resolving via RSK counters) which make many our next C trigger far more potent and we can loop these the same fashion increasing the C potency down the whole series we get per life gain event. when we max out on RSK counter making off our C triggers(to make the remaining C triggers better) we can then update our number of C and BR before our next life gain event happens to power the whole process up even further. while we could do most of this without BR we wouldn't be able to change the raw amount of life gained, it would just make that life event a bit more profitable to our board state. with BR we get board state and life gain updates between each life gain event which makes our life gain f(x and l) rather than just xl where l is the length of the series. adding BR allows us to manipulate the raw life gain amount, which is very important at the YB level. i don't think it's a layer, but i do think it's part of the same chain. also C is operating at a trigger level event that is not implicitly tied to a casting event, where everything else i do is strictly tied to casting events starting them. not sure that last part means anything just yet, but it can't hurt to get more than just casting triggers going on within the same larger chain.
Yes that's true, for each life gain event you can trigger many Cradles, which counts as a layer, and then for each trigger of CoV you can get increasingly more counters thanks to Doubling Season, so that counts as another layer. Anyways, it looks like we are in agreement, BR isn't worth a layer in conjunction with CoV, although it does bump up those number of counters that you get. However, that improvement will get dwarfed by the improvement by the Doubling Seasons anyway.
It does look like you are still working on two chains, one with Boon Reflection into Yawgmoth's Bargain, one with Cradle of Vitality. Just remember that you won't really get a benefit from having multiple chains.
well the end goal of C is to make more BR which then feed into YB. the last of the C triggers from the very last life gain event will be stuck just making DS/RSK/IB(or something else entirely) but all of them before that can directly(ish) make more BR in some capacity. the DS creation is used to fuel the BR creation in this case not the other way around. i could just make straight BR copies but it's a far better usage of mana to go w/ populate amplification->DS making->BR making instead. again i do get 1 set of C triggers that i can't wrap back into the last life gain event but it's not like that mana will go to waste as i can use it to make whatever permanent benefits me the most for whatever action/spell is coming next anyway(of course proceeded by making a bunch of DS before we do that). while it is a a lower layer this last "bad" batch of C triggers will more be an added bonus that will likely disappear at higher layers. the fact through all of this that i happen to make more DS as a means to an end is just an added bonus. making more life will make far more DS than anything else i could do so i am trying to use my best tools to do that, one of which happens to be DS creation, which happens to have added benefit to the rest of my board state as the deck works its way through it's paces
Well, any interaction that can populate can increase the number of BRs. I'm just saying that there are more effective things that you could be doing. If, say, getting lots of CoV triggers is Layer 4, and getting a large life gain via BRs is Layer 5, then the effect of the CoVs is really weak compared to the effect of the BRs. Heck, even if they were the same layers (say Layer 5), each life gain would be applying Layer 5 twice, so it still wouldn't get you too Layer 6. Adding a sixth layer is way better than creating any number of five-layer chains.
ah, yeah i guess that's true. it's not a layer(well layer adding layer anyway)so no matter how potent it feels that additional value will just disappear as we get into deeper and deeper layers.
i think i might kinda work a bit backwards here and see if i can get some mana layers out of the deck in an effort to see if we can't get a bit more segregation. hopefully that opens a few doors for layer past where i am currently.
I'm getting up to speed on your thoughts for the standard challenge, but if you aren't at this point already I think we should be working towards a stage combo for sure.
The new flash-granting land makes life much, much easier, and Thousand-Year Storm is a scaling mechanism that works for all instants and sorceries. Bolas's Citadel could even potentially let us leverage both life AND mana as resources.
I've started a new thread specifically for the Standard challenge, so we should post our discussion there. So far, I've made a measly 11-layer deck, I haven't dared go for the stage combo yet! But yeah, let's think about it.
so i tried doing mana layers and i just got frustrated. so what i did do is revisit the longest chains i had made so far. it's still missing the exile loop but i'm sure i can fit it in here somewhere. i re-worked the start to open up playing other colors as restrictions/ways to chain. it starts much slower but gets where it needs to, and actually works properly this time. think i'm just gonna work on this list for awhile while i continue to learn the in's and out's of layers etc. plus not being all red should open up some interesting lines for me to look into while i try to extend this deck further.
