One advantage to a double spell stage is that one of them can be the Tibalt's Trickery used in the opening as the way to counter the useful spell. Something like Quandrix command? Though some shenanigans are needed to make those mana costs line up nicely...
Hmm, I'm not seeing how to get the loop going with just one copy of Tibalt's Trickery and Quandrix Command. A second copy of Quandrix Command can make it work I think.
For the mana, I guess we need either blue or green to be cheap, and then have something that requires a Tibalt's Trickery for a red or the other of blue/green.
Speaking of slow starts, I took a look at an even more recent focus. I couldn't find a way to play a Turn 1 Tibalt's Trickery in either Standard format it's in, An Offer You Can't Refuse feels like it should work but there's nothing 0-mana to hit with it. Taking the most recent 9 sets of Pioneer would add Tormod's Crypt as an option, but I had a hard time keeping Offer from going infinite.
So I tried Turn 2 instead, which is enough time to go off in ELD-AFR Standard. I don't know what people have previously come up with for this card pool, but the results here (assuming they work) are pretty entertaining regardless.
Ashaya + Moraug generate a ton of combat phases, which avoids going infinite because Moraug's trigger only works during main phases and because Ashaya doesn't turn tokens into lands. Den of the Bugbear can be cloned once it's animated, but later copies will enter tapped and therefore only be usable with the help of a fresh Witherbloom. When we're entering the Toralf section, we'll need Aberrant Mind Sorcerer to stick something back on top of our library so Clackbridge Troll doesn't deck us, we can then draw it with Charge Through. Between big combat steps, we'll use excess damage to clean up all of our attacking Surtland Flingers, as well as any opposing Goat tokens.
My impression is that the initial round of Moraug combats end up just being a chance to get a bunch of untaps, then the second main phase is where we can play our final combo pieces and clone a bunch of lands. The first combat of the second batch should be where we hit Graham's number, and then we can just keep going from there.
Edit: I'd dismissed An Offer You Can't Refuse based on earlier strategies where I was trying to use Lithoform Blight to only gate certain colors of mana, but switching to Beledros Witherbloom makes things a lot simpler. I think we're fine as long as we stay away from 1-mana instants.
Losing Genesis Ultimatum sounds painful, but if we expand to IKO-SNC, I think we can port most of the above into a 19-card Turn 1 strat:
Edit: Wait, do we even need Toralf and Troll/Specialist for these? Even before accounting for them, the Witherbloom combo looks pretty busy beaver-y to me.
For the last four years of Standard, we have written threads for the max damage challenge for each format. For those interested, we got:
2018-2019 A stage plus a bunch of layers on turn 2. (F_{w+?}(?))
2019-2020 3 stages and 6 layers on turn 3. (F_{w3+6}(51))
2020-2021 2 stages and 7 layers on turn 2. (F_{w2+7}(F_{w2+7}(F_w2+5}(49))))
2021-2022 4 stages and 8 layers on turn 2. (F_{w4+8}(18))
We still have time to adjust the last deck, in case anyone is interested!
Anyway, for the latest standard we used Tibalt's Trickery to bring out Wizard's Spellbook, and then tap it to exile Invoke the Winds and untap it. We can keep activating it to untap it and cast new spells, so this is a pretty efficient way to get started.
@CaptainMarcia: Could you explain the Beledros Witherbloom combo in more detail?
Update on the 7-card challenge: If, in the Precursor Golem deck, we replace Wheel of Sun and Moon with Junktroller, we will bump up the damage from more than 2^^2^^6 to more than 2^^2^^8 - assuming we have an enpty library. This beats out the Devilish Valet deck very narrowly, since the number of Precursor Golems when the second Precursor Golem trigger for Sudden Strength is resolved will match the number of Elemental tokens when Conclave Phalanx is resolved, but in the former deck we have many more vanilla Golems and Junktrollers.
For the last four years of Standard, we have written threads for the max damage challenge for each format. For those interested, we got:
2018-2019 A stage plus a bunch of layers on turn 2. (F_{w+?}(?))
2019-2020 3 stages and 6 layers on turn 3. (F_{w3+6}(51))
2020-2021 2 stages and 7 layers on turn 2. (F_{w2+7}(F_{w2+7}(F_w2+5}(49))))
2021-2022 4 stages and 8 layers on turn 2. (F_{w4+8}(18))
We still have time to adjust the last deck, in case anyone is interested!
