Fair enough, I was thinking along the lines of the previous standard decks that stole the opponent's 60 lands for landfall triggers. Waste has just been the default non-card. there have even been ideas for vintage decks where the only way to activate an Eldrazi is with the opponent's wastes.
Fair enough, I was thinking along the lines of the previous standard decks that stole the opponent's 60 lands for landfall triggers. Waste has just been the default non-card. there have even been ideas for vintage decks where the only way to activate an Eldrazi is with the opponent's wastes.
I was trying to aim for the cautious end with the rules in the original post, but alternatives are certainly also interesting to explore.
Speaking of alternatives, a recent Reddit post has gotten me thinking about another possible challenge. This one isn't really focusing on cards as a limit, but the restriction is big enough that this thread feels to me like it might be a better place than the 60-card one.
The original challenge was finding the best way to kill the opponent with a Legacy-legal deck that isn't able to cast spells. The original post suggested a turn 3 kill with Dark Depths, and it looks like a dredge strategy can win on turn 1.
So, to build off that, how much damage could we deal? (Perhaps switching from the Legacy card pool to Vintage, but it might not even matter.) One thing that could be helpful is Priest of Fell Rites, since it can get back arbitrary creatures without casting a spell. Angel of Glory's Rise can turn one reanimation into many, and reanimating creatures can turn into reanimating artifacts and enchantments.
I think I can now exceed Graham's Number in 8 cards!
The main improvement is that Renegade Doppelganger or Unstable Shapeshifter can serve the purpose of Doubling Season, without needing an extra card (which was Astral Dragon). The downside of this is lower initial growth rates; I brought the growth rate back up a bit with precise card selection.
Start with Black Lotus and Show and Tell to put Bolas's Citadel onto the battlefield.
Cast Boulderbranch Golem from library. (-7, +6; 19 life)
Cast Saw in Half from library, targeting Boulderbranch Golem. (-3, +6; 22 life)
Cast Inverter of Truth from library; it moves Black Lotus, Show and Tell, Boulderbranch Golem, and Saw in Half from graveyard into library. (-4; 18 life)
Cast Black Lotus, and cast Boulderbranch Golem. (-7, +6; 17 life)
Cast Saw in Half on Inverter of Truth. Two copies trigger. (-3; 14 life)
The first trigger exiles Show and Tell and sends Saw in Half and Inverter of Truth into the library.
Before the second trigger resolves, sacrifice Black Lotus for 3 mana, and cast Saw in Half targeting Boulderbranch Golem. (-3, +6; 17 life)
The second trigger exiles Inverter of Truth and sends Black Lotus, Saw in Half, and Boulderbranch Golem into the library.
Cast Black Lotus, and cast Boulderbranch Golem. (-7, +6; 16 life)
Cast Saw in Half on an Inverter of Truth. Two copies trigger. (-3; 13 life)
The first trigger sends Saw in Half into the library.
Before the second trigger resolves, sacrifice Black Lotus for 3 mana, and cast Saw in Half targeting Boulderbranch Golem. (-3, +6; 16 life)
The second trigger sends Black Lotus, Saw in Half, and Boulderbranch Golem into the library.
With enough mana now, cast Unstable Shapeshifter from hand, and then cast Black Lotus and Boulderbranch Golem (-7, +6; 15 life); Unstable Shapeshifter becomes a copy of Boulderbranch Golem.
Cast Saw in Half on an Inverter of Truth. (-3; 12 life) Two copies trigger, and Unstable Shapeshifter triggers twice; put the Inverter triggers on top.
The first Inverter trigger sends Saw in Half into the library.
Before the second trigger resolves, sacrifice Black Lotus for 3 mana, and cast Saw in Half targeting the Shapeshifter-Golem. (-3, +6; 15 life)
The second trigger sends Black Lotus, Saw in Half, and Unstable Shapeshifter into the library.
Cast Black Lotus one more time, then cast another pair of Saws on an Inverter and the original Golem (life-neutral). (Unstable Shapeshifter gets exiled.)
Cast Boulderbranch Golem. (-7, +6; 14 life) Both Shapeshifters trigger to become the full 6/5 Golem.
Let those triggers resolve one by one, and after each one resolves, cast another life-neutral Saw pair on an Inverter and the 6/5 Shapeshifter-Golem. There are now four Unstable Shapeshifters, two copying 3/3 Golems and two copying Inverters.
Now we can begin the full loop:
Cast a Saw pair on a Shapeshifter-Inverter and the original Golem.
Cast Boulderbranch Golem. (net -1 life) All Shapeshifters trigger.
After each of those Shapeshifter triggers resolve, cast a Saw pair on an Inverter and the 6/5 Shapeshifter-Golem. The first two times, it has to target a plain Inverter; each subsequent time can target a Shapeshifter-Inverter that does not have a waiting trigger to become a 6/5 Golem.
The net result is -1 life, and +1 and then *3-2 to the number of Shapeshifters, which works out to *3+1.
This can be repeated 7 times, ending with 7 life and 9841 Shapeshifters.
Cast the final card, Life of the Party, from hand. All the Shapeshifters turn into that.
Attack with all possible creatures, getting triggers from Life of the Party and the Shapeshifter copies of it; put the original's trigger on the bottom.
Cast a Saw pair on an Inverter and the original Golem, this time letting the triggers turning Shapeshifters into Inverters resolve first, so that afterwards they become Golems and get to stay Golems for a while.
A trigger from Life of the Party resolves, giving a big boost to the power of a Shapeshifter that is now copying a Golem. Start Sawing again with that one.
(As before, leave the high-value Shapeshifter triggers on the stack until they are ready to be consumed. Now that there is excess life being gained from the big Golems, it can be spent on extra Saws on small Golems. This should work out to a number of Knuth arrows somewhere around the base-2 logarithm of the starting power.)
Repeat with each Life of the Party trigger, until the final one resolves for the original Life of the Party, which is left to deal the big damage.
Cast a Saw pair on a Shapeshifter-Inverter and the original Golem.
