Hmm yeah I don't see a way to get infinite mana with just three cards, Mishra's workshop is I think the only other card that is +3 mana from nothing like black lotus, but it doesn't cast salvagers.
For 4 cards with unlimited mana, we can do Mondrak, Glory Dominus, Ratadrabik of Urborg, Cadric, Soul Kindler, and... something. Junji, the Midnight Sky would be ideal if not for the life loss. The best I could find is Colfenor, the Last Yew, which adds 2 layers (because the stack has to clear to recast cards) to the 4 from the other cards for a total of 6. (How to do it: Sacrificing each Colfenor token gets multiple triggers to return all the other cards. Cast Ratadrabik and Cadric first and get copies of them. Then, cast Mondrak and get a bunch of Cadric triggers. After each of those triggers resolves and gives a bunch of legendary Mondrak tokens, sacrifice a single legendary Ratadrabik token to get a bunch of Ratadrabik/Ratadrabik triggers, and alternate resolving those triggers with sacrificing legendary Mondrak tokens, so that the Ratadrabik count is boosted for each sacrifice of a legendary Mondrak token.)
Unfortunately, adding Black Lotus, Channel and Lich's Mirror for the no-mana-given version doesn't work with these cards, because it is possible to set off the Lich's Mirror reset with Ratadrabik triggers still on the stack, giving a higher starting point, and repeat to go infinite. If we weren't constrained to Vintage legality, 2x Black Lotus and Auriok Salvagers would work as an alternative way of getting infinite mana.
For 5 cards with unlimited mana, I think we can add Kodama of the East Tree to Mondrak, Glory Dominus, Ratadrabik of Urborg, Cadric, Soul Kindler, and Colfenor, the Last Yew. Ratadrabik can now be the starting point; the Mondrak count doesn't get increased at that point, but we still get a multiplication for each legendary Ratadrabik token, and then an exponentiation for each sacrifice of a Mondrak token getting back Ratadrabik and Cadric, for a layer-1 foundation. After that, Mondrak, Kodama, and Colfenor each add 4 layers above that, for a total of 13 layers.
(Correction) Mondrak doesn't get re-increased enough to count for a layer from multiplying its own nonlegendary tokens, dropping it to 3 layers; thus Mondrak ends up at layer 4 whether you use this procedure or the other procedure from above, and the total is 12 layers.
It doesn't work for this combo since you need so much mana of different colors to get set up, but in other token-making combos you may be able to use Salvage Scout duplicates to cycle Black Lotus for cheaper.
Those four steps are the layers: Precursor-Helix triggers, Helix copies, Precursor-Slaughter triggers, Slaughter copies. (Helix copies translate at a fixed rate to Slaughter casts, but the number of triggers varies.)
Right. The life gain in step 2 is from the Helix copies, and the untaps in step 4 are from the Slaughter copies. I failed to notice that the triggers and spell copies are different layers since they aren't one to one, but compound based on the growing number of golem tokens.
I think you might have the order backwards. When we flashback Helix, we get a fixed number of Precursor-Helix triggers. We don't get more of those, but the number of Helix copies we get from cashing in a Precursor-Helix trigger increases each time, as our number of golems increases. (If we could get more life or Helixes from a later layer, we'd go infinite.) Then, each time we spend that life to buyback Slaughter, we get an increasingly large batch of Precursor-Slaughter triggers, and each time we cash in a Precursor-Slaughter trigger we get an increasing number of Slaughter copies. Then after looping that as many times as we have the life to pay for, that output determines how many Helix copies we get from the next Precursor-Helix trigger.
The result is that the four layers are Precursor-Helix triggers, Helix copies, Precursor-Slaughter triggers, and Slaughter copies.
Oh I see. I think I misunderstood the meaning of your numbered list in the writeup:
For each Precursor when we play Helix, get a Precursor-Helix trigger
For each golem when we resolve a Precursor-Helix trigger, gain life that determines the number of times we cast Slaughter
For each Precursor when we play Slaughter, get a Precursor-Slaughter trigger
For each golem when we resolve a Precursor-Slaughter trigger, get a round of Salvaging Station untaps
I thought this was describing the layers, but it was just describing the procedure. Those layers make more sense.