Anyway, for the latest standard we used Tibalt's Trickery to bring out Wizard's Spellbook, and then tap it to exile Invoke the Winds and untap it. We can keep activating it to untap it and cast new spells, so this is a pretty efficient way to get started.
@CaptainMarcia: Could you explain the Beledros Witherbloom combo in more detail?
Update on the 7-card challenge: If, in the Precursor Golem deck, we replace Wheel of Sun and Moon with Junktroller, we will bump up the damage from more than 2^^2^^6 to more than 2^^2^^8 - assuming we have an enpty library. This beats out the Devilish Valet deck very narrowly, since the number of Precursor Golems when the second Precursor Golem trigger for Sudden Strength is resolved will match the number of Elemental tokens when Conclave Phalanx is resolved, but in the former deck we have many more vanilla Golems and Junktrollers.
We play Gift on the Sorcerer to get a bunch of recursion triggers, then counter it with Trickery so we can start picking it back up. We then replay Gift on Witherbloom to refresh her, and spend 10 life to untap all of our lands. However many lands we have, we can spend most of that mana to double our Orvars that many times, refreshing the Sorcerer as necessary so we can keep recycling Gift and Trickery. When we're about to run out of mana, we use one of our last Gifts to copy the Den of the Bugbear, making a bunch of (tapped) copies of it, then we refresh Witherbloom again to spend another 10 life and use all of our new lands. Repeat until we run out of life.
If we're in the middle of using Surtland Flinger, most of these Gifts would go to the same Orvar token, so that once we're ready for the next Flinger trigger, it can throw that Orvar for increased damage. (We'll also need to save some mana to start the next round.) If skipping Toralf is an option, we can use a Gift to give lifelink to the next Flinger and have it throw the Orvar at itself. (In that version of the deck, we'd probably replace Crash Through with something like Infuriate, due to no longer needing to draw cards.)
Unfortunately it isn't Busy Beaver, nor is it arrow stacking like the Toralf stage. Each time we cast Alchmist's Gift, we double the number of Orvars. So X mana becomes 2^X lands, and paying 10 life turns that into mana again. So 10X creates 2^^X copies of whatever creature we want.
To get the Busy Beaver function, we need to implement a Turing-complete computational model; the model we chose for our Vintage deck was the Waterfall model. (jfb1337's idea). We have to be able to create any possible program/input up to whatever size limitation, in order to be sure that we are actually implementing the Busy Beaver function.
To get the Ackermann function, we have a couple of ways of doing it. The more traditional way is to have a bunch of alternating groups of spells abilities on the stack. The topmost group increases "the number" that we are trying to maximize, then when we resolve down to the second group from the top, we resolve one (or a fixed number) of abilities from the second group, and that allows us to create "the number" copies of abilities for the topmost group again. When we resolve down to the third group from the top, we resolve one of the abilities from the third group, then create the top two layers with "the number" of copies.
Of course, we need some mechanism that allows us to recreate our groups of abilities back up to the topmost group, without allowing us to create any more. This is done by a "stage resource", like mana, life, or creature tokens. We spend mana for each group or pair of groups to build X or 2X groups, then as we resolve the groups, we build up mana that we can then spend to exactly recreate the missing groups without gaining any more. We keep resolving until all the group sizes go to zero.
The other way is to have ability groups intrinsically come attached with some natural number. This is what we first thought of, but with permanents using power/toughness or counters. Instead, the only implementation came recently for the stack, using Toralf abilities, with the attached number being damage.
So yeah, we will still need Toralf or some other stage implementation.
We should really move this conversation to the standard thread.
Its a bit of a shame current standard doesn't have any 0 mv spells, though we still get to go off turn 2 with exactly: untapped red land goldhound untapped land, 1mv spell + Tibalt's trickery into Wizard's Spellbook.
The "quick" overview on the current standard deck is:
Setup: get 1/1 nonlegendary copies of Jin and Orvar, and unmodified copies of our utility creatures (mage's attendant and Aberrant Mind sorcerer especially) then cast first day of class for haste, + Arlinn for creatureflash, and Sigarda's Summons for flying.
Cast (and counter!) vanquish the weak to copy our creatures, doing slightly worse than doubling the orvars for every 4 mana.
G stage
G gives X black mana by casting the pump mode of Choose your weapon on a snow covered swamp animated via Avalanche caller. This also lets us cast Skyclave shade from the graveyard.
Use most of this black to make more utility creatures, counter and return any real spells on the stack and end with making X Jins.