Cast Boulderbranch Golem. (net -1 life) All Shapeshifters trigger.
After each of those Shapeshifter triggers resolve, cast a Saw pair on an Inverter and the 6/5 Shapeshifter-Golem. The first two times, it has to target a plain Inverter; each subsequent time can target a Shapeshifter-Inverter that does not have a waiting trigger to become a 6/5 Golem.
The net result is -1 life, and +1 and then *3-2 to the number of Shapeshifters, which works out to *3+1.
This can be repeated 7 times, ending with 7 life and 9841 Shapeshifters.
Are those numbers correct? The initial saw pair accounts for the +1, but after that we only cast one saw pair for each shapeshifter with a trigger. Each saw increases the number of creatures with the shapeshifter ability by -1+2 = 1. So I think we go from N to (N+1)*2-2 = 2*N instead of the N*3+1 you have.
That would result in 512 shapeshifters instead of 9841. That should still be enough to beat grahams number though.
I had another run in with the "oracle text" on mtgsalvation. It says "Whenever another creature enters the battlefield, Unstable Shapeshifter becomes a copy of that creature and gains this ability." That would lead to the combo not working, since the Saw in Half copies of a shapeshifter that has become a copy of the golem or inverter would just be that golem or inverter. The shapeshifter ability would not be transferred to the new copies since it was only gained later.
Fortunately the actual gatherer text is "Whenever another creature enters the battlefield, Unstable Shapeshifter becomes a copy of that creature, except it has this ability." It gives the shapeshifter ability by modifying the copy effect with an "except", so the ability gets copied properly onto the Saw in Half copies.
So as far as I can tell the combo should work. That's an amazing build!
Cast a Saw pair on a Shapeshifter-Inverter and the original Golem.
Cast Boulderbranch Golem. (net -1 life) All Shapeshifters trigger.
After each of those Shapeshifter triggers resolve, cast a Saw pair on an Inverter and the 6/5 Shapeshifter-Golem. The first two times, it has to target a plain Inverter; each subsequent time can target a Shapeshifter-Inverter that does not have a waiting trigger to become a 6/5 Golem.
The net result is -1 life, and +1 and then *3-2 to the number of Shapeshifters, which works out to *3+1.
This can be repeated 7 times, ending with 7 life and 9841 Shapeshifters.
Are those numbers correct? The initial saw pair accounts for the +1, but after that we only cast one saw pair for each shapeshifter with a trigger. Each saw increases the number of creatures with the shapeshifter ability by -1+2 = 1. So I think we go from N to (N+1)*2-2 = 2*N instead of the N*3+1 you have.
What you're missing is that the Shapeshifter count is increased both by Sawing Shapeshifter-Golems and by Sawing Shapeshifter-Inverters.
Ah, I misunderstood the procedure after attacking. I thought we'd go through the main loop described earlier again to turn life into more shapeshifters. That one includes the golem cast for efficiency. But it is of course enough to turn life into shapeshifters less efficiently using only Saw in Half.
What you're missing is that the Shapeshifter count is increased both by Sawing Shapeshifter-Golems and by Sawing Shapeshifter-Inverters.
I still count only two Saws for each Shapeshifter ability that is around when we cast the golem. And both of those Saws destroy 1 and create 2 creatures with the ability, whether it's an inverter or golem. I still don't see how you get the *3.
I still count only two Saws for each Shapeshifter ability that is around when we cast the golem. And both of those Saws destroy 1 and create 2 creatures with the ability, whether it's an inverter or golem. I still don't see how you get the *3.
That makes it a change of +2; to get the final number, the change has to be added to the initial number.
Wow this combo seems insane. I really like how we need to mulligan to have cards start in the library.
So the main 'engine' of the combo is that we cast Saw on an inverter for 3 life to get two inverter triggers, the first needs to immediately get Saw back, then in response to the other we cast saw again for 3 more life on a bolderbranch golem to gain 3+3 life and the second inverter trigger puts the saw back in the library again.
We can repeat this until we run out of 6 power golem-shapeshifters.
This then gets supercharged in combat because we now have a lot more power and therefore life to work with and can gain life 12, 24, 48 ... or (MUCH) more at a time. We now have a more 'normal' saw in half stage.
I think there might be some clever trigger stacking we can do to do a bit better than those combos, but not enough to change the big O.
I wonder what other applications there might be for these strategies. I imagine they could add at least a layer to 9-card, although I haven't found a method yet. Extending to multiple stages seems trickier.
I guess using one of the ones that needs to hit the opponent could work? though I don't think we can actually attack with small creatures like that... and Karlach, Fury of Avernus is unfortunately legendary
I think World at war works? Instead of exiling black lotus we keep it in play through combat, then after combat we use it to cast world at war from hand, and then use the excess life to cast it as part of the Saw loop.GAH rebound will exile it from the first cast
Edit: yeah I think all of the extra combat cards don't work. They either need to be activated in combat, go infinite, or are legendary. World at War would work if we could get it into the yard post combat.
Speaking of alternatives, a recent Reddit post has gotten me thinking about another possible challenge. This one isn't really focusing on cards as a limit, but the restriction is big enough that this thread feels to me like it might be a better place than the 60-card one.
The original challenge was finding the best way to kill the opponent with a Legacy-legal deck that isn't able to cast spells. The original post suggested a turn 3 kill with Dark Depths, and it looks like a dredge strategy can win on turn 1.
So, to build off that, how much damage could we deal? (Perhaps switching from the Legacy card pool to Vintage, but it might not even matter.) One thing that could be helpful is Priest of Fell Rites, since it can get back arbitrary creatures without casting a spell. Angel of Glory's Rise can turn one reanimation into many, and reanimating creatures can turn into reanimating artifacts and enchantments.
