We have enough creature types, we can use the spiral rise construction that needs 7 clocks (including halt) which uses way less than a hundred clocks in the absolute worst cases.
Though that does also end up needing a bunch more bishops and tokens.
Yeah, the Spiral Rise construction is a safe way to go universal without exceeding the creature type limit. But I think the number of bishops required for it will be way higher than with more direct constructions. And this 13 card deck is right in the range of bishops it can create where that seems to be the relevant limit.
I don't even know what a good universal tag system would be to start, but I think compiling to spiral rise and later compiling to flooding clocks both give an exponential increase to the numbers involved. So I don't have much hope of getting a universal program that's small enough that way. Though it would be interesting to see what that actually looks like.
Start by casting Fathom Mage, then cast Saw in Half on it to make two of them (still 1/1). Now cast Keeper of the Cadence. It triggers evolve on both Fathom Mages. Activate Keeper of the Cadence to put Saw in Half into the library, then resolve the first evolve and the on-evolve trigger to draw it. Cast it on the now-2/2 Fathom Mage, making two more 1/1 Fathom Mages, then resolve the rest, redrawing Saw in Half again. (We now have one 2/2 and two 1/1 Fathom Mages.)
Cast Saw in Half on Keeper of the Cadence, making two 1/3s, which both trigger evolve on the Fathom Mages. Let the 2/2 Fathom Mage evolve to 3/3 first, and Saw it into two 2/2s. We get four more redraws of Saw from evolving the two 1/1 Fathom Mages to 3/3; use the first three to Saw the new 2/2 Fathom Mages into four 1/1s, and one of those into two 1/1s. (We now have two 3/3 Fathom Mages, five 1/1 Fathom Mages, and two 1/3 Keeper of the Cadence, and Saw in Half in hand.)
The process used now is: Saw a ?/3 into two ?/2s, triggering evolve on all the 1/1 Fathom Mages. Each time a 1/1 Fathom Mage evolves into 2/2, it redraws Saw, which is cast on that now-2/2 to turn it into two 1/1 Fathom Mages; except for the last time, where we keep Saw in hand. The net result is to go from X 1/1 Fathom Mages to (X-1)*2 1/1 Fathom Mages and one 2/2 Fathom Mage (as well as whatever was produced by the initial Saw).
Follow that process using the two 3/3 Fathom Mages and one 1/3 Keeper of the Cadence. We now have 26 1/1 Fathom Mages, 7 2/2 Fathom Mages, two 1/2 Keeper of the Cadence, and one 1/3 Keeper of the Cadence.
Cast Life of the Party. Cast Saw in Half on the remaining 1/3 Keeper of the Cadence, triggering evolve on the 26 1/1 Fathom Mages. Use the first 25 draws to Saw Life of the Party, ending with 26 Life of the Party. Attack with them.
Note that this arrangement has some losses at the higher values, because of evolve only increasing power and toughness by one at a time. However, the hyperoperations should quickly overwhelm those losses.
Unfortunately, adding Black Lotus, Channel and Lich's Mirror for the no-mana-given version doesn't work with these cards, because it doesn't provide infinite mana during combat.
Notes for potential modifications: Sharp-Eyed Rookie can replace Fathom Mage. Watchful Radstag seems potentially useful but is redundant if we're using Saw in Half.
Came across this thread as someone who isn't very familiar with this notation, and my curiosity has sparked a few questions. My baseline understanding is that 2^^^2 represents an exponential tower of 2s that is 2^^2 high. What I'm not sure is how to count or see these arrows (tetrations?) in a particular setup. On another note, I've seen some setups described in a notation of 2^^^^^(2^^^^2) or similar and I have no idea how that compares to other notations with only a singular line of arrows. For one last question, I've seen people talk about getting a higher amount of damage than Graham's number, but such talk confuses me. I'm not too familiar with Graham's number but I though it was G(64) where G(n) is using a stack of G(n-1) arrows, which I thought would be incomprehensibly larger than the handful of arrows that I've seen to describe damages said to be larger than Graham's. Am I misunderstanding the notation or what Graham's actually is?
Perhaps I'm providing too much to address in one post, but I've also thought about a variant of this challenge for the 3-card blind format, where both players have 3 cards that start in their opening hand and decide all random effects for their opponent. The challenge there is to find the longest match of 3cb, accomplished by one side having icatian moneychanger, forbidden orchard, millenium calendar. Such a deck stores up enough counters on moneychanger to survive the onslaught of spirits after playing calendar and repeatedly tapping orchard. When deciding the other player's hand, the best the 3cb discord came up with was gaea's cradle, heroes' bane, scepter of celebration, which was said to be about 2^^994 turns of storing up moneychanger (again, I have no idea where that comes from). I wanted to expand this challenge to higher X-card blind setups. The challenge has some differences than many of the lines described in this forum since you have several turns to work with to build up a board state/damage. A 5-card blind setup I came up with is moneychanger, orchard, calendar, deadeye navigator, ugin's nexus vs cradle, chromatic orrery, parallel lives, astral dragon, sen triplets. (Really only 9 relevant cards, Sen's only used so that the setup cards can be split between both players). The setup gets all their cards and deadeye navigator into play (don't need ugin's nexus right away) and starts blinking astral dragon to make parallel lives dragon tokens which increase in some level of tetration. I'm guessing the fastest growth uses the last dragon blink each turn to make token copies of cradle (with summoning sickness) instead but I have no idea. When calendar is at 999 counters, play ugin's nexus and use the last dragon blink to create a whole bunch of nexus copies. Soulbound with one of the dragon nexus tokens and sacrifice the rest to legend rule to take a bunch of extra turns, then activate the deadeye ability on the navigator and the dragon nexus (holding priority) to exile the last nexus and get navigator soulbonded back to the astral dragon. Then repeat the growing process for all the extra turns, using the 2nd to last turn to make copies of calendar each of which deals 1000 damage from the next untap (not that letting each token deal 1000 damage one time makes a difference in the notation). I have no idea what the proper notation for the length of this game (how long moneychanger has to store up to survive all the damage) is.
Edit: Realized after writing this all up that Gaea's Cradle is legendary so you can't (usefully) make copies of it. I think a similar effect as I wanted can be achieved by using coalition relic and doubling season instead of chromatic orrery and parallel lives
Welcome! Yeah this can be pretty unintuitive and confusing for a newcomer, especially with all of the unique layer/stage terminology that developed in the 60 card thread and ported over here.
To answer your questions:
In general, each arrow corresponds to a link in a chain of triggers/effects/spells that turn a small number of one resource into an increasing number of another resource.