Skyclave shade taps for G thanks to Ashaya, Soul of the Wild.
G for the archery mode of Choose your weapon gets X copies, two of which kill skyclave shade ready for the next landfall trigger. (Use the remaining black to get choose your weapon back.)
W stage
W for thraben exorcism makes copies of an enchantment. Path to the world tree fetches the plains, scaled herbalist puts it in play, tap for w, sac it to Roiling Regrowth Boseiju Reaches Skyward (chapter 2 via Vorinclex, Monstrous Raider) puts it back in the library.
(we can net green mana in here by saccing the swamp and skyclave shade to roiling regrowth and getting two casts of skyclave shade each of which taps for G)
A few layers after to round out the deck:
meeting of the five to cast the charm
tibalt's trickery to cast meeting of the five
sea gate storm caller so tibalt's trickery can cast tibalt's trickery.
Xorn for more treasures for red
Thieves' Tools for treasures
Jin gitaxias for more ETBs
Lithoform engine+spectral steel for more casts.
There probably isn't a working w^4 deck, all the iisted decks were works in progress.
The general idea for the extra GDD ETB is to require it for some essential pupose that doesn't extend the hyperstage. I suppose if we have something that can bring it back from outside our hand, like Moggcatcher, we won't get that extra ETB.
Remind me, how do we get infinite use of Rebuild without needing expensive things like a GDD ETB or a sorcery flashback?
Play Vedalken Orrery for Mirrorworks triggers, then spend 3 life to flashback Acorn Harvest, and let Spellweaver Volute resolve to cast Smite the Monstrous. Even if we have only 1 TYS, it can still copy many instances of Smite, pushing many PB triggers on the stack. The stack looks like this:
top
Smite the Monstrous-PB
Smite the Monstrous-PB
...
Smite the Monstrous-PB
Smite the Monstrous-PB
some Smite the Monstrous copies from TYS
Smite the Monstrous copy from Spellweaver Volute
Mirrorworks trigger of Vedalken Orrery
Bounce Vedalken Orrery to hand; there is still one token of it. Next, for each Smite the Monstrous-PB trigger, we can do these:
play Goblin Dark-Dwellers for ETB, casting Rebuild
Mirrorworks trigger resolves, having a token Vedalken Orrery
replay our various artifacts; we can even increase number of our enchantments; near the end, we may hold PB and TYS card in hand.
...Until there are 3 Smite the Monstrous-PB triggers. Use one to bounce Horobi, use another one to bounce Goblin Dark-Dwellers, but do not play the usual things. Only get Cowardice in hand.
Let the final Smite the Monstrous-PB trigger redirect the Smite, and resolve the Smite to destroy Child of Alara. The stack looks like this:
top
Mimic Vat trigger with Child of Alara
death trigger of Child of Alara
Verdant Succession trigger of Child of Alara
some Smite the Monstrous copies from TYS
Smite the Monstrous copy from Spellweaver Volute
Mirrorworks trigger of Vedalken Orrery
Use Mimic Vat to exile Child of Alara, and use Mirror of Fate to put it in library. Play Goblin Dark-Dwellers, Rebuild/keep our artifacts in hand.
After death trigger swept out everything (and we gained 3 life from Centaur Safeguard; the other Centaur Safeguard went to board), Verdant Succession trigger bring Child of Alara back. Then Mirrorworks trigger makes a token Vedalken Orrery. Replay enchantments. Now we may play Vedalken Orrery again for next loop.
We can continue looping forever, increasing the counting number in TYS.
EDIT:
Wait... if we use Rebuild to take artifacts to hand in the final, we will leave Goblin Dark-Dwellers on board, then it will be cleaned by Child of Alara.
However, for a deck using Metallurgeon as key artifact creature, we can do more because Engineered Explosives on 2 can make its tokens.
With two Smite the Monstrous-PB triggers, first bounces and replay GDD, casting Rebuild, hold Metallurgeon in hand. Then second bounces GDD.
Play Metallurgeon for BM triggers. Use Engineered Explosives to kill Metallurgeon, making a haste token, then BM fetches. Engineered Explosives can come back with another play of GDD.
At the end, after we put Child of Alara in library, we use the haste Metallurgeon to bounce artifacts to hand. So we keep GDD in hand.
Thanks for the help @Deedlit11 and @FortyTwo! I'll move my other thoughts to the Standard thread, unless a dedicated thread for the Graham's Number challenge would be better.