1 Black Lotus
2 Show and tell
3 Omniscience
- i needabyssal persecutor in here, just to lazy to change all the numbers -
4 enter the infinite - we draw our deck
5 Mycosynth lattice - enters nothing happens
6 vedalken orrery - now we operate at instant speed
7 mirrorworks - so this will be useful for getting some non creature tokens, and does add more value to non token creatures entering too
8,9 Doubling season, mana crypt - we play DS and then with the MW trigger on the stack we play mana crypt. we let crypt resolve and pay for the MW triggers w/ crytp itelf. we get 2 more crypts. we use 1 of those to pay for the MW triggers for DS, we get 2 more DS tokens.
10 Runaway steam-kin - we get MW trigger and use our last avalible crypt to pay for it, getting 8 more RSK.
11 thousand-year storm - each RSK gets 8 counters each. we pull 6 counters off of each getting 54 mana, and leaving 3 counters on each RSK, and we now have our spell doubler
12 inexorable tide - we use 2 mana we pay for the MW trigger, we get 8 more copies of IT as tokens.
13 Vitu-ghazi guildmage -when we cast this we get 9 proliferate triggers netting us 8 mana per RSK per trigger netting 8*9*9 mana. we now have the populate engine online(well sort of. making us more RSK doens't do us a lot of good. its only a good idea to make more RSK if we are abut to cast a red spell to get counters on them we can proliferate in the first place). we remove the most counters we can from each RSK(without dropping below 1 counter) and then turn those into populate waves(PW). all but the last of these waves will be making DS and the last will be making more IT copies. we will be repeating this process as we cast spells for a bit.
14 mirror gallery - cool so now we can have multiples of legendary stuff
15 karn, silver golem - so now we can turn anything into a creature that isn't already, which then allows us to populate those once we can get a token copy of them.
16 puresteel paladin - not important to make copies of this but we want to go as wide as possible so we should pay for all MW triggers.
17 leonin shikari - so now we can move equipment around at instant speed to whatever creature it is most beneficial to do so.
18 illusionist's bracers - so things are gonna get a bit weird here. we actually will save all counters from our proliferate engine and just let IB resolve. so we use 2 of that mana and pay for our MW trigger. we get a lot of IB. we equip the original and all but one of the new copies to VGG. the one token we didn't equip we animate via Karn. now we start making PW at 4 mana a clip. each activation will get an amount of copies of the ability equal to the IBs on VGG. all of these except the last will be making DS, and the last will make IB. we will equip the IB to VGG and activate our next PW, repeating the process until we are out of mana(again leaving counters on all RSKs). this is our new updated updating process. it will be this way unless we are moving into cast a red spell, and the only change will be our very last populate ability will make RSK instead of DS or bracers(we still make IB too so we basically lose 1 populate abilities worth of DS making if we are going move to casting a red spell).
19 precursor golem - yup
20 arcane adaptation - now we make all creatures golems and any targeted spell will scale to our current board state
21 thopter engineer -(red spell modified procedure here) we have haste, and an added body to boot
22 boon reflection - our life gain can now be super powered(maybe i need cradle of vitality to make this a full layer?)
23 goblin bombardment -(red spell) we now have a sac outlet(we can just point this at our own stuff for the time being)
24 firesong and sunspeaker(FS+SS) -(red spell) so this makes our red damage spells better. this card allows me to get 2 separate loops out of 1 spell.
25 chandra's phoenix(CP) -(red spell) we will play this out and then sac off all token copies first and then the original.