For example, with that 3cb deck:
By spending a turn, we get an attack that makes X creatures (one arrow)
we can tap cradle to make X mana (but we only get to do this once per turn so it is not also worth an arrow)
we spend that mana four at a time to double X
giving the 2^^994 estimate (994 is 1000 minus the setup turns and maybe one turn of buffer because the actual number is not exactly 2^^X)
the numbers with multiple arrow strings are mostly just being precise, if the biggest part of the combo only happens once (IE, getting all of the ugin's nexus turns) it can be best approximated by a number like 2^^^^(2^^^^990) which is between 2^^^^^3 and 2^^^^^4
This is why panharmonicon is an improvement to ugin's nexus, because doing a combo with an extra arrow the whole time is going to be more like 2^^^^^990
Breaking Ghram's number was thought to be impossible for a long time, but we found a way to simulate the Ackermann Function. my favorite example of this is the "catboy thor" deck:
Which had a construct tail swipe a goblin for 9 with one lifelinking toralf in play, this quickly grows as we keep copying toralf and hunted phantasm and occasionally urza to make a fresh construct to absorb the 1 damage triggers.
many Toralfs can only make many smaller triggers so this process is finite.
The stack becomes a system of layers for each value:
7 mana makes a copy
A 1 damage trigger makes 1 mana
A 2 damage trigger makes X 1 damage triggers
A 3 damage trigger makes X 2 damage triggers
A 4 damage trigger makes X 3 damage triggers
...
That's "only" a few layers from 9 damage sure, but then we start making flingers at the end of that.
each flinger tosses a construct and starts the whole toralf combo over, starting at the new X.
That is how we can get more than a handful of arrows.
Looks like there are now 296 creature types, which is exactly how many were needed for Iijil’s construction above! Of course we also needed 14 million bishops, so that part still needs to be worked out.
One turn allows Court of Vantress to make copies of Parallel Lives, for an exponentiation.
One of the Whale tokens produces many Kraken tokens, which can block over many turns, for a tetration.
One of the Fish tokens produces many of the Whale tokens, for a pentation.
Reef Worm produces many of the Fish tokens, for a hexation.
Player 1 first uses Bow of Nylea to accumulate life, then casts Tempting Wurm, letting Player 2 put their cards onto the battlefield. Court of Vantress triggers to make Player 2 the monarch, and then in Player 2's upkeep, it targets Parallel Lives and makes two copies of it because of Parallel Lives. On the next turn, Player 1 attacks with Tempting Wurm and deals damage to Player 2, taking the monarchy, and then on Player 2's upkeep, Court of Vantress becomes a copy of Parallel Lives with its ability added. Next, Tempting Wurm attacks a second time and Reef Worm blocks it, producing 16 of its Fish tokens, and in Player 2's turn, 15 of them attack and take back the monarchy.
If the Tempting Wurm is killed by blockers, use Bow of Nylea to get it back.
Court of Vantress can copy Bow of Nylea, but Player 2 has no way to get mana to activate its ability.
For higher numbers of cards, we could do something similar with Ochre Jelly, but it gets tricky because Ochre Jelly has to be cast with mana to work (or perhaps given +1/+1 counters some other way).
Looks like there are now 296 creature types, which is exactly how many were needed for Iijil’s construction above! Of course we also needed 14 million bishops, so that part still needs to be worked out.
I can improve my original 1.6 million bishops by stockpiling extra Arcbond triggers on the stack.
Previously I'd use groups of 2 bishops to double the amount of signal tokens when going to the next type until the last type stops the heartbeat and causes everything but dedicated output to die. The improvement sacrifices one such doubling. This frees up a couple of bishops and those are used to ensure that the designated output survives and grows under additional arcbonds, even after the heartbeat that kept the main program alive stops.
That way we can put arcbond on everything in the main program and accumulate a ton of arcbond triggers until the main program dies and no new triggers come in. Then we resolve all the stockpiled arcbonds, growing the output along the way.
Effectively we removed a factor of 2 and added a factor of x * y. Where x is the number of bishops in the main program (that eventually die) and y is the number of arcbond effects we have on each of those bishops. y will depend on the specifics of the setup, like how many Precursor Golems are around when you cast Arcbond. It gets a bit complicated because you can't have any arcbond on the creatures that need to survive, so timing the cast correctly during a long sequence of type changes will be fun.
Playing around with my old simulater I think that we would get to ~440 million bishops even if y is 1. So the number of required bishops should be covered.
I'm not quite sure 296 creature types is enough. In addition to the 296 clocks we might need two types to allow the bishops that are part of the program to stay alive, a growing output type and a heartbeat type. I doubt the compiled universal program provides a clock that is usable for that.
We also can't use Wall because in this deck we can't target Artificial Evolution with itself. There might be other bookkeeping types we need that I'm not thinking of right now.
Anyway, we are reaaaally close to being able to specify a working turing complete computation.
I don't remember what we get in between computations with that setup?
Can we 'just' rebuild the whole thing from scratch using the halting type to keep the bishops alive until the end? (outputting more of the halting type when they die?)
that leaves us with a bunch of clocks with BB(x) damaged tokens and the halting type with BB(x) fresh tokens, but no bishops.
Wall is a problem though so yeah at least one type short.
I think just one more type to hold all of the bishops out of the way and a few bishops to help reprogram before the next computation will be enough if we can't rebuild from scratch after a computation.
Also we don't need a heartbeat, we can have every clock make the bishop's type and then they never die.
The start gets us 2 Precursor Golem triggers on Audacious Swap. The first of those triggers gets 53 copies and is used to generate a billion golems before the second trigger. The second trigger gives us the last batch of Audacios Swap copies we can ever get.
Recall that Audacious Swap copies can cast Artificial Evolution on all our creatures at once thanks to Precursor Golem. But the same is not true for Replication Technique because the original needs to copy Vessel of Endless Rest to tuck itself back.
The plan is to use about a million of the Audacious Swap copies to set up the bishops for an universal computation.
After that we want to use a fixed number of Audacious Swap copies to reprogram the output of the last computation into the input of the next computation. If the bishops stay alive and are reuseable that should take 10 or 20 copies. If the bishops aren't reuseable we need about a million copies to set them up again. Either way we can reprogram the output into input with ~1 Artificial Evolution.
Repeat until we run out of Audacious Swap copies.
So now that I have looked at it closer it is not actually necessary to keep the bishops alive. We get a fixed number of BB repetitions either way. The fixed number is just ~100000 times bigger if we can keep bishops. So I'd say it is nice to have, but missing out is not a disaster.
Except that the targets of the Audacious Swap copies that are on the stack absolutely need to stay alive, or the later copies won't do anything at all. So missing out is a disaster after all. We need to be able to designate a type that stays alive through the computation.