The difference between Legacy and Vintage is actually significant for this. In Vintage, we can get started relatively easily: reveal four Chancellor of the Tangle, play Bazaar of Baghdad and activate it and discard two Chancellors and a Golgari Grave-Troll, cycle Street Wraith and dredge the Golgari Grave-Troll, exile a Simian Spirit Guide for one more mana, exile two Jack-o-Lantern from the graveyard to fix mana, and unearth a Priest of Fell Rites with three remaining non-fixed cards in the graveyard and one in hand (or four in graveyard by discarding one instead of a Chancellor).
In Legacy, it's harder to get started. The Geier Reach Sanitarium method you mentioned in the linked post doesn't leave enough cards to get the mana to unearth a Priest of Fell Rites. Starting with Dakmor Salvage + cycle Edge of Autumn does a bit better; continuing similarly to above does allow unearthing a Priest of Fell Rites on the draw only, with four remaining non-fixed cards in the graveyard. But to do it on the play, I needed to use a more complicated method. Start by revealing two Chancellor of the Tangle and putting three Leyline of Anticipation onto the battlefield. Play Nykthos, Shrine to Nyx and activate it for 6 blue mana. Use the last card -- Waker of Waves -- to put a Golgari Grave-Troll in the graveyard and a Vizier of Tumbling Sands in hand. Cycle that, untapping Nykthos, activate Nykthos again for another 6 blue mana, and dredge the Golgari Grave-Troll with the draw. Then, as before, exile two Jack-o-Lantern from the graveyard to fix mana, and unearth a Priest of Fell Rites with three remaining non-fixed cards in the graveyard.
Speaking of alternatives, a recent Reddit post has gotten me thinking about another possible challenge. This one isn't really focusing on cards as a limit, but the restriction is big enough that this thread feels to me like it might be a better place than the 60-card one.
The original challenge was finding the best way to kill the opponent with a Legacy-legal deck that isn't able to cast spells. The original post suggested a turn 3 kill with Dark Depths, and it looks like a dredge strategy can win on turn 1.
So, to build off that, how much damage could we deal? (Perhaps switching from the Legacy card pool to Vintage, but it might not even matter.) One thing that could be helpful is Priest of Fell Rites, since it can get back arbitrary creatures without casting a spell. Angel of Glory's Rise can turn one reanimation into many, and reanimating creatures can turn into reanimating artifacts and enchantments.
The difference between Legacy and Vintage is actually significant for this. In Vintage, we can get started relatively easily: reveal four Chancellor of the Tangle, play Bazaar of Baghdad and activate it and discard two Chancellors and a Golgari Grave-Troll, cycle Street Wraith and dredge the Golgari Grave-Troll, exile a Simian Spirit Guide for one more mana, exile two Jack-o-Lantern from the graveyard to fix mana, and unearth a Priest of Fell Rites with three remaining non-fixed cards in the graveyard and one in hand (or four in graveyard by discarding one instead of a Chancellor).
In Legacy, it's harder to get started. The Geier Reach Sanitarium method you mentioned in the linked post doesn't leave enough cards to get the mana to unearth a Priest of Fell Rites. Starting with Dakmor Salvage + cycle Edge of Autumn does a bit better; continuing similarly to above does allow unearthing a Priest of Fell Rites on the draw only, with four remaining non-fixed cards in the graveyard. But to do it on the play, I needed to use a more complicated method. Start by revealing two Chancellor of the Tangle and putting three Leyline of Anticipation onto the battlefield. Play Nykthos, Shrine to Nyx and activate it for 6 blue mana. Use the last card -- Waker of Waves -- to put a Golgari Grave-Troll in the graveyard and a Vizier of Tumbling Sands in hand. Cycle that, untapping Nykthos, activate Nykthos again for another 6 blue mana, and dredge the Golgari Grave-Troll with the draw. Then, as before, exile two Jack-o-Lantern from the graveyard to fix mana, and unearth a Priest of Fell Rites with three remaining non-fixed cards in the graveyard.
For 3 cards with unlimited mana: Mondrak, Glory Dominus, Ratadrabik of Urborg, Twinflame making two copies of each; have the originals and one copy of each die to the legend rule, generating six Ratadrabik triggers for Mondrak and four Ratadrabik triggers for Ratadrabik. Resolve the triggers for Mondrak first, getting >2^^6 nonlegendary copies of Mondrak, then resolve the rest for >2^^7 nonlegendary copies of Ratadrabik. Now activate one of the Mondrak tokens, sacrificing the two remaining legendary tokens and getting >2^^7 Ratadrabik triggers for each. Again, resolve the triggers for Mondrak first for >2^^2^^7 copies of Mondrak, and then resolve the rest for >2^^2^^7 copies of Ratadrabik. Those tokens have haste and can attack.
(Cadric, Soul Kindler would have been better if its haste were copiable.)
The total mana consumption is 16, so this can also become a 6-card solution with Black Lotus, Channel, and Chromatic Orrery.
For 3 cards with unlimited mana: Mondrak, Glory Dominus, Ratadrabik of Urborg, Twinflame making two copies of each; have the originals and one copy of each die to the legend rule, generating six Ratadrabik triggers for Mondrak and four Ratadrabik triggers for Ratadrabik. Resolve the triggers for Mondrak first, getting >2^^6 nonlegendary copies of Mondrak, then resolve the rest for >2^^7 nonlegendary copies of Ratadrabik. Now activate one of the Mondrak tokens, sacrificing the two remaining legendary tokens and getting >2^^7 Ratadrabik triggers for each. Again, resolve the triggers for Mondrak first for >2^^2^^7 copies of Mondrak, and then resolve the rest for >2^^2^^7 copies of Ratadrabik. Those tokens have haste and can attack.
(Cadric, Soul Kindler would have been better if its haste were copiable.)
The total mana consumption is 16, so this can also become a 6-card solution with Black Lotus, Channel, and Chromatic Orrery.
Awesome find! I wonder if there's any other deck sizes that would want Mondrak.
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.
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.
Ooh, that's neat. I like the idea of a way to get infinite mana without Lich's Mirror, although that's true that the second Lotus doesn't fit the Vintage legal restriction.
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.
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.