26 darksteel forge - our creatures are now indestructible
27 harness the storm - (red spell)
28 willbender -
29 ixidron - now our harness loop is up and running
30,31 fiery confluence -(red spell) so we will actually choose all 3 modes on each of the castings of this spell. this means because of how its worded(there is only 1 target) that golem will spread this spell. because of FS+SS it also has lifelink. so we get a ton of stuff going on here. we get a loop going with CP for a bit of damage and cast trigger(and we can make more RSK that will have counters) and a bunch of life. we will resolve our first CP loop and then resolve our first life gain trigger. before we let the next stuff resolve though we will introduce another thing we can loop.
32 wydwen, the biting gale - so now we can see that for each life we gain we will be able to loop castings of WBG. this we can do for each instance of life gain and an amount of times equal to the amount of life we gained. so we cast WBG and get ready to loop some more. but we just cast a multicolored spell so lets loop off that too. as with CP we will be sac'ing of our extra token copies of WBG to bombardment to get some value out of them.
33 lobber crew - so right now this is where my loop ends. every time we cast WBG we untap our army of lobbers and hit for some damage. this is as far as i've gotten. i had another layer after this(well 2 actually) but i found an infinite so i'm back to this point. untapping crew has to be able to better than just 1 damage(or bracers/rings amount of damage). i'm still looking for options but i'm sure i can move past this.
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It’s just kind an idea but maybe this concept is why I’m finding it hard understand why the deck feels so under powered via the layer = power definition?
I get that you feel that your deck should get more than 5 layers with those 20 cards, it's probably because layers and Knuth arrows are so strong. So enormous, gigantic numbers can be expressed with very few Knuth arrows. For example, 10^100 is more than the number of particles in the observable universe, and 10^10^100 can't even be written within the observable universe. And that's just one Knuth arrow, double arrows pretty much immediately shoot you into realms of numbers beyond anything that we can associate to any physical thing.
The thing is, you can't really say "my intuition tells me that you're wrong, I feel like my deck should get 20+ Knuth arrows." No one's intuition is that good. Without looking at how the numbers are increasing, which is what the layers are for, there's no way to determine how large a number you're going to get. In short, you have to do the math. ALL these numbers are too big to comprehend.
Edit: i’m not claiming I’m at 20+ layers by any means. I’m just looking to rectify what I see with what I understand. At most I’m saying I’m at 7 layers with my current list. Nothing even close to 10+ and certainly not 20+ or stage level.
Only imperceptibly, it is much more profitable to implement another layer instead. At these scales x+1 is a tiny difference. Furthermore even 2x or 100x is essentially the same as just x once it gets pushed through another layer.
Take the Polyraptor+Forerunner of the empire combo from standard as an example, if you increase the starting number of polyraptors by 10 then sure, you end up with about 10 times as many dinos, but if you instead increased Forerunner's toughness by 10 you'd have 2^10=1024 as many polyraptors. Similarly up the chain until we reach the final limiting resource IE the last copy of Emergency powers or w/e the limiting factor is. Having more of that resource is far more important than having more of something earlier. Ideally you can remake whatever the last resource is x more times and get another layer.
We are effectively using big O notation (Wiki link) for our approximate damage numbers. As a bit of an oversimplification: Big O notation doesn't care about constants.
As for stages Iijil's post linked in the OP (and here) Does a better job than I could explaining how the limitations of the stack prevent things from going infinite.
Actually, your deck gets its power from layer stacking just like all the other layer decks. It doesn't do any "maximum interaction" that other decks don't do, not in any meaningful way anyway.
Ah, this is a very important point. If the layer being implemented is the very top layer, then the number of times it is being implemented is the next most significant thing after the total number of layers. You see that Knuth arrow notation has three basic numbers to them; there is a number to the left, a number to the right, and the number of arrows. For the most part, you compare two different numbers by looking at which has more arrows, and if they have the same number of arrows, look at the number on the right. (I'm assuming we use the same number on the left; typically we use 2 as the left number.) There are exceptions of course - if the number on the right is less than 4, then the number actually reduces down to a smaller expression. (2^^^^3 = 2^^^4, 2^^^^2 = 4, 2^^^^1 = 2.) Anyway, yeah, the number of times you implement the top layer is important, right after the number of layers.