One last thing I'm unsure about: Does the Flooding Waterfall Compilation actually allow us to use the same bishops on Input of arbitrary size? Or does the input to the Waterfall Program change the number of bishops in the compiled Flooding Waterfall Program? I still haven't checked the compilation details. That is something to keep in mind when I do.
I believe there are now 298 creature types. This page still lists 296 types as established as of MH3, but since then, Bloomburrow has added Skunk and Weasel. If those are the only additions and none have been removed, that makes 298 - for the moment. We also have Duskmourn on the way with the addition of Glimmer, although admittedly we don't know for sure if Duskmourn will remove any types.
oof yeah needing the copies to still have targets does mean we need a type that never dies and is therefore not part of the program.
Yes the UTM only needs the inputs to change, we don't need to make new bishops between computations if we can keep the originals alive. If the same bishops are all alive, then being able to reset the clocks with X sized inputs will give us something like BB(log(X)) outputs from the next computation from that construction.
Cast the two creatures, then cast Electroduplicate targeting Ratadrabik, producing two tokens. The legend rule applies. Keep one token, and the other two die, getting four triggers, each of which produces two nonlegendary tokens, for a total of nine Ratadrabiks.
Now cast Electroduplicate by flashback targeting Mondrak, producing two tokens. Again, keep one token as the legend rule applies, this time getting 18 Ratadrabik triggers and ending up with more than 2^^18 copies of Mondrak.
Sacrifice the remaining legendary Ratadrabik token and one nonlegendary Ratadrabik token, getting some triggers for more than 2^^19 copies of Ratadrabik. Finally, sacrifice the remaining legendary Mondrak token and one nonlegendary Ratadrabik token, getting more than 2^^19 Ratadrabik triggers and ending up with more than 2^^2^^19 copies of Mondrak.
Unfortunately, this doesn't easily become a solution for without free mana, because it spends 21 mana in total.
Start by casting Fathom Mage, then cast Saw in Half on it to make two of them (still 1/1). Now cast Keeper of the Cadence. It triggers evolve on both Fathom Mages. Activate Keeper of the Cadence to put Saw in Half into the library, then resolve the first evolve and the on-evolve trigger to draw it. Cast it on the now-2/2 Fathom Mage, making two more 1/1 Fathom Mages, then resolve the rest, redrawing Saw in Half again. (We now have one 2/2 and two 1/1 Fathom Mages.)
Cast Saw in Half on Keeper of the Cadence, making two 1/3s, which both trigger evolve on the Fathom Mages. Let the 2/2 Fathom Mage evolve to 3/3 first, and Saw it into two 2/2s. We get four more redraws of Saw from evolving the two 1/1 Fathom Mages to 3/3; use the first three to Saw the new 2/2 Fathom Mages into four 1/1s, and one of those into two 1/1s. (We now have two 3/3 Fathom Mages, five 1/1 Fathom Mages, and two 1/3 Keeper of the Cadence, and Saw in Half in hand.)
The process used now is: Saw a ?/3 into two ?/2s, triggering evolve on all the 1/1 Fathom Mages. Each time a 1/1 Fathom Mage evolves into 2/2, it redraws Saw, which is cast on that now-2/2 to turn it into two 1/1 Fathom Mages; except for the last time, where we keep Saw in hand. The net result is to go from X 1/1 Fathom Mages to (X-1)*2 1/1 Fathom Mages and one 2/2 Fathom Mage (as well as whatever was produced by the initial Saw).
Follow that process using the two 3/3 Fathom Mages and two 1/3 Keeper of the Cadence. We now have 50 1/1 Fathom Mages, 8 2/2 Fathom Mages, and four 1/2 Keeper of the Cadence. Cast Saw one more time to turn one 2/2 Fathom Mage into two 1/1 Fathom Mages (now 52 1/1 Fathom Mages and 7 2/2 Fathom Mages).
Cast Eldrazi Linebreaker, triggering evolve on the Fathom Mages. The first to resolve should raise a 2/2 Fathom Mage to 3/3 and draw Saw. Cast Saw on that Fathom Mage, making two 2/2s and triggering evolve on the 52 1/1 Fathom Mages. With the resulting 52 redraws of Saw, cast it on the two new 2/2s and the resulting new 1/1s, producing 54 1/1s. We still have on the stack 58 evolve triggers from Eldrazi Linebreaker entering, and now those Fathom Mages are all 2/2, so they go up to 3/3 with those evolves. Redraw Saw 58 times and cast it 57 times on the 1/1s. We now have 58 3/3 Fathom Mages and 111 1/1 Fathom Mages.
Follow the main process from above, consuming the 58 3/3 Fathom Mages, ending up with 2^58*109+2 1/1 Fathom Mages and 174 2/2 Fathom Mages.
Cast Saw in Half on the 3/3 Eldrazi Linebreaker, triggering evolve on the 1/1 Fathom Mages. Use the draws except the last to Saw Eldrazi Linebreakers, ending with 2^58*109+3 Eldrazi Linebreakers.
Proceed to combat, and the Eldrazi Linebreakers trigger. Target a different creature with each, and continue Sawing for increasing hyperoperations. After the last one resolves, attack with the boosted creature.
I think these are the current winners for everything up to 13 cards. I feel like there has to be a way for 9 to hit F_{w+2}, but I wasn't able to come up with a way to do so last time I tried. Maybe the Eldrazi Linebreaker strategy above will help?
13 is still a sticking point. Is there a way we can establish a lower bound for it? It'd be nice if we can at least prove that it beats the 3-4 stage decks it replaced.
It'd be easy to make a "proper" Busy Beaver deck at 14 cards by adding something like Possibility Storm, but that feels like a somewhat unexciting note to end a writeup on. What would really be cool is if we can incorporate traditional stages by finding the minimum cards to build a stage on top of the Turing Machine. Extending that to hyperstage and megastage versions would be even more exciting, but those would also be a much larger undertaking.
Start by casting Fathom Mage, then cast Saw in Half on it to make two of them (still 1/1). Now cast Keeper of the Cadence. It triggers evolve on both Fathom Mages. Activate Keeper of the Cadence to put Saw in Half into the library, then resolve the first evolve and the on-evolve trigger to draw it. Cast it on the now-2/2 Fathom Mage, making two more 1/1 Fathom Mages, then resolve the rest, redrawing Saw in Half again. (We now have one 2/2 and two 1/1 Fathom Mages.)
Cast Saw in Half on Keeper of the Cadence, making two 1/3s, which both trigger evolve on the Fathom Mages. Let the 2/2 Fathom Mage evolve to 3/3 first, and Saw it into two 2/2s. We get four more redraws of Saw from evolving the two 1/1 Fathom Mages to 3/3; use the first three to Saw the new 2/2 Fathom Mages into four 1/1s, and one of those into two 1/1s. (We now have two 3/3 Fathom Mages, five 1/1 Fathom Mages, and two 1/3 Keeper of the Cadence, and Saw in Half in hand.)