The first Replication Technique can make a second Precursor and use the main Vessel to tuck itself back, then playing Audacious Swap gets two Precursor-Swap triggers. Using Casualty to tuck Vessel lets us replay Technique to get to 12 Precursors and 45 regular golems, so the first Precursor-Swap trigger gives 56 Swaps.
Building a board like this is pretty clunky, especially making new Dralnu's Crusades (copying one and editing it twice costs 5 Swaps), but using the methods here, I think it's enough to set up and run a computation that outputs three or four Knuth arrows. (It helps that having multiple Precursors means we can cast Artificial Evolution once to hack all of our creatures multiple times.) From there, we can replay Scrambleverse to retake all but one of the creatures, then replay Soulblast to kill all those creatures and get a bunch of Bishop triggers that fill our board with a corresponding number of golems we own. Then we can resolve the second Precursor-Swap trigger for a that many Swaps and use them to build a proper computation, and finish with Soulblast.
15-card can add Possibility Storm, which I think gets it to about BB{2}(2^^12). 16-card could add Sakashima's Will to get many computations per Precursor-Swap trigger and reach BB{3}, but honestly, if these actually work, I'm not sure the writeup even needs a 16-card strategy. BB{2}(2^^12) is already a big step over the Eiganjo Uprising 16-card deck.
Edit: I miscounted - it's 12 Precursors, 42 regular golems, 53 Swaps from the trigger. That should still be enough for three arrows, but I think it ends up just below the number we'd need for four.
I did some programming to pin down the damage for this 14 card deck a bit more. Those programs can be found on github. Here's what I figured out:
I found a way to write a waterfall program that runs a given n state, m symbol turing machine using 8+4m+mn clocks and a low number of bishops, under 13 per clock pair. That allows us to explicitly implement a universal turing machine. For example the 15 state, 2 symbol UTM by T. Neary and D. Woods takes roughly 14000 bishops. That UTM is the smallest I found for this conversion.
To simulate a TM using that UTM in MTG we would need roughly 2^(length(encoding(TM))) vanillas for the input. And the encoding(TM) that the UTM requires could be lengthy. But we can generate an initial batch of vanillas by programming the bishops to directly run the BB(15) champion instead of the UTM. Afterwards we can reprogram the bishops to run the UTM and have BB(15) vanillas to use for the input. That is enough to cover any losses from the encoding.
Restarting a computation after writing new input (and optionally reprogramming the bishops) requires casts of Scrambleverse, Arcbond, Artificial Evolution and Soulblast. So we need to resolve 8 Audacious Swap copies for each repetition of the BB computation. So we can roughly say that our final damage will be more than BB^X(15) when we get more than 8X+15000 Audacious Swap copies from the second Precursor Golem trigger.
To figure out how many golems we can get before the second trigger I wrote a simulator, that goes through a given boardstate step by step and can display the results. Obviously I can't run that for long enough to complete even a significant tetration. But the intermediate boardstates have convinced me that the small exponentiation and layer framework described by Deedlit11 works.
Incidentally, I think I have some good cheap computations.
For exponentiation, we can use a heartbeat clock, a part-flooding clock, and a decrement clock. For the heartbeat clock, we will have one creature that keeps dying and creating another creature, and also creating another creature for the decrement clock, so the decrement clock will normally stay the same. The part-flooding clock will still have a "special" creature type, and we will have one creature of that special type that will create another one when it dies. But we will have two Bishop of Wingss for the non-special creature type, so that when they die, twice as many of the non-special ones get created. The special creature type dying will also create a creature for the heartbeat clock, delaying the heartbeat one turn, causing the decrement clock to go down 1. So each time the part-flooding group dies, the number of non-special creatures double, and the decrement clock goes down by 1. So when the decrement clock goes from N down to 0, the nonspecial creatures will have doubled N times, so this gives us exponentiation. (So the decrement clock is the input clock and the clock causing the computation to halt, and the part-flooding clock is the output clock.)
I think we just need one creature type for the decrement clock, which can be Samurai if we use Eiganjo Uprising for the opponent's creatures. For the heartbeat clock, I think we can also use one creature type, and have maybe 4 copies of Bishop of Wings, which, when a creature of the heartbeat type dies, will create a creature of the heartbeat type, a creature of the decrement type, and two creatures of the same type as Bishop of Wings, to keep those creatures from dying. (So I guess that type can be the output clock, since we will have the most of those.) If we make Angel the heartbeat creature type, we will need 4 copies of AE to hack the Bishops. For the part-flooding type, we will need two creature types, one copy of Dralnu's Crusade to make the special creature type to also be the non-special creature type, and 4 copies of Bishop of Wings, 1 to create a special creature when the special creature dies, 1 to create a heartbeat creature when the special creature dies, and 2 to create 2 non-special creatures whenever a non-special creature dies. So that looks like 10 copies of AE needed, but we can save 2 AE's by using Spirit for one of the creature types.
So, we will need 1 Dralnu's Crusade, 8 Bishop of Wings, and 12 Artifical Evolutions, not counting what we need for input. For input, we need 1 each of heartbeat/special/non-special, then the rest go into the decrement creature type. I guess we will need another 3 AEs, for 15 total.
For tetration, we can turn the decrement clock into a second part-flooding clock, and make another decrement clock and heartbeat clock. So the original heartbeat clock and part-flooding clock work exactly the same way, except the heartbeat clock now creates one of the second part-flooding clock rather than the new decrement clock. So the second part-flooding clock decrements once each time the first part-flooding clock hits 0, so if the second part-flooding clock starts at N, we will double the first part-flooding clock N times before the second hits 0. Then, we will create a special creature for each special creature that dies (so we only need one Bishop of Wings here rather than two), which will be more than 2^N, since we add a special creature to the second pf clock each time the first pf clock decrements without hitting 0. We also have a second heartbeat clock that will maintain the new decrement clock, and the second pf clock will increment the second heartbeat clock when it dies, causing the decrement clock to decrement. So the decrement clock will decrement each time the second pf clock hits 0, resulting in an exponentiation. So if the decrement clock starts at N, we will exponentiate the second pf clock N times, resulting in more than 2^^N output.