So the next question is: if I have a lower layer that implements the next lower layer X+1 times rather than X times, won't the effects ripple up into the higher layers, and lead to a larger overall estimate? And the answer is a resounding no! Let's take a more extreme example: let's say deck 1 implements 2^^^X as their layer 3, and deck 2 implements 2^^^(X^X) as their layer 3. How does this look at layer 4? Now 2^^^(X^X) is greater than 2^^^X, so implementing layer 3 in deck 2 is stronger than implementing layer 3 in deck 1. But, 2^^^(X^X) is MUCH less than 2^^^(2^^^X), so implementing layer 3 twice in deck 1 is stronger than implementing layer 3 once in deck 2. Now, what if I implement layer 3 twice in deck 2? First, we apply X^X to 2^^^(X^X) to get (2^^^(X^X))^(2^^^(X^X)). This looks complicated, but exponentiation is such a weak operation compared to triple arrows, so this is actually much less than 2^^^(X^X + 1). So after applying 2^^^X, we get a number that is less than 2^^^(2^^^(X^X + 1)), and therefore much less than 2^^^(2^^^(2^^^X)), which is layer 3 of deck 1 applied 3 times. In general, applying layer 3 in deck 2 X times is weaker than applying layer 3 in deck 1 X+1 times. So the advantage is minimal. Now, you might say there is some advantage - yes, so if everything else in the deck is exactly the same, then deck 2 would nudge out deck 1. But obviously if deck 1 had more layers, or the top layer was applied more times, it would be greater.
What if we take a more extreme example: Let's say deck 1 has Cackling Counterpart, but no Riftsweeper, so each card draw took X to 2^^^^X roughly. Then, deck 2 is your deck with Riftsweeper, so with each card draw we can cast CC twice, and it takes X to 2^^^^(2^^^^X). So this is a much more extreme example, do the effects ripple up all the way to the top? And the answer is no again. Say Layer 5 is YB with IBs attached to it; if deck 1 has X IBs, it will apply 2^^^^X X times, so we will get about 2^^^^^X. However, deck two will apply 2^^^^X 2X times, so we get 2^^^^^(2X). Still a tangible advantage, but now you can see the advantage is much smaller. And, just like I explained above, if we apply 2^^^^^(2X) X times, it will be greater than 2^^^^^^X but less than 2^^^^^^(X+1). So Deck 2 will win if we apply Layer 6 exactly the same number of times as deck 1, but if deck 1 applies Layer 6 even one more time, it wins.
Note that, in my analyses, I haven't just been giving the number of layers; I've been giving precise estimates, like "your deck deals a final damage between 2^^^^^17 and 2^^^^^18." If a different deck was determined to be more than 2^^^^^18, then that's that; if it happened to also be between 2^^^^^17 and 2^^^^^18, then we would have to analyze further to determine exactly which deck won. I don't recall two totally completely different decks winding up being this close, but it can happen in the same deck where we want to determine which final cards to put in, and it often can be hard to decide which cards lead to the greatest advantage.
As I said above, if the total number of layers are the same, then we do indeed compare the number of implementations of the top layer to decide which deck is better. (More precisely, we determine which Knuth arrow numbers the decks lie between; a deck could have fewer implementations of the top layer but maybe it starts off from a higher base. So we do want to determine exact Knuth arrow bounds to determine how much damage a deck deals.) Now, you may be wondering, "Can't a deck with a smaller number of layers beat out a deck with a higher number of layers if the number of implementations of the former is large enough?" And the answer is yes, in a technical sense it can. But the number of implmentations is itself a number with the higher number of Knuth arrows. For example, there are certainly numbers X so that 2^^^^X is greater than 2^^^^^17, for example. But that only happens when X is greater than 2^^^^^16! So how are you generating that X in the first place? You need some recursive structure that gets you to five arrows anyway.
The proliferate thing is nice, it's very convenient. But convenience in and of itself doesn't lead to more powerful recursion; at best, it makes it easier to implement the processes that do lead to more powerful recursion. It doesn't generate anything by itself, it's a means to an end.