The process used now is: Saw a ?/3 into two ?/2s, triggering evolve on all the 1/1 Fathom Mages. Each time a 1/1 Fathom Mage evolves into 2/2, it redraws Saw, which is cast on that now-2/2 to turn it into two 1/1 Fathom Mages; except for the last time, where we keep Saw in hand. The net result is to go from X 1/1 Fathom Mages to (X-1)*2 1/1 Fathom Mages and one 2/2 Fathom Mage (as well as whatever was produced by the initial Saw).
Follow that process using the two 3/3 Fathom Mages and two 1/3 Keeper of the Cadence. We now have 50 1/1 Fathom Mages, 8 2/2 Fathom Mages, and four 1/2 Keeper of the Cadence. Cast Saw one more time to turn one 2/2 Fathom Mage into two 1/1 Fathom Mages (now 52 1/1 Fathom Mages and 7 2/2 Fathom Mages).
Cast Eldrazi Linebreaker, triggering evolve on the Fathom Mages. The first to resolve should raise a 2/2 Fathom Mage to 3/3 and draw Saw. Cast Saw on that Fathom Mage, making two 2/2s and triggering evolve on the 52 1/1 Fathom Mages. With the resulting 52 redraws of Saw, cast it on the two new 2/2s and the resulting new 1/1s, producing 54 1/1s. We still have on the stack 58 evolve triggers from Eldrazi Linebreaker entering, and now those Fathom Mages are all 2/2, so they go up to 3/3 with those evolves. Redraw Saw 58 times and cast it 57 times on the 1/1s. We now have 58 3/3 Fathom Mages and 111 1/1 Fathom Mages.
Follow the main process from above, consuming the 58 3/3 Fathom Mages, ending up with 2^58*109+2 1/1 Fathom Mages and 174 2/2 Fathom Mages.
Cast Saw in Half on the 3/3 Eldrazi Linebreaker, triggering evolve on the 1/1 Fathom Mages. Use the draws except the last to Saw Eldrazi Linebreakers, ending with 2^58*109+3 Eldrazi Linebreakers.
Proceed to combat, and the Eldrazi Linebreakers trigger. Target a different creature with each, and continue Sawing for increasing hyperoperations. After the last one resolves, attack with the boosted creature.
Cast and sacrifice Black Lotus for GGG and cast Channel. (20 life, G floating)
Cast Minion Reflector. (15 life, G)
Cast Sharp-Eyed Rookie and pay {2} for a copy. (12 life)
Cast Academy Manufactor. (9 life) Minion Reflector and both Sharp-Eyed Rookies trigger.
Resolve one Sharp-Eyed Rookie trigger, raising it to 3/3 and getting a Clue, a Food, and a Treasure.
Cast Saw in Half on that Sharp-Eyed Rookie, producing two 2/2s.
Pay {2} for the Minion Reflector trigger. (7 life) Get a copy of Academy Manufactor, which triggers all three Sharp-Eyed Rookies, which each become 3/3 and produce a total of nine each of Clue, Food, and Treasure tokens.
(The remaining Sharp-Eyed Rookie trigger from the original Academy Manufactor does nothing.)
Sacrifice the ten Foods. (17 life)
Cast Halo-Charged Skaab, sacrificing one Treasure. (13 life) It triggers its own ability, Minion Reflector, and the three Sharp-Eyed Rookies.
Sacrifice a Clue (11 life) to draw the eighth card, then resolve Halo-Charged Skaab's ability to put Saw in Half on top, and sacrifice a Clue (9 life) to draw it.
Resolve one Sharp-Eyed Rookie trigger, raising it to 4/4 and getting +3 of each token.
[Start Sawing Halo-Charged Skaabs and Sharp-Eyed Rookies; for optimality, hold off from Sawing Academy Manufactors (because they are still 1/3) until there are as many 1/1 Sharp-Eyed Rookies as possible.]
...
Cast Mana-Charged Dragon. Put the Sharp-Eyed Rookie triggers lower on the stack, and the Minion Reflector trigger on top. Resolve the Minion Reflector trigger; the copy also triggers the Sharp-Eyed Rookies. Before those resolve, cast a pair of Saws on a Halo-Charged Skaab and the Mana-Charged Dragon copy. The Sharp-Eyed Rookies trigger from the 3/3 Mana-Charged Dragon tokens and go to 3/3, and their triggers from the original Mana-Charged Dragon and the copy raise them to 5/5.
Also, the newly revealed Exalted Sunborn is potentially useful, being the first token-multiplying nonlegendary creature, but I didn't find any immediate improvements with it.
Play Black Lotus, Channel, and Sharp-Eyed Rookie. 19 life.
Play Academy Manufactor, triggering Rookie to make it a 3/3. 16 life, 1 food/treasure/clue.
Play Saw in Half on Manufactor. Eat the food. 15 life.
Play Roaming Throne choosing Human. Rookie triggers twice but only one trigger succeeds, making it a 4/4 and getting three of each token (then eat the food). 14 life, 3 treasure.
Play Keeper of the Cadence, making Rookie a 5/5 and getting another three of each token. Put Saw back into the library and use three clues to draw it and the other two cards. 4 life, 5 treasure.
Play Saw on Rookie to turn it into two 3/3s. 2 life, 4 treasure.
Play Karlach, Fury of Avernus, triggering both Rookies twice. Resolve two triggers, then loop Saw and play it on a Manufactor so the third makes nine of each token and the fourth makes even more. Then load up on 1/1 Rookies.
Continue from there, playing Eldrazi Linebreaker when needed. At the end of the main phase, we can dump our remaining Saws into copies of Eldrazi Linebreaker and Roaming Throne set to Eldrazi, to maximize the number of Linebreaker triggers we'll get in combat. The second-to-last Linebreaker trigger ends with maxing out on Roaming Thrones set to Tiefling, then we use the last one to attack and get that many Karlach triggers for additional combats. Repeat the rest with each one, then in the final combat, use the last Linebreaker trigger to swing for however much damage that adds up to.
Edit: Nope, Keeper isn't an option because of being able to loop artifact creatures.
Play Black Lotus, Channel, and Sharp-Eyed Rookie. 19 life.
Play Academy Manufactor, triggering Rookie to make it a 3/3 and make one of each token. Eat the food. 17 life, 1 treasure.
Play Saw in Half on Rookie to make two 2/2 Rookies. 15 life.
Play Roaming Throne choosing Zombie. Both Rookies become 3/3. 13 life, 2 treasure.