I just noticed that in the Precursor Golem deck, we actually get 10 Golems after the first Twinflame; I forgot about the 2 vanilla Golems that are created when we copy a Precursor Golem. So we get two more copies of Sudden Strength from the first Precursor Golem trigger, bumping the final dmaage up to 2^^2^^10. (with an empty library)
I found Folk Medicine for the 7 card Valet variation. We get a bit less out of the first use, since we need to keep 3 mana in reserve. But after creating 2^^2^^6 creatures we can flash it back and go again for 2^^2^^2^^6 damage.
We should probably move the limited card challenges to the new thread.
Thinking about using Toralf or Saw in Half in a 60-card deck... Saw in Half seems to require less setup than normal stages, but the fact that it is three mana instant that we are using at the stage level maybe means we have to use up more space early on. Possibly we could save it for an additional stage, but certainly not in the Busy Beaver deck, and the non-Busy Beaver deck has cheap additional stages.
For Toralf... the distinctiveness of the layers as damage triggers makes me wonder whether there is something interesting we can do with them. But, we do need *some* sort of destructive ability in the hyperstage transition, in order for a small payment from the lower stage to create a larger effect in the higher stage, without going infinite. I guess we have some freedom on what that could be... something produced by low damage triggers from Toralf.
Without really having concrete ideas, I was kind of hoping a different primary stage might make the hyperstage easier in the gigastage setup.
Yeah, it doesn't, and I couldn't find an instant that would also grant haste. So no dice for that idea. Anyway, that damage number has been thoroughly outclassed.
I've not seen stages based on Saw in half before; how do they work?
You make something big and then use something like Temur Ascendancy + Wheel of Sun and Moon to let you keep replaying Saw in Half until the creature's power gets low. There's a more detailed explanation here.
So, say we have N copies of Doubling Season, along with Temur Ascendancy, Mystic Sanctuary, a 4/4 Astral Dragon, and we have Saw in Half in our hand. We cast Saw in Half on the Astral Dragon; thise causes 2^(N+1) 2/2 Astral Dragons to be created, creating 2^(N+1) ETB triggers. When we resolve the first ETB trigger, we can create copies of Doubling Season, except instead of 2 token copies, we get 2^(N+1) copies. So now we have 2^(N+1) + N copies of Doubling Season, so the second ETB trigger will create 2^(2^(N+1) + N + 1) Doubling Season tokens, or more than 2^2^N. So after 2^(N+1) ETB triggers, the number of Doubling Seasons will be more than 2^2^2^...^2^(N+1), with 2^(N+1) 2's in the exponential tower. This is more than 2^^N, so casting Saw in Half on a 4/4 Astral Dragon is a little better than tetration (double Knuth arrows).
Now, suppose the Astral Dragon is instead an 8/8. We again create 2^(N+1) new Astral Dragons, except now these are 4/4, so we get 2^(N+1) triggers of Temur Ascendancy. (or more if we make copies of Temur Ascendancy) Each of those triggers can redraw Saw in Half, provided we use one of our Astral Dragon ETB triggers to make copies of Mystic Sanctuary, allowing us to move Saw in Half from the graveyard to on top of the library. So, before we use each of our 2^(N+1) draws, we cast Saw in Half on a 4/4 Astral Dragon, using one ETB trigger on the ensuing 2/2 Astral Dragons to copy Mystic Sanctuary and put Saw in Half on top of the library again, and the rest to copy Doubling Season, increasing the number of Doubling Seasons from X to more than 2^^X. Applying X -> 2^^X a total of 2^(N+1) times will take the number of Doubling Seasons to more than 2^^^(2^(N+1)), or better than 2^^^N. So using Saw in Half on an 8/8 Astral Dragon is better than applying pentation (triple Knuth arrows).
The pattern continues like this; using Saw in Half on a 16/16 Astral Dragon will create 2^(N+1) 8/8 Astral Dragons, each of which we can Saw in Half to apply more than triple Knuth arrows, so we wind up with more than 2^^^^(2^(N+1)) Doubling Seasons in the end. Or more generally, using Saw in Half on an Astral Dragon with 2^M power will be better than applying M Knuth arrows.
For the mana, I guess we need either blue or green to be cheap, and then have something that requires a Tibalt's Trickery for a red or the other of blue/green.
So I tried Turn 2 instead, which is enough time to go off in ELD-AFR Standard. I don't know what people have previously come up with for this card pool, but the results here (assuming they work) are pretty entertaining regardless.