If you read some of the earlier pages in this thread (I think most are in the first 10 pages, so you don't have to read too far), you will see decks contributed by various people that I analyze. So you can take a look at those. I think the most layers from a deck that someone posted on this thead was 22?
In addition, there is a sequence of five writeups detailing our earlier deck champions. The first two were written by metroidcomposite, take a look at
http://rpgdl.com/metroidcomposite/phpconversionold.php
and
http://rpgdl.com/metroidcomposite/phpconversion.php
Also, you can look at Stakfish's Polyraptor deck, it's the second article listed at
http://alex.shankland.org/index.php/category/mtg/megacombos/
I hope those help - although I can already see you protesting that the updates aren't as "smooth" as your deck
As for why the ease of updating isn't worth more layers - I don't know what to say, it's obvious to me that ease isn't going to make for more powerful recursion, it can only facilitate it. It's also possible that your deck could have stuff like 2^^^(2^X) rather than 2^^^X, but as I explained above, that advantage disappears at the higher levels.
i guess smooth is a bad way to describe it. it's more how the updates are immediate(even if they are happening via lower layer structures). i don't need to drop down through my stack to do get to the updates, but it looks like that isn't a source of power, just of convince.
edit: also reading through the stage explanation is starting to make sense, sort of ... lol i'll prob still have to read through a bunch more because the specifics get really messy and they unfortunately are a required messiness to really comprehend everything going on.
Getting back to the gigastage deck - last time, I mentioned that the loss of Simian Spirit Guide meant that we needed to add another card, like Mana Crypt, to get started. Well, I just noticed that with Mana Crypt + Salvaging Station + Karn, Silver Golem can give us as much colorless mana as we want. This doesn't lead to unlimited damage, since colorless mana is just a facilitator - we need untapped artifacts like Mimic Vat to create more enchantments, and colorless mana won't get us more of those. So it is legal for this challenge, and it allows us to keep World at War, as well as probably keep Words of Wisdom.
@Stakfish - so, what do you think about our deck having an infinite mana combo in it? If we want to avoid it, we would lose World at War, and have to switch from Words of Wisdom back to Reforge the Soul. Which is not much in the grand scheme of things, the question is whether we dislike this enough to not pick the actual maximum damage deck?
All that being said I think I have a much better idea of the layer system which will hopefully lead to understanding the full blown stage stuff as i get more and more comfortable with some of the more complex end of this stuff.
So a quick question about layers in general: do we want events that potentially could start multiple chains or is it generally better to stick with one chain and more narrow additions to it?
And a stage question: so with the PB and BM stage(and I think most of them) that it starts with a series of triggered events that try to enter the stack at the same time which allows us to stack them all however we want. I’m guessing this structure of events is pretty required to set these things up? Again I’m still pretty much in the dark with stages but I’m just tying to pick up a few of the bare minimum set up requirements.
What you definitely don't want to have happen is multiple chains that are dependent on each other. Very often what happens is that we run into timing and stack issues trying to get both chains working. For example, casting a spell could be Layer N, because it gets X copies from TYS, and each copy implements Layer N-1. But, if we have to alternate two spells, then we are in trouble, because if we cast the two spells in succession, then all the copies of one are above all the copies of the other. So we only get one alternation, and it's not Layer N at all. Stuff like that is why you don't want multiple dependent chains.
No, in the PB and BM stage, we don't have different abilities entering the stack at the same time. We first cast the Metallurgeon, getting Bloodbond March triggers; then, after bringing the M back to the battlefield, we tap a token M, putting a bunch of PB triggers on the stack; then, after we bounce M back to our hand, we replay it to get a bunch of BM triggers; and so on. So the groups enter the stack one after the other, not at the same time.