Play Halo-Charged Skaab for two Skaab triggers and two Rookie triggers. Use two clues to draw the remaining two cards, then the third and a Skaab trigger to redraw Saw. 3 life, 1 treasure.
Play Saw on Academy Manufactor, then resolve both Rookie triggers to make them 4/4s and get six of each token. Use two treasures to eat the food, then resolve the Skaab trigger. 9 life, 4 treasure.
Play Karlach, Fury of Avernus to trigger both Rookies. Resolve one of them, then draw and play Saw on Skaab for four Skaab triggers. 4 life, 5 treasure.
Resolve a Skaab trigger, then draw and play Saw on Manufactor. Resolve the second Rookie trigger for 9 of each token. 12 life, 10 treasure.
Resolve two Skaab triggers to play Saw twice and turn a 5/5 Rookie into two 3/3s, then a 3/3 into two 2/2s. Resolve the fourth to topdeck Saw again. 4 life, 8 treasure.
Play Eldrazi Linebreaker to trigger both 2/2 Rookies…
I tried a start like this last night and couldn’t get it to work, so I’m not sure whether I overlooked something then or I’m missing something now.
Though that does also end up needing a bunch more bishops and tokens.
I don't even know what a good universal tag system would be to start, but I think compiling to spiral rise and later compiling to flooding clocks both give an exponential increase to the numbers involved. So I don't have much hope of getting a universal program that's small enough that way. Though it would be interesting to see what that actually looks like.
Start by casting Fathom Mage, then cast Saw in Half on it to make two of them (still 1/1). Now cast Keeper of the Cadence. It triggers evolve on both Fathom Mages. Activate Keeper of the Cadence to put Saw in Half into the library, then resolve the first evolve and the on-evolve trigger to draw it. Cast it on the now-2/2 Fathom Mage, making two more 1/1 Fathom Mages, then resolve the rest, redrawing Saw in Half again. (We now have one 2/2 and two 1/1 Fathom Mages.)
Cast Saw in Half on Keeper of the Cadence, making two 1/3s, which both trigger evolve on the Fathom Mages. Let the 2/2 Fathom Mage evolve to 3/3 first, and Saw it into two 2/2s. We get four more redraws of Saw from evolving the two 1/1 Fathom Mages to 3/3; use the first three to Saw the new 2/2 Fathom Mages into four 1/1s, and one of those into two 1/1s. (We now have two 3/3 Fathom Mages, five 1/1 Fathom Mages, and two 1/3 Keeper of the Cadence, and Saw in Half in hand.)
The process used now is: Saw a ?/3 into two ?/2s, triggering evolve on all the 1/1 Fathom Mages. Each time a 1/1 Fathom Mage evolves into 2/2, it redraws Saw, which is cast on that now-2/2 to turn it into two 1/1 Fathom Mages; except for the last time, where we keep Saw in hand. The net result is to go from X 1/1 Fathom Mages to (X-1)*2 1/1 Fathom Mages and one 2/2 Fathom Mage (as well as whatever was produced by the initial Saw).
Follow that process using the two 3/3 Fathom Mages and one 1/3 Keeper of the Cadence. We now have 26 1/1 Fathom Mages, 7 2/2 Fathom Mages, two 1/2 Keeper of the Cadence, and one 1/3 Keeper of the Cadence.
Cast Life of the Party. Cast Saw in Half on the remaining 1/3 Keeper of the Cadence, triggering evolve on the 26 1/1 Fathom Mages. Use the first 25 draws to Saw Life of the Party, ending with 26 Life of the Party. Attack with them.
Note that this arrangement has some losses at the higher values, because of evolve only increasing power and toughness by one at a time. However, the hyperoperations should quickly overwhelm those losses.
Unfortunately, adding Black Lotus, Channel and Lich's Mirror for the no-mana-given version doesn't work with these cards, because it doesn't provide infinite mana during combat.
Notes for potential modifications: Sharp-Eyed Rookie can replace Fathom Mage. Watchful Radstag seems potentially useful but is redundant if we're using Saw in Half.
keeper of the cadence is just barely big enough with 5 toughness and can't recur itself.
watchful radstag seems like it is going to be busted in one of these, but not yet.
Perhaps I'm providing too much to address in one post, but I've also thought about a variant of this challenge for the 3-card blind format, where both players have 3 cards that start in their opening hand and decide all random effects for their opponent. The challenge there is to find the longest match of 3cb, accomplished by one side having icatian moneychanger, forbidden orchard, millenium calendar. Such a deck stores up enough counters on moneychanger to survive the onslaught of spirits after playing calendar and repeatedly tapping orchard. When deciding the other player's hand, the best the 3cb discord came up with was gaea's cradle, heroes' bane, scepter of celebration, which was said to be about 2^^994 turns of storing up moneychanger (again, I have no idea where that comes from). I wanted to expand this challenge to higher X-card blind setups. The challenge has some differences than many of the lines described in this forum since you have several turns to work with to build up a board state/damage. A 5-card blind setup I came up with is moneychanger, orchard, calendar, deadeye navigator, ugin's nexus vs cradle, chromatic orrery, parallel lives, astral dragon, sen triplets. (Really only 9 relevant cards, Sen's only used so that the setup cards can be split between both players). The setup gets all their cards and deadeye navigator into play (don't need ugin's nexus right away) and starts blinking astral dragon to make parallel lives dragon tokens which increase in some level of tetration. I'm guessing the fastest growth uses the last dragon blink each turn to make token copies of cradle (with summoning sickness) instead but I have no idea. When calendar is at 999 counters, play ugin's nexus and use the last dragon blink to create a whole bunch of nexus copies. Soulbound with one of the dragon nexus tokens and sacrifice the rest to legend rule to take a bunch of extra turns, then activate the deadeye ability on the navigator and the dragon nexus (holding priority) to exile the last nexus and get navigator soulbonded back to the astral dragon. Then repeat the growing process for all the extra turns, using the 2nd to last turn to make copies of calendar each of which deals 1000 damage from the next untap (not that letting each token deal 1000 damage one time makes a difference in the notation). I have no idea what the proper notation for the length of this game (how long moneychanger has to store up to survive all the damage) is.
Edit: Realized after writing this all up that Gaea's Cradle is legendary so you can't (usefully) make copies of it. I think a similar effect as I wanted can be achieved by using coalition relic and doubling season instead of chromatic orrery and parallel lives
To answer your questions:
In general, each arrow corresponds to a link in a chain of triggers/effects/spells that turn a small number of one resource into an increasing number of another resource.