My impression is that the initial round of Moraug combats end up just being a chance to get a bunch of untaps, then the second main phase is where we can play our final combo pieces and clone a bunch of lands. The first combat of the second batch should be where we hit Graham's number, and then we can just keep going from there.
Edit: I'd dismissed An Offer You Can't Refuse based on earlier strategies where I was trying to use Lithoform Blight to only gate certain colors of mana, but switching to Beledros Witherbloom makes things a lot simpler. I think we're fine as long as we stay away from 1-mana instants.
Losing Genesis Ultimatum sounds painful, but if we expand to IKO-SNC, I think we can port most of the above into a 19-card Turn 1 strat:
Edit: And here's an increasingly silly 22-card strat for just M21-SNC:
Edit: Wait, do we even need Toralf and Troll/Specialist for these? Even before accounting for them, the Witherbloom combo looks pretty busy beaver-y to me.2018-2019 A stage plus a bunch of layers on turn 2. (F_{w+?}(?))
2019-2020 3 stages and 6 layers on turn 3. (F_{w3+6}(51))
2020-2021 2 stages and 7 layers on turn 2. (F_{w2+7}(F_{w2+7}(F_w2+5}(49))))
2021-2022 4 stages and 8 layers on turn 2. (F_{w4+8}(18))
We still have time to adjust the last deck, in case anyone is interested!
Anyway, for the latest standard we used Tibalt's Trickery to bring out Wizard's Spellbook, and then tap it to exile Invoke the Winds and untap it. We can keep activating it to untap it and cast new spells, so this is a pretty efficient way to get started.
Update on the 7-card challenge: If, in the Precursor Golem deck, we replace Wheel of Sun and Moon with Junktroller, we will bump up the damage from more than 2^^2^^6 to more than 2^^2^^8 - assuming we have an enpty library. This beats out the Devilish Valet deck very narrowly, since the number of Precursor Golems when the second Precursor Golem trigger for Sudden Strength is resolved will match the number of Elemental tokens when Conclave Phalanx is resolved, but in the former deck we have many more vanilla Golems and Junktrollers.
ZNR to SNC
ELD to AFR
GRN to M21
XLN to M20
Also the writeups:
unfinished ELD to AFR
GRN to M21
XLN to M20
Alex Shankland did a writeup of the previous year at
http://alex.shankland.org/index.php/2018/06/13/how-to-deal-more-than-grahams-number-damage-in-magic-the-gathering/
but I think that site is dead - maybe it's available on wayback.
Edit: Yup
AKH to M19
For the Beledros Witherbloom combo, say we have 10*N spare life and 4 mana up, with our field containing a used Beledros Witherbloom and an animated Den of the Bugbear, as well as The World Tree, Aberrant Mind Sorcerer, and several copies of Orvar, the All-Form. In hand, we have Alchemist's Gift and Tibalt's Trickery.
We play Gift on the Sorcerer to get a bunch of recursion triggers, then counter it with Trickery so we can start picking it back up. We then replay Gift on Witherbloom to refresh her, and spend 10 life to untap all of our lands. However many lands we have, we can spend most of that mana to double our Orvars that many times, refreshing the Sorcerer as necessary so we can keep recycling Gift and Trickery. When we're about to run out of mana, we use one of our last Gifts to copy the Den of the Bugbear, making a bunch of (tapped) copies of it, then we refresh Witherbloom again to spend another 10 life and use all of our new lands. Repeat until we run out of life.
If we're in the middle of using Surtland Flinger, most of these Gifts would go to the same Orvar token, so that once we're ready for the next Flinger trigger, it can throw that Orvar for increased damage. (We'll also need to save some mana to start the next round.) If skipping Toralf is an option, we can use a Gift to give lifelink to the next Flinger and have it throw the Orvar at itself. (In that version of the deck, we'd probably replace Crash Through with something like Infuriate, due to no longer needing to draw cards.)
Does that all make sense?
Edit: Wait, is that just regular arrow stacking?
To get the Busy Beaver function, we need to implement a Turing-complete computational model; the model we chose for our Vintage deck was the Waterfall model. (jfb1337's idea). We have to be able to create any possible program/input up to whatever size limitation, in order to be sure that we are actually implementing the Busy Beaver function.
To get the Ackermann function, we have a couple of ways of doing it. The more traditional way is to have a bunch of alternating groups of spells abilities on the stack. The topmost group increases "the number