I got side tracked a bit with fumbling around while I was figuring out some basic layers stuff but I remembered something about an interaction you mentioned when I was wrongly pointing out what I thought where my layers. So in my setup cradle of vitality and boon reflection can interact within the same chain. I think it only works because my mana is derived from +1/+1 counters. So hopefully I will be setting up a life gain entity in my deck that will gain life in multiple connected events and not just in one giant lump. If it’s in a series of life gain events then these 2 cards can amplify each other as the series of life gain events begin to resolve. So BR is just a replacement effect so it doesn’t use the stack anyway, but when a life gain event happens we will get many CoV triggers. We will need to have access to at least 2 mana as this all starts but that’s it. So after our life gain event has happened we pay for our first CoV trigger. We put these counters on a RSK. We then remove the counters to pump back into our DS making IB powered populate engine. We use it the same way we normally would but in this case we are pretty much solely concerned with making DS. So we do that and use our mana to most efficiently make DS. So as before when we get down to our last mana left we save 2 and let our next CoV trigger come and be paid for. This one will be powered up by the last CoV trigger resolving. So we keep repeating this process until we reach the last of our CoV triggers for any given life gain event. This time we still make a lot of DS until we get down to the end of our mana and populate abilities. This time we save our 2 mana but use our last 2 populate abilities to make a wave of CoV and a wave of BR. Both are now updated fully leading into our next life gain event. BR being fully updated will make the raw life gain substantially higher and we will have an updated amount of CoVs to be able to take maximum advantage of that updated life gain amount.
I think it means that if I can somehow covert an event into a +1/+1 counter making event that I can probably manage to get a layer out of it. Most likely this works because I do get my mana from counters and might not work in most set ups.
in a way YB and CoV kinda compete for who gets to abuse the life gain first but in the end i don't think it matters which one goes first. whoever uses the life gain event first just makes sure at the end of their loop cycle they update whichever looping mechanism is about to start and then at the end of that loop we re-update the first loop to be ready to go again once the next life gain event has occurred. my gut says i would do the YB loop before i do the CoV loop for every iteration except the last one and then on the last one do the YB loop as late as possible.
No, gaining more life via Boon Reflection doesn't make more +1/+1 counters, each Cradle of Vitality triggers once off a life gain event.Whoops, that's wrong... what I meant was that you don't get a layer for Boon Reflection on top of Cradle of Vitality, since if you gain B life and have C Cradle of Vitalities you will just gain BC life. So it's that multiplicative effect that I was talking about earlier, so it's not multiple layers.
Yes, Boon Reflection does feed into Yawgmoth's Bargain, but that would be a different chain from one with Cradle of Vitality. I was just saying you couldn't have Boon Reflection and Cradle of Vitality as different layers in the same chain, since both feed off of life gain.
It does look like you are still working on two chains, one with Boon Reflection into Yawgmoth's Bargain, one with Cradle of Vitality. Just remember that you won't really get a benefit from having multiple chains.
i think i might kinda work a bit backwards here and see if i can get some mana layers out of the deck in an effort to see if we can't get a bit more segregation. hopefully that opens a few doors for layer past where i am currently.
The new flash-granting land makes life much, much easier, and Thousand-Year Storm is a scaling mechanism that works for all instants and sorceries. Bolas's Citadel could even potentially let us leverage both life AND mana as resources.
I've started a new thread specifically for the Standard challenge, so we should post our discussion there. So far, I've made a measly 11-layer deck, I haven't dared go for the stage combo yet! But yeah, let's think about it.
2000 posts
1 Black Lotus
2 Show and tell
3 Omniscience
- i needabyssal persecutor in here, just to lazy to change all the numbers -
4 enter the infinite - we draw our deck
5 Mycosynth lattice - enters nothing happens
6 vedalken orrery - now we operate at instant speed
7 mirrorworks - so this will be useful for getting some non creature tokens, and does add more value to non token creatures entering too
8,9 Doubling season, mana crypt - we play DS and then with the MW trigger on the stack we play mana crypt. we let crypt resolve and pay for the MW triggers w/ crytp itelf. we get 2 more crypts. we use 1 of those to pay for the MW triggers for DS, we get 2 more DS tokens.