For example, with that 3cb deck:
By spending a turn, we get an attack that makes X creatures (one arrow)
we can tap cradle to make X mana (but we only get to do this once per turn so it is not also worth an arrow)
we spend that mana four at a time to double X
giving the 2^^994 estimate (994 is 1000 minus the setup turns and maybe one turn of buffer because the actual number is not exactly 2^^X)
the numbers with multiple arrow strings are mostly just being precise, if the biggest part of the combo only happens once (IE, getting all of the ugin's nexus turns) it can be best approximated by a number like 2^^^^(2^^^^990) which is between 2^^^^^3 and 2^^^^^4
This is why panharmonicon is an improvement to ugin's nexus, because doing a combo with an extra arrow the whole time is going to be more like 2^^^^^990
Breaking Ghram's number was thought to be impossible for a long time, but we found a way to simulate the Ackermann Function. my favorite example of this is the "catboy thor" deck:
2 Channel
3 Mycosynth Lattice
4 Urza, Lord High Artificer
5 Cogwork Assembler
6 Toralf, God of Fury
7 Hunted Phantasm
8 Cubwarden
9 Tail Swipe
10 Surtland Flinger
Which had a construct tail swipe a goblin for 9 with one lifelinking toralf in play, this quickly grows as we keep copying toralf and hunted phantasm and occasionally urza to make a fresh construct to absorb the 1 damage triggers.
many Toralfs can only make many smaller triggers so this process is finite.
The stack becomes a system of layers for each value:
7 mana makes a copy
A 1 damage trigger makes 1 mana
A 2 damage trigger makes X 1 damage triggers
A 3 damage trigger makes X 2 damage triggers
A 4 damage trigger makes X 3 damage triggers
...
That's "only" a few layers from 9 damage sure, but then we start making flingers at the end of that.
each flinger tosses a construct and starts the whole toralf combo over, starting at the new X.
That is how we can get more than a handful of arrows.
There are other ways to break through, This is my old writeups of the work done in the standard version of the challenge https://old.reddit.com/user/StandardStageCombo/submitted/
One of the Whale tokens produces many Kraken tokens, which can block over many turns, for a tetration.
One of the Fish tokens produces many of the Whale tokens, for a pentation.
Reef Worm produces many of the Fish tokens, for a hexation.
Player 1 first uses Bow of Nylea to accumulate life, then casts Tempting Wurm, letting Player 2 put their cards onto the battlefield. Court of Vantress triggers to make Player 2 the monarch, and then in Player 2's upkeep, it targets Parallel Lives and makes two copies of it because of Parallel Lives. On the next turn, Player 1 attacks with Tempting Wurm and deals damage to Player 2, taking the monarchy, and then on Player 2's upkeep, Court of Vantress becomes a copy of Parallel Lives with its ability added. Next, Tempting Wurm attacks a second time and Reef Worm blocks it, producing 16 of its Fish tokens, and in Player 2's turn, 15 of them attack and take back the monarchy.
If the Tempting Wurm is killed by blockers, use Bow of Nylea to get it back.
Court of Vantress can copy Bow of Nylea, but Player 2 has no way to get mana to activate its ability.
For higher numbers of cards, we could do something similar with Ochre Jelly, but it gets tricky because Ochre Jelly has to be cast with mana to work (or perhaps given +1/+1 counters some other way).
It's a bit of a shame that the bow gives deathtouch or they'd need to pump the wurm a bunch to get through the 9/9 token
Way more interesting than the win in omega style match of 1 shot infinite life vs scalding tongs
Previously I'd use groups of 2 bishops to double the amount of signal tokens when going to the next type until the last type stops the heartbeat and causes everything but dedicated output to die. The improvement sacrifices one such doubling. This frees up a couple of bishops and those are used to ensure that the designated output survives and grows under additional arcbonds, even after the heartbeat that kept the main program alive stops.
That way we can put arcbond on everything in the main program and accumulate a ton of arcbond triggers until the main program dies and no new triggers come in. Then we resolve all the stockpiled arcbonds, growing the output along the way.
Effectively we removed a factor of 2 and added a factor of x * y. Where x is the number of bishops in the main program (that eventually die) and y is the number of arcbond effects we have on each of those bishops. y will depend on the specifics of the setup, like how many Precursor Golems are around when you cast Arcbond. It gets a bit complicated because you can't have any arcbond on the creatures that need to survive, so timing the cast correctly during a long sequence of type changes will be fun.
Playing around with my old simulater I think that we would get to ~440 million bishops even if y is 1. So the number of required bishops should be covered.
I'm not quite sure 296 creature types is enough. In addition to the 296 clocks we might need two types to allow the bishops that are part of the program to stay alive, a growing output type and a heartbeat type. I doubt the compiled universal program provides a clock that is usable for that.
We also can't use Wall because in this deck we can't target Artificial Evolution with itself. There might be other bookkeeping types we need that I'm not thinking of right now.
Anyway, we are reaaaally close to being able to specify a working turing complete computation.
Can we 'just' rebuild the whole thing from scratch using the halting type to keep the bishops alive until the end? (outputting more of the halting type when they die?)
that leaves us with a bunch of clocks with BB(x) damaged tokens and the halting type with BB(x) fresh tokens, but no bishops.
Wall is a problem though so yeah at least one type short.
I think just one more type to hold all of the bishops out of the way and a few bishops to help reprogram before the next computation will be enough if we can't rebuild from scratch after a computation.
Also we don't need a heartbeat, we can have every clock make the bishop's type and then they never die.
Copying the deck here to see what we are talking about:
2 Channel
3 Vessel of Endless Rest
4 Precursor Golem
5 Replication Technique
6 Audacious Swap
7 Scrambleverse
9 Bishop of Wings
10 Artificial Evolution
11 Arcbond
12 Comeuppance
13 Soulblast
The start gets us 2 Precursor Golem triggers on Audacious Swap. The first of those triggers gets 53 copies and is used to generate a billion golems before the second trigger. The second trigger gives us the last batch of Audacios Swap copies we can ever get.
Recall that Audacious Swap copies can cast Artificial Evolution on all our creatures at once thanks to Precursor Golem. But the same is not true for Replication Technique because the original needs to copy Vessel of Endless Rest to tuck itself back.
The plan is to use about a million of the Audacious Swap copies to set up the bishops for an universal computation.
After that we want to use a fixed number of Audacious Swap copies to reprogram the output of the last computation into the input of the next computation. If the bishops stay alive and are reuseable that should take 10 or 20 copies. If the bishops aren't reuseable we need about a million copies to set them up again. Either way we can reprogram the output into input with ~1 Artificial Evolution.
Repeat until we run out of Audacious Swap copies.