Counting things up, the first heartbeat clock requires 4 copies of Bishop of Wings, the first part-flooding clock requires 4 copies of Bishops and 1 Dralnu's Crusade, the second heartbeat clock requires 2 copies of Bishops, the second part-flooding clock requires 3 copies of Bishops and 1 Dralnu's Crusade, and the decrement clock doesn't require anything. So it looks like we need 2 Dralnu's Crusades and 13 Bishop of Wings, along with one creature of each of the 6 creature types we need other than the decrement creature type. We will need 30 AE's if I've counted correctly.
More generally, it looks like each additional Knuth arrow will use up one more Dralnu's Crusades, 5 more Bishop of Wings, 3 more creature types used, and 3 more creatures of types besides the decrement type, along with 15 more copies of AE.
I'm not quite sure how to make things work with Xathrid Necromancers in the most efficient way; it looks like the numbers are going to be considerably higher. Maybe I'll look at it later.
My initial concern was that there is some accumulation of vanillas in the heartbeat clocks everytime you stop them for a step. But while that does make them beat slower afterwards they also become correspondingly more powerful. That does make it annoying to formally prove the construction does what we expect, but it should still work. The decreasing variables of the layer sequence become (life(input)-life(heartbeat_input)) instead of the simple life(input) that we would have without the growing heartbeat.
With that construction we can squeeze a hexation out of the initial 53 Audations Swap casts. And since we can use all the bishops of that program as input as well it is even a pretty big one. I think we reach 2^^^^24 with this construction.
Here are the costs in Audacious Swap casts I get for that:
The free Vanillas are the 5 Vanillas that are targeted by Audacious Swap copies, one of which gets exiled to cast Soulblast. The 6th free Vanilla is the target of the original Audacious Swap, that didn't get a copy targeting it. The program ensures that the 4 vanillas targeted by Audacious Swap survive the computation, along with a Bishop that turns the output into Golems. If I forgot anything that should be included in the costs please let me know.
Operations like -15000 and /8 just disappear in the rounding with numbers like 2^^^^24. So my conclusion is that this 14 card deck can deal more than BB^(2^^^^24)(15) damage.
The first Replication Technique can make a second Precursor and use the main Vessel to tuck itself back, then playing Audacious Swap gets two Precursor-Swap triggers. Using Casualty to tuck Vessel lets us replay Technique to get to 12 Precursors and 45 regular golems, so the first Precursor-Swap trigger gives 56 Swaps.
Building a board like this is pretty clunky, especially making new Dralnu's Crusades (copying one and editing it twice costs 5 Swaps), but using the methods here, I think it's enough to set up and run a computation that outputs three or four Knuth arrows. (It helps that having multiple Precursors means we can cast Artificial Evolution once to hack all of our creatures multiple times.) From there, we can replay Scrambleverse to retake all but one of the creatures, then replay Soulblast to kill all those creatures and get a bunch of Bishop triggers that fill our board with a corresponding number of golems we own. Then we can resolve the second Precursor-Swap trigger for a that many Swaps and use them to build a proper computation, and finish with Soulblast.
15-card can add Possibility Storm, which I think gets it to about BB{2}(2^^12). 16-card could add Sakashima's Will to get many computations per Precursor-Swap trigger and reach BB{3}, but honestly, if these actually work, I'm not sure the writeup even needs a 16-card strategy. BB{2}(2^^12) is already a big step over the Eiganjo Uprising 16-card deck.
Edit: I miscounted - it's 12 Precursors, 42 regular golems, 53 Swaps from the trigger. That should still be enough for three arrows, but I think it ends up just below the number we'd need for four.
I did some programming to pin down the damage for this 14 card deck a bit more. Those programs can be found on github. Here's what I figured out:
I found a way to write a waterfall program that runs a given n state, m symbol turing machine using 8+4m+mn clocks and a low number of bishops, under 13 per clock pair. That allows us to explicitly implement a universal turing machine. For example the 15 state, 2 symbol UTM by T. Neary and D. Woods takes roughly 14000 bishops. That UTM is the smallest I found for this conversion.
To simulate a TM using that UTM in MTG we would need roughly 2^(length(encoding(TM))) vanillas for the input. And the encoding(TM) that the UTM requires could be lengthy. But we can generate an initial batch of vanillas by programming the bishops to directly run the BB(15) champion instead of the UTM. Afterwards we can reprogram the bishops to run the UTM and have BB(15) vanillas to use for the input. That is enough to cover any losses from the encoding.
Restarting a computation after writing new input (and optionally reprogramming the bishops) requires casts of Scrambleverse, Arcbond, Artificial Evolution and Soulblast. So we need to resolve 8 Audacious Swap copies for each repetition of the BB computation. So we can roughly say that our final damage will be more than BB^X(15) when we get more than 8X+15000 Audacious Swap copies from the second Precursor Golem trigger.
To figure out how many golems we can get before the second trigger I wrote a simulator, that goes through a given boardstate step by step and can display the results. Obviously I can't run that for long enough to complete even a significant tetration. But the intermediate boardstates have convinced me that the small exponentiation and layer framework described by Deedlit11 works.
Incidentally, I think I have some good cheap computations.
For exponentiation, we can use a heartbeat clock, a part-flooding clock, and a decrement clock. For the heartbeat clock, we will have one creature that keeps dying and creating another creature, and also creating another creature for the decrement clock, so the decrement clock will normally stay the same. The part-flooding clock will still have a "special" creature type, and we will have one creature of that special type that will create another one when it dies. But we will have two Bishop of Wingss for the non-special creature type, so that when they die, twice as many of the non-special ones get created. The special creature type dying will also create a creature for the heartbeat clock, delaying the heartbeat one turn, causing the decrement clock to go down 1. So each time the part-flooding group dies, the number of non-special creatures double, and the decrement clock goes down by 1. So when the decrement clock goes from N down to 0, the nonspecial creatures will have doubled N times, so this gives us exponentiation. (So the decrement clock is the input clock and the clock causing the computation to halt, and the part-flooding clock is the output clock.)