10 Runaway steam-kin - we get MW trigger and use our last avalible crypt to pay for it, getting 8 more RSK.
11 thousand-year storm - each RSK gets 8 counters each. we pull 6 counters off of each getting 54 mana, and leaving 3 counters on each RSK, and we now have our spell doubler
12 inexorable tide - we use 2 mana we pay for the MW trigger, we get 8 more copies of IT as tokens.
13 Vitu-ghazi guildmage -when we cast this we get 9 proliferate triggers netting us 8 mana per RSK per trigger netting 8*9*9 mana. we now have the populate engine online(well sort of. making us more RSK doens't do us a lot of good. its only a good idea to make more RSK if we are abut to cast a red spell to get counters on them we can proliferate in the first place). we remove the most counters we can from each RSK(without dropping below 1 counter) and then turn those into populate waves(PW). all but the last of these waves will be making DS and the last will be making more IT copies. we will be repeating this process as we cast spells for a bit.
14 mirror gallery - cool so now we can have multiples of legendary stuff
15 karn, silver golem - so now we can turn anything into a creature that isn't already, which then allows us to populate those once we can get a token copy of them.
16 puresteel paladin - not important to make copies of this but we want to go as wide as possible so we should pay for all MW triggers.
17 leonin shikari - so now we can move equipment around at instant speed to whatever creature it is most beneficial to do so.
18 illusionist's bracers - so things are gonna get a bit weird here. we actually will save all counters from our proliferate engine and just let IB resolve. so we use 2 of that mana and pay for our MW trigger. we get a lot of IB. we equip the original and all but one of the new copies to VGG. the one token we didn't equip we animate via Karn. now we start making PW at 4 mana a clip. each activation will get an amount of copies of the ability equal to the IBs on VGG. all of these except the last will be making DS, and the last will make IB. we will equip the IB to VGG and activate our next PW, repeating the process until we are out of mana(again leaving counters on all RSKs). this is our new updated updating process. it will be this way unless we are moving into cast a red spell, and the only change will be our very last populate ability will make RSK instead of DS or bracers(we still make IB too so we basically lose 1 populate abilities worth of DS making if we are going move to casting a red spell).
19 precursor golem - yup
20 arcane adaptation - now we make all creatures golems and any targeted spell will scale to our current board state
21 thopter engineer -(red spell modified procedure here) we have haste, and an added body to boot
22 boon reflection - our life gain can now be super powered(maybe i need cradle of vitality to make this a full layer?)
23 goblin bombardment -(red spell) we now have a sac outlet(we can just point this at our own stuff for the time being)
24 firesong and sunspeaker(FS+SS) -(red spell) so this makes our red damage spells better. this card allows me to get 2 separate loops out of 1 spell.
25 chandra's phoenix(CP) -(red spell) we will play this out and then sac off all token copies first and then the original.
26 darksteel forge - our creatures are now indestructible
27 harness the storm - (red spell)
28 willbender -
29 ixidron - now our harness loop is up and running
30,31 fiery confluence -(red spell) so we will actually choose all 3 modes on each of the castings of this spell. this means because of how its worded(there is only 1 target) that golem will spread this spell. because of FS+SS it also has lifelink. so we get a ton of stuff going on here. we get a loop going with CP for a bit of damage and cast trigger(and we can make more RSK that will have counters) and a bunch of life. we will resolve our first CP loop and then resolve our first life gain trigger. before we let the next stuff resolve though we will introduce another thing we can loop.
32 wydwen, the biting gale - so now we can see that for each life we gain we will be able to loop castings of WBG. this we can do for each instance of life gain and an amount of times equal to the amount of life we gained. so we cast WBG and get ready to loop some more. but we just cast a multicolored spell so lets loop off that too. as with CP we will be sac'ing of our extra token copies of WBG to bombardment to get some value out of them.
33 lobber crew - so right now this is where my loop ends. every time we cast WBG we untap our army of lobbers and hit for some damage. this is as far as i've gotten. i had another layer after this(well 2 actually) but i found an infinite so i'm back to this point. untapping crew has to be able to better than just 1 damage(or bracers/rings amount of damage). i'm still looking for options but i'm sure i can move past this.