So now that I have looked at it closer it is not actually necessary to keep the bishops alive. We get a fixed number of BB repetitions either way. The fixed number is just ~100000 times bigger if we can keep bishops. So I'd say it is nice to have, but missing out is not a disaster.Except that the targets of the Audacious Swap copies that are on the stack absolutely need to stay alive, or the later copies won't do anything at all. So missing out is a disaster after all. We need to be able to designate a type that stays alive through the computation.
One last thing I'm unsure about: Does the Flooding Waterfall Compilation actually allow us to use the same bishops on Input of arbitrary size? Or does the input to the Waterfall Program change the number of bishops in the compiled Flooding Waterfall Program? I still haven't checked the compilation details. That is something to keep in mind when I do.
I believe there are now 298 creature types. This page still lists 296 types as established as of MH3, but since then, Bloomburrow has added Skunk and Weasel. If those are the only additions and none have been removed, that makes 298 - for the moment. We also have Duskmourn on the way with the addition of Glimmer, although admittedly we don't know for sure if Duskmourn will remove any types.
Yes the UTM only needs the inputs to change, we don't need to make new bishops between computations if we can keep the originals alive. If the same bishops are all alive, then being able to reset the clocks with X sized inputs will give us something like BB(log(X)) outputs from the next computation from that construction.
Cast the two creatures, then cast Electroduplicate targeting Ratadrabik, producing two tokens. The legend rule applies. Keep one token, and the other two die, getting four triggers, each of which produces two nonlegendary tokens, for a total of nine Ratadrabiks.
Now cast Electroduplicate by flashback targeting Mondrak, producing two tokens. Again, keep one token as the legend rule applies, this time getting 18 Ratadrabik triggers and ending up with more than 2^^18 copies of Mondrak.
Sacrifice the remaining legendary Ratadrabik token and one nonlegendary Ratadrabik token, getting some triggers for more than 2^^19 copies of Ratadrabik. Finally, sacrifice the remaining legendary Mondrak token and one nonlegendary Ratadrabik token, getting more than 2^^19 Ratadrabik triggers and ending up with more than 2^^2^^19 copies of Mondrak.
Unfortunately, this doesn't easily become a solution for without free mana, because it spends 21 mana in total.
Cast Saw in Half on Keeper of the Cadence, making two 1/3s, which both trigger evolve on the Fathom Mages. Let the 2/2 Fathom Mage evolve to 3/3 first, and Saw it into two 2/2s. We get four more redraws of Saw from evolving the two 1/1 Fathom Mages to 3/3; use the first three to Saw the new 2/2 Fathom Mages into four 1/1s, and one of those into two 1/1s. (We now have two 3/3 Fathom Mages, five 1/1 Fathom Mages, and two 1/3 Keeper of the Cadence, and Saw in Half in hand.)
The process used now is: Saw a ?/3 into two ?/2s, triggering evolve on all the 1/1 Fathom Mages. Each time a 1/1 Fathom Mage evolves into 2/2, it redraws Saw, which is cast on that now-2/2 to turn it into two 1/1 Fathom Mages; except for the last time, where we keep Saw in hand. The net result is to go from X 1/1 Fathom Mages to (X-1)*2 1/1 Fathom Mages and one 2/2 Fathom Mage (as well as whatever was produced by the initial Saw).
Follow that process using the two 3/3 Fathom Mages and two 1/3 Keeper of the Cadence. We now have 50 1/1 Fathom Mages, 8 2/2 Fathom Mages, and four 1/2 Keeper of the Cadence. Cast Saw one more time to turn one 2/2 Fathom Mage into two 1/1 Fathom Mages (now 52 1/1 Fathom Mages and 7 2/2 Fathom Mages).
Cast Eldrazi Linebreaker, triggering evolve on the Fathom Mages. The first to resolve should raise a 2/2 Fathom Mage to 3/3 and draw Saw. Cast Saw on that Fathom Mage, making two 2/2s and triggering evolve on the 52 1/1 Fathom Mages. With the resulting 52 redraws of Saw, cast it on the two new 2/2s and the resulting new 1/1s, producing 54 1/1s. We still have on the stack 58 evolve triggers from Eldrazi Linebreaker entering, and now those Fathom Mages are all 2/2, so they go up to 3/3 with those evolves. Redraw Saw 58 times and cast it 57 times on the 1/1s. We now have 58 3/3 Fathom Mages and 111 1/1 Fathom Mages.
Follow the main process from above, consuming the 58 3/3 Fathom Mages, ending up with 2^58*109+2 1/1 Fathom Mages and 174 2/2 Fathom Mages.
Cast Saw in Half on the 3/3 Eldrazi Linebreaker, triggering evolve on the 1/1 Fathom Mages. Use the draws except the last to Saw Eldrazi Linebreakers, ending with 2^58*109+3 Eldrazi Linebreakers.
Proceed to combat, and the Eldrazi Linebreakers trigger. Target a different creature with each, and continue Sawing for increasing hyperoperations. After the last one resolves, attack with the boosted creature.
- 3 damage with Chancellor of the Dross
- 6 damage with Black Lotus, Ball Lightning
- 19 damage with Black Lotus, Channel, Mistcutter Hydra
- 40 damage with Black Lotus, Channel, Reality Smasher, Wine of Blood and Iron
- 274,877,906,944 damage with Black Lotus, Show and Tell, Omniscience, Devilish Valet, Sparkcaster
- 2^^2^^7 damage with Black Lotus, Channel, Chromatic Orrery, Mondrak, Glory Dominus, Ratadrabik of Urborg, Twinflame
- 2^^^^(2^^(2^37))) damage with Black Lotus, Channel, Salvaging Station, Cogwork Assembler, Precursor Golem, Slaughter, Smiting Helix
- F_{w+1}(9840) damage with Black Lotus, Show and Tell, Bolas's Citadel, Boulderbranch Golem, Saw in Half, Inverter of Truth, Unstable Shapeshifter, Life of the Party
- F_{w+1}(2^^^2^^65) damage with Black Lotus, Channel, Lich's Mirror, Doubling Season, Temur Ascendancy, Astral Dragon, Mystic Sanctuary, Saw in Half, Dromoka, the Eternal
- F_{w2+2}(2^^65) damage with Black Lotus, Channel, Lich's Mirror, Doubling Season, Astral Dragon, Codex Shredder, Glorious Sunrise, Saw in Half, Hornbash Mentor, Bloodthorn Taunter
- F_{w2+3}(F_{w2+2}(2^^65)) damage with Black Lotus, Channel, Lich's Mirror, Doubling Season, Astral Dragon, Codex Shredder, Glorious Sunrise, Saw in Half, Hornbash Mentor, Bloodthorn Taunter, Finest Hour
- F_{w3+2}(18) damage with Black Lotus, Channel, Lich's Mirror, Doubling Season, Astral Dragon, Codex Shredder, Chandra's Ignition, Saw in Half, Bloodthorn Taunter, Hornbash Mentor, Scattershot Archer, Rite of Passage
- ??? damage with Black Lotus, Channel, Vessel of Endless Rest, Precursor Golem, Replication Technique, Audacious Swap, Scrambleverse, Coat of Arms, Bishop of Wings, Artificial Evolution, Arcbond, Comeuppance, Soulblast
I think these are the current winners for everything up to 13 cards. I feel like there has to be a way for 9 to hit F_{w+2}, but I wasn't able to come up with a way to do so last time I tried. Maybe the Eldrazi Linebreaker strategy above will help?13 is still a sticking point. Is there a way we can establish a lower bound for it? It'd be nice if we can at least prove that it beats the 3-4 stage decks it replaced.