Honestly, I've also found it difficult at times to keep track of the exact number of layers, but the general idea is that adding a layer requires repeating everything before it an increasing number of times, and being able to go all the way down to the bottom before going back up.
Like, in the Saw deck, saw you have two 33/33 Astral Dragons. You split one into 17/17 Astral Dragons, and then one of those into 9/9s, and then one of those into 5/5s, and then you go through the rest of the 9/9s, and each time, your output is increasing. Then repeat all that with the rest of the 17/17s, and you can finish all of that before doing back to the other 33/33.
That's part of a stage, where the layers are just the same thing with different numbers attached, but the same logic applies to layers made of different things. You take take something from a higher layer, trade it for a large number of things in a lower layer, then trade each of those things for increasing numbers of things in the layer below that, and the number of layers is how many of those you can stack together.
Thanks again for clarifying; that makes a bit more sense. This early post from Deedlit11 also helped me understand more about how the layers work.
So even the 5-card deck is using the same principal. We could describe it using one layer:
The amount of power gained by Devilish Valet for each of 38 Sparkcaster castings is accelerating. Therefore, Devilish Valet's power grows by exponentiation.
Using the same language for the 6-card deck:
The delta of the token multiplier gained by the set of Doubling Season tokens is accelerating. Therefore, the multiplier grows by exponentiation.
The number of Doubling Season tokens created for each of the 32 Astral Dragons is accelerating. Therefore, the number of Doubling Seasons grows by tetration.
The intralayer resource exchange is: We trade 1 Astral Dragon triggered ability for more than one token multiplier event.
...and for the 7-card deck, I would assume it is something like:
The number of Smiting Helix copies gained by using Cogwork Assembler on Precursor Golem is accelerating. Therefore, the Smiting Helix copies grow by exponentiation.
The number of Slaughter castings gained by the life gain of Smiting Helix is accelerating. Therefore, the Slaughter castings grow by tetration.
The number of Slaughter copies gained by using Cogwork Assembler on Precursor Golem is accelerating. Therefore, the Slaughter copies grow by pentation.
The amount of mana gained by using Salvaging Stations is accelerating. Therefore, the amount of mana grows by hexation.
The intralayer resource exchanges are: We trade 7 mana for another Precursor Golem which fuels more than one Smiting helix copy event, and more than one Slaughter copy event.
However, what I don't understand is what causes the buildup of layers for some of these effects.
It seems to me like the resources found in each layer don't always increase by its immediately senior layer like I inferred from Deedlit11's explanation of "Also, you have to ability to decrease X2 by 1 (or a fixed amount) to increase X1 by more; the ability to decrease X3 by 1 to increase X2 by X1 or thereabouts, the ability to decrease X4 by 1 to increase X3 by X1 or thereabouts, and so on up to Xn."
Using Deedlit's language and the list in your writeup we have:
We can decrease X4 by 1 to increase X1 and X3 by a bunch (since we will get a bunch of mana with which to create more Precursor Golems), but I don't see how we get more Slaughter buybacks from a later layer. Certainly we get more Slaughter buybacks from the increase in X1, but my intuition tells me that this is a multiplicative effect (i.e. for each copy of Smiting Helix we get 0.75 Slaughter buybacks).
I don't see where we get more life from a senior layer at the cost of X3 or X4 resources. I'm sure I'm missing something but where does X2 become a layer?
I'm extremely intrigued by all of the work that's been done on this and the related 60-card thread. Still trying to get my head wrapped around the math, but CaptainMarcia's writeup of 1-16 card decks has helped a ton for me.
I had a question about how the layering interacts when creature power scales to the same degree as creature count. In particular I was curious if using a card like Craterhoof Behemoth is efficient at all and what happens to the layering when all of the creature tokens in some of these strategies compound their damage dealing capabilities.
In particular, I was looking at the Precursor Golem/Smiting Helix/Slaughter 7-card deck. If each of the 2^^^^(2^^(227 trillion)) Golem tokens have 2^^^^(2^^(227 trillion)) power what is the resulting damage output?