I think we just need one creature type for the decrement clock, which can be Samurai if we use Eiganjo Uprising for the opponent's creatures. For the heartbeat clock, I think we can also use one creature type, and have maybe 4 copies of Bishop of Wings, which, when a creature of the heartbeat type dies, will create a creature of the heartbeat type, a creature of the decrement type, and two creatures of the same type as Bishop of Wings, to keep those creatures from dying. (So I guess that type can be the output clock, since we will have the most of those.) If we make Angel the heartbeat creature type, we will need 4 copies of AE to hack the Bishops. For the part-flooding type, we will need two creature types, one copy of Dralnu's Crusade to make the special creature type to also be the non-special creature type, and 4 copies of Bishop of Wings, 1 to create a special creature when the special creature dies, 1 to create a heartbeat creature when the special creature dies, and 2 to create 2 non-special creatures whenever a non-special creature dies. So that looks like 10 copies of AE needed, but we can save 2 AE's by using Spirit for one of the creature types.
So, we will need 1 Dralnu's Crusade, 8 Bishop of Wings, and 12 Artifical Evolutions, not counting what we need for input. For input, we need 1 each of heartbeat/special/non-special, then the rest go into the decrement creature type. I guess we will need another 3 AEs, for 15 total.
For tetration, we can turn the decrement clock into a second part-flooding clock, and make another decrement clock and heartbeat clock. So the original heartbeat clock and part-flooding clock work exactly the same way, except the heartbeat clock now creates one of the second part-flooding clock rather than the new decrement clock. So the second part-flooding clock decrements once each time the first part-flooding clock hits 0, so if the second part-flooding clock starts at N, we will double the first part-flooding clock N times before the second hits 0. Then, we will create a special creature for each special creature that dies (so we only need one Bishop of Wings here rather than two), which will be more than 2^N, since we add a special creature to the second pf clock each time the first pf clock decrements without hitting 0. We also have a second heartbeat clock that will maintain the new decrement clock, and the second pf clock will increment the second heartbeat clock when it dies, causing the decrement clock to decrement. So the decrement clock will decrement each time the second pf clock hits 0, resulting in an exponentiation. So if the decrement clock starts at N, we will exponentiate the second pf clock N times, resulting in more than 2^^N output.
Counting things up, the first heartbeat clock requires 4 copies of Bishop of Wings, the first part-flooding clock requires 4 copies of Bishops and 1 Dralnu's Crusade, the second heartbeat clock requires 2 copies of Bishops, the second part-flooding clock requires 3 copies of Bishops and 1 Dralnu's Crusade, and the decrement clock doesn't require anything. So it looks like we need 2 Dralnu's Crusades and 13 Bishop of Wings, along with one creature of each of the 6 creature types we need other than the decrement creature type. We will need 30 AE's if I've counted correctly.
More generally, it looks like each additional Knuth arrow will use up one more Dralnu's Crusades, 5 more Bishop of Wings, 3 more creature types used, and 3 more creatures of types besides the decrement type, along with 15 more copies of AE.
I'm not quite sure how to make things work with Xathrid Necromancers in the most efficient way; it looks like the numbers are going to be considerably higher. Maybe I'll look at it later.
My initial concern was that there is some accumulation of vanillas in the heartbeat clocks everytime you stop them for a step. But while that does make them beat slower afterwards they also become correspondingly more powerful. That does make it annoying to formally prove the construction does what we expect, but it should still work. The decreasing variables of the layer sequence become (life(input)-life(heartbeat_input)) instead of the simple life(input) that we would have without the growing heartbeat.
With that construction we can squeeze a hexation out of the initial 53 Audations Swap casts. And since we can use all the bishops of that program as input as well it is even a pretty big one. I think we reach 2^^^^24 with this construction.
Here are the costs in Audacious Swap casts I get for that:
The free Vanillas are the 5 Vanillas that are targeted by Audacious Swap copies, one of which gets exiled to cast Soulblast. The 6th free Vanilla is the target of the original Audacious Swap, that didn't get a copy targeting it. The program ensures that the 4 vanillas targeted by Audacious Swap survive the computation, along with a Bishop that turns the output into Golems. If I forgot anything that should be included in the costs please let me know.
Operations like -15000 and /8 just disappear in the rounding with numbers like 2^^^^24. So my conclusion is that this 14 card deck can deal more than BB^(2^^^^24)(15) damage.
The costs look good to me, assuming I haven't forgotten anything. I'm not sure how to evaluate more than that, but it sounds great!
Private Mod Note
():
Rollback Post to RevisionRollBack
To post a comment, please login or register a new account.
Speaking of alternatives, a recent Reddit post has gotten me thinking about another possible challenge. This one isn't really focusing on cards as a limit, but the restriction is big enough that this thread feels to me like it might be a better place than the 60-card one.
The original challenge was finding the best way to kill the opponent with a Legacy-legal deck that isn't able to cast spells. The original post suggested a turn 3 kill with Dark Depths, and it looks like a dredge strategy can win on turn 1.
So, to build off that, how much damage could we deal? (Perhaps switching from the Legacy card pool to Vintage, but it might not even matter.) One thing that could be helpful is Priest of Fell Rites, since it can get back arbitrary creatures without casting a spell. Angel of Glory's Rise can turn one reanimation into many, and reanimating creatures can turn into reanimating artifacts and enchantments.
I don't think there's a way to use Saw in Half or Artificial Evolution under these conditions, but I think we could still hit Graham's Number with the help of Toralf, God of Fury.
The main improvement is that Renegade Doppelganger or Unstable Shapeshifter can serve the purpose of Doubling Season, without needing an extra card (which was Astral Dragon). The downside of this is lower initial growth rates; I brought the growth rate back up a bit with precise card selection.
Start with Black Lotus and Show and Tell to put Bolas's Citadel onto the battlefield.