It'd be easy to make a "proper" Busy Beaver deck at 14 cards by adding something like Possibility Storm, but that feels like a somewhat unexciting note to end a writeup on. What would really be cool is if we can incorporate traditional stages by finding the minimum cards to build a stage on top of the Turing Machine. Extending that to hyperstage and megastage versions would be even more exciting, but those would also be a much larger undertaking.
I still don't have a way to extend it to 9 cards, though. Looks like the additional combat effects either go infinite or would need additional help.
For 8 cards, I think Black Lotus, Channel, Minion Reflector, Sharp-Eyed Rookie, Academy Manufactor, Saw in Half, Halo-Charged Skaab, Mana-Charged Dragon attains F_{w+1}(2^^^^something).
Cast and sacrifice Black Lotus for GGG and cast Channel. (20 life, G floating)
Cast Minion Reflector. (15 life, G)
Cast Sharp-Eyed Rookie and pay {2} for a copy. (12 life)
Cast Academy Manufactor. (9 life) Minion Reflector and both Sharp-Eyed Rookies trigger.
Resolve one Sharp-Eyed Rookie trigger, raising it to 3/3 and getting a Clue, a Food, and a Treasure.
Cast Saw in Half on that Sharp-Eyed Rookie, producing two 2/2s.
Pay {2} for the Minion Reflector trigger. (7 life) Get a copy of Academy Manufactor, which triggers all three Sharp-Eyed Rookies, which each become 3/3 and produce a total of nine each of Clue, Food, and Treasure tokens.
(The remaining Sharp-Eyed Rookie trigger from the original Academy Manufactor does nothing.)
Sacrifice the ten Foods. (17 life)
Cast Halo-Charged Skaab, sacrificing one Treasure. (13 life) It triggers its own ability, Minion Reflector, and the three Sharp-Eyed Rookies.
Sacrifice a Clue (11 life) to draw the eighth card, then resolve Halo-Charged Skaab's ability to put Saw in Half on top, and sacrifice a Clue (9 life) to draw it.
Resolve one Sharp-Eyed Rookie trigger, raising it to 4/4 and getting +3 of each token.
[Start Sawing Halo-Charged Skaabs and Sharp-Eyed Rookies; for optimality, hold off from Sawing Academy Manufactors (because they are still 1/3) until there are as many 1/1 Sharp-Eyed Rookies as possible.]
...
Cast Mana-Charged Dragon. Put the Sharp-Eyed Rookie triggers lower on the stack, and the Minion Reflector trigger on top. Resolve the Minion Reflector trigger; the copy also triggers the Sharp-Eyed Rookies. Before those resolve, cast a pair of Saws on a Halo-Charged Skaab and the Mana-Charged Dragon copy. The Sharp-Eyed Rookies trigger from the 3/3 Mana-Charged Dragon tokens and go to 3/3, and their triggers from the original Mana-Charged Dragon and the copy raise them to 5/5.
Also, the newly revealed Exalted Sunborn is potentially useful, being the first token-multiplying nonlegendary creature, but I didn't find any immediate improvements with it.
Play Academy Manufactor, triggering Rookie to make it a 3/3. 16 life, 1 food/treasure/clue.
Play Saw in Half on Manufactor. Eat the food. 15 life.
Play Roaming Throne choosing Human. Rookie triggers twice but only one trigger succeeds, making it a 4/4 and getting three of each token (then eat the food). 14 life, 3 treasure.
Play Keeper of the Cadence, making Rookie a 5/5 and getting another three of each token. Put Saw back into the library and use three clues to draw it and the other two cards. 4 life, 5 treasure.
Play Saw on Rookie to turn it into two 3/3s. 2 life, 4 treasure.
Play Karlach, Fury of Avernus, triggering both Rookies twice. Resolve two triggers, then loop Saw and play it on a Manufactor so the third makes nine of each token and the fourth makes even more. Then load up on 1/1 Rookies.
Continue from there, playing Eldrazi Linebreaker when needed. At the end of the main phase, we can dump our remaining Saws into copies of Eldrazi Linebreaker and Roaming Throne set to Eldrazi, to maximize the number of Linebreaker triggers we'll get in combat. The second-to-last Linebreaker trigger ends with maxing out on Roaming Thrones set to Tiefling, then we use the last one to attack and get that many Karlach triggers for additional combats. Repeat the rest with each one, then in the final combat, use the last Linebreaker trigger to swing for however much damage that adds up to.
Play Black Lotus, Channel, and Sharp-Eyed Rookie. 19 life.
Play Academy Manufactor, triggering Rookie to make it a 3/3 and make one of each token. Eat the food. 17 life, 1 treasure.
Play Saw in Half on Rookie to make two 2/2 Rookies. 15 life.
Play Roaming Throne choosing Zombie. Both Rookies become 3/3. 13 life, 2 treasure.
Play Halo-Charged Skaab for two Skaab triggers and two Rookie triggers. Use two clues to draw the remaining two cards, then the third and a Skaab trigger to redraw Saw. 3 life, 1 treasure.
Play Saw on Academy Manufactor, then resolve both Rookie triggers to make them 4/4s and get six of each token. Use two treasures to eat the food, then resolve the Skaab trigger. 9 life, 4 treasure.
Play Karlach, Fury of Avernus to trigger both Rookies. Resolve one of them, then draw and play Saw on Skaab for four Skaab triggers. 4 life, 5 treasure.
Resolve a Skaab trigger, then draw and play Saw on Manufactor. Resolve the second Rookie trigger for 9 of each token. 12 life, 10 treasure.
Resolve two Skaab triggers to play Saw twice and turn a 5/5 Rookie into two 3/3s, then a 3/3 into two 2/2s. Resolve the fourth to topdeck Saw again. 4 life, 8 treasure.
Play Eldrazi Linebreaker to trigger both 2/2 Rookies…
I tried a start like this last night and couldn’t get it to work, so I’m not sure whether I overlooked something then or I’m missing something now.