At first I thought this would add a layer for an extra card since each golem is doing as much damage as the number of golems. Still not coming close to the 8-card deck in the writeup but I'm just trying to understand how the math works. Looking at it further, though, it seems like the damage would just be (2^^^^(2^^(227 trillion)))^2. What is required to actually add a layer? How do the stages have to interact?
I may be using a bunch of these terms incorrectly compared to how you all understand them, so please correct me if that's the case. Thanks for any help you can provide in my understanding.
~
As a side note, I found a more mana-efficient option to reach the same result in the 4-card deck. Timbermare is another 5-power creature with Haste. However, with only 4 CMC, it demonstrates that perhaps there is design room for a future card with more power and Haste at 5 CMC with 1 green (one can only hope).
If we're using un cards, you may as well just go Black Lotus, Channel, Mox Lotus
It doesn't work for this combo since you need so much mana of different colors to get set up, but in other token-making combos you may be able to use Salvage Scout duplicates to cycle Black Lotus for cheaper.
Right. The life gain in step 2 is from the Helix copies, and the untaps in step 4 are from the Slaughter copies. I failed to notice that the triggers and spell copies are different layers since they aren't one to one, but compound based on the growing number of golem tokens.
Oh I see. I think I misunderstood the meaning of your numbered list in the writeup:
I thought this was describing the layers, but it was just describing the procedure. Those layers make more sense.
Thanks for helping me understand.
Thanks again for clarifying; that makes a bit more sense. This early post from Deedlit11 also helped me understand more about how the layers work.
So even the 5-card deck is using the same principal. We could describe it using one layer:
Using the same language for the 6-card deck:
...and for the 7-card deck, I would assume it is something like:
However, what I don't understand is what causes the buildup of layers for some of these effects.
It seems to me like the resources found in each layer don't always increase by its immediately senior layer like I inferred from Deedlit11's explanation of "Also, you have to ability to decrease X2 by 1 (or a fixed amount) to increase X1 by more; the ability to decrease X3 by 1 to increase X2 by X1 or thereabouts, the ability to decrease X4 by 1 to increase X3 by X1 or thereabouts, and so on up to Xn."
Using Deedlit's language and the list in your writeup we have:
X1 = Smiting Helix copies
X2 = Slaughter buybacks
X3 = Slaughter copies
X4 = Salvaging Station untaps
We can decrease X4 by 1 to increase X1 and X3 by a bunch (since we will get a bunch of mana with which to create more Precursor Golems), but I don't see how we get more Slaughter buybacks from a later layer. Certainly we get more Slaughter buybacks from the increase in X1, but my intuition tells me that this is a multiplicative effect (i.e. for each copy of Smiting Helix we get 0.75 Slaughter buybacks).
I don't see where we get more life from a senior layer at the cost of X3 or X4 resources. I'm sure I'm missing something but where does X2 become a layer?
I'm extremely intrigued by all of the work that's been done on this and the related 60-card thread. Still trying to get my head wrapped around the math, but CaptainMarcia's writeup of 1-16 card decks has helped a ton for me.
I had a question about how the layering interacts when creature power scales to the same degree as creature count. In particular I was curious if using a card like Craterhoof Behemoth is efficient at all and what happens to the layering when all of the creature tokens in some of these strategies compound their damage dealing capabilities.
In particular, I was looking at the Precursor Golem/Smiting Helix/Slaughter 7-card deck. If each of the 2^^^^(2^^(227 trillion)) Golem tokens have 2^^^^(2^^(227 trillion)) power what is the resulting damage output?
At first I thought this would add a layer for an extra card since each golem is doing as much damage as the number of golems. Still not coming close to the 8-card deck in the writeup but I'm just trying to understand how the math works. Looking at it further, though, it seems like the damage would just be (2^^^^(2^^(227 trillion)))^2. What is required to actually add a layer? How do the stages have to interact?
I may be using a bunch of these terms incorrectly compared to how you all understand them, so please correct me if that's the case. Thanks for any help you can provide in my understanding.
~
As a side note, I found a more mana-efficient option to reach the same result in the 4-card deck. Timbermare is another 5-power creature with Haste. However, with only 4 CMC, it demonstrates that perhaps there is design room for a future card with more power and Haste at 5 CMC with 1 green (one can only hope).