Cast Boulderbranch Golem from library. (-7, +6; 19 life)
Cast Saw in Half from library, targeting Boulderbranch Golem. (-3, +6; 22 life)
Cast Inverter of Truth from library; it moves Black Lotus, Show and Tell, Boulderbranch Golem, and Saw in Half from graveyard into library. (-4; 18 life)
Cast Black Lotus, and cast Boulderbranch Golem. (-7, +6; 17 life)
Cast Saw in Half on Inverter of Truth. Two copies trigger. (-3; 14 life)
The first trigger exiles Show and Tell and sends Saw in Half and Inverter of Truth into the library.
Before the second trigger resolves, sacrifice Black Lotus for 3 mana, and cast Saw in Half targeting Boulderbranch Golem. (-3, +6; 17 life)
The second trigger exiles Inverter of Truth and sends Black Lotus, Saw in Half, and Boulderbranch Golem into the library.
Cast Black Lotus, and cast Boulderbranch Golem. (-7, +6; 16 life)
Cast Saw in Half on an Inverter of Truth. Two copies trigger. (-3; 13 life)
The first trigger sends Saw in Half into the library.
Before the second trigger resolves, sacrifice Black Lotus for 3 mana, and cast Saw in Half targeting Boulderbranch Golem. (-3, +6; 16 life)
The second trigger sends Black Lotus, Saw in Half, and Boulderbranch Golem into the library.
With enough mana now, cast Unstable Shapeshifter from hand, and then cast Black Lotus and Boulderbranch Golem (-7, +6; 15 life); Unstable Shapeshifter becomes a copy of Boulderbranch Golem.
Cast Saw in Half on an Inverter of Truth. (-3; 12 life) Two copies trigger, and Unstable Shapeshifter triggers twice; put the Inverter triggers on top.
The first Inverter trigger sends Saw in Half into the library.
Before the second trigger resolves, sacrifice Black Lotus for 3 mana, and cast Saw in Half targeting the Shapeshifter-Golem. (-3, +6; 15 life)
The second trigger sends Black Lotus, Saw in Half, and Unstable Shapeshifter into the library.
Cast Black Lotus one more time, then cast another pair of Saws on an Inverter and the original Golem (life-neutral). (Unstable Shapeshifter gets exiled.)
Cast Boulderbranch Golem. (-7, +6; 14 life) Both Shapeshifters trigger to become the full 6/5 Golem.
Let those triggers resolve one by one, and after each one resolves, cast another life-neutral Saw pair on an Inverter and the 6/5 Shapeshifter-Golem. There are now four Unstable Shapeshifters, two copying 3/3 Golems and two copying Inverters.
Now we can begin the full loop:
This can be repeated 7 times, ending with 7 life and 9841 Shapeshifters.
Cast the final card, Life of the Party, from hand. All the Shapeshifters turn into that.
Attack with all possible creatures, getting triggers from Life of the Party and the Shapeshifter copies of it; put the original's trigger on the bottom.
Cast a Saw pair on an Inverter and the original Golem, this time letting the triggers turning Shapeshifters into Inverters resolve first, so that afterwards they become Golems and get to stay Golems for a while.
A trigger from Life of the Party resolves, giving a big boost to the power of a Shapeshifter that is now copying a Golem. Start Sawing again with that one.
(As before, leave the high-value Shapeshifter triggers on the stack until they are ready to be consumed. Now that there is excess life being gained from the big Golems, it can be spent on extra Saws on small Golems. This should work out to a number of Knuth arrows somewhere around the base-2 logarithm of the starting power.)
Repeat with each Life of the Party trigger, until the final one resolves for the original Life of the Party, which is left to deal the big damage.
Some other things I found:
Also attaining F_{w+1}, but not as high, and only on the draw: Black Lotus, Channel, Chromatic Orrery, Unstable Shapeshifter, Mycoid Shepherd, Saw in Half, Soulfire Grand Master, Life of the Party
Some cards with dual-purpose potential: Conclave Mentor, Packsong Pup, Swiftgear Drake
That would result in 512 shapeshifters instead of 9841. That should still be enough to beat grahams number though.
I had another run in with the "oracle text" on mtgsalvation. It says "Whenever another creature enters the battlefield, Unstable Shapeshifter becomes a copy of that creature and gains this ability." That would lead to the combo not working, since the Saw in Half copies of a shapeshifter that has become a copy of the golem or inverter would just be that golem or inverter. The shapeshifter ability would not be transferred to the new copies since it was only gained later.
Fortunately the actual gatherer text is "Whenever another creature enters the battlefield, Unstable Shapeshifter becomes a copy of that creature, except it has this ability." It gives the shapeshifter ability by modifying the copy effect with an "except", so the ability gets copied properly onto the Saw in Half copies.
So as far as I can tell the combo should work. That's an amazing build!
EDIT: Wait. How are we casting Boulderbranch Golem for the loop with Unstable Shapeshifter triggers on the stack? Or in combat?
We're not. Boulderbranch Golem is only cast after each batch of Shapeshifter triggers is finished, and is no longer cast once we attack.
I still count only two Saws for each Shapeshifter ability that is around when we cast the golem. And both of those Saws destroy 1 and create 2 creatures with the ability, whether it's an inverter or golem. I still don't see how you get the *3.
So the main 'engine' of the combo is that we cast Saw on an inverter for 3 life to get two inverter triggers, the first needs to immediately get Saw back, then in response to the other we cast saw again for 3 more life on a bolderbranch golem to gain 3+3 life and the second inverter trigger puts the saw back in the library again.
We can repeat this until we run out of 6 power golem-shapeshifters.
This then gets supercharged in combat because we now have a lot more power and therefore life to work with and can gain life 12, 24, 48 ... or (MUCH) more at a time. We now have a more 'normal' saw in half stage.
I think there might be some clever trigger stacking we can do to do a bit better than those combos, but not enough to change the big O.
I guess using one of the ones that needs to hit the opponent could work? though I don't think we can actually attack with small creatures like that... and Karlach, Fury of Avernus is unfortunately legendary
GAH rebound will exile it from the first castI think World at war works? Instead of exiling black lotus we keep it in play through combat, then after combat we use it to cast world at war from hand, and then use the excess life to cast it as part of the Saw loop.
Edit: yeah I think all of the extra combat cards don't work. They either need to be activated in combat, go infinite, or are legendary. World at War would work if we could get it into the yard post combat.
Edit: Hmm, maybe something before combat then? Maybe an X cost pump effect like Exponential growth or Finale of devastation?
I have done some looking into that challenge.
The difference between Legacy and Vintage is actually significant for this. In Vintage, we can get started relatively easily: reveal four Chancellor of the Tangle, play Bazaar of Baghdad and activate it and discard two Chancellors and a Golgari Grave-Troll, cycle Street Wraith and dredge the Golgari Grave-Troll, exile a Simian Spirit Guide for one more mana, exile two Jack-o-Lantern from the graveyard to fix mana, and unearth a Priest of Fell Rites with three remaining non-fixed cards in the graveyard and one in hand (or four in graveyard by discarding one instead of a Chancellor).
In Legacy, it's harder to get started. The Geier Reach Sanitarium method you mentioned in the linked post doesn't leave enough cards to get the mana to unearth a Priest of Fell Rites. Starting with Dakmor Salvage + cycle Edge of Autumn does a bit better; continuing similarly to above does allow unearthing a Priest of Fell Rites on the draw only, with four remaining non-fixed cards in the graveyard. But to do it on the play, I needed to use a more complicated method. Start by revealing two Chancellor of the Tangle and putting three Leyline of Anticipation onto the battlefield. Play Nykthos, Shrine to Nyx and activate it for 6 blue mana. Use the last card -- Waker of Waves -- to put a Golgari Grave-Troll in the graveyard and a Vizier of Tumbling Sands in hand. Cycle that, untapping Nykthos, activate Nykthos again for another 6 blue mana, and dredge the Golgari Grave-Troll with the draw. Then, as before, exile two Jack-o-Lantern from the graveyard to fix mana, and unearth a Priest of Fell Rites with three remaining non-fixed cards in the graveyard.
For 3 cards with unlimited mana: Mondrak, Glory Dominus, Ratadrabik of Urborg, Twinflame making two copies of each; have the originals and one copy of each die to the legend rule, generating six Ratadrabik triggers for Mondrak and four Ratadrabik triggers for Ratadrabik. Resolve the triggers for Mondrak first, getting >2^^6 nonlegendary copies of Mondrak, then resolve the rest for >2^^7 nonlegendary copies of Ratadrabik. Now activate one of the Mondrak tokens, sacrificing the two remaining legendary tokens and getting >2^^7 Ratadrabik triggers for each. Again, resolve the triggers for Mondrak first for >2^^2^^7 copies of Mondrak, and then resolve the rest for >2^^2^^7 copies of Ratadrabik. Those tokens have haste and can attack.
(Cadric, Soul Kindler would have been better if its haste were copiable.)
The total mana consumption is 16, so this can also become a 6-card solution with Black Lotus, Channel, and Chromatic Orrery.
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.
Edit: I guess if we allow un cards, black lotus into mana screw gets us there with any of Energy Refractor/Gemstone Array/Chromatic Orrery/prismite etc.
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.
I did some programming to pin down the damage for this 14 card deck a bit more. Those programs can be found on github. Here's what I figured out:
I found a way to write a waterfall program that runs a given n state, m symbol turing machine using 8+4m+mn clocks and a low number of bishops, under 13 per clock pair. That allows us to explicitly implement a universal turing machine. For example the 15 state, 2 symbol UTM by T. Neary and D. Woods takes roughly 14000 bishops. That UTM is the smallest I found for this conversion.
To simulate a TM using that UTM in MTG we would need roughly 2^(length(encoding(TM))) vanillas for the input. And the encoding(TM) that the UTM requires could be lengthy. But we can generate an initial batch of vanillas by programming the bishops to directly run the BB(15) champion instead of the UTM. Afterwards we can reprogram the bishops to run the UTM and have BB(15) vanillas to use for the input. That is enough to cover any losses from the encoding.
Restarting a computation after writing new input (and optionally reprogramming the bishops) requires casts of Scrambleverse, Arcbond, Artificial Evolution and Soulblast. So we need to resolve 8 Audacious Swap copies for each repetition of the BB computation. So we can roughly say that our final damage will be more than BB^X(15) when we get more than 8X+15000 Audacious Swap copies from the second Precursor Golem trigger.
To figure out how many golems we can get before the second trigger I wrote a simulator, that goes through a given boardstate step by step and can display the results. Obviously I can't run that for long enough to complete even a significant tetration. But the intermediate boardstates have convinced me that the small exponentiation and layer framework described by Deedlit11 works.
My initial concern was that there is some accumulation of vanillas in the heartbeat clocks everytime you stop them for a step. But while that does make them beat slower afterwards they also become correspondingly more powerful. That does make it annoying to formally prove the construction does what we expect, but it should still work. The decreasing variables of the layer sequence become (life(input)-life(heartbeat_input)) instead of the simple life(input) that we would have without the growing heartbeat.
With that construction we can squeeze a hexation out of the initial 53 Audations Swap casts. And since we can use all the bishops of that program as input as well it is even a pretty big one. I think we reach 2^^^^24 with this construction.
Here are the costs in Audacious Swap casts I get for that:
The free Vanillas are the 5 Vanillas that are targeted by Audacious Swap copies, one of which gets exiled to cast Soulblast. The 6th free Vanilla is the target of the original Audacious Swap, that didn't get a copy targeting it. The program ensures that the 4 vanillas targeted by Audacious Swap survive the computation, along with a Bishop that turns the output into Golems. If I forgot anything that should be included in the costs please let me know.
Operations like -15000 and /8 just disappear in the rounding with numbers like 2^^^^24. So my conclusion is that this 14 card deck can deal more than BB^(2^^^^24)(15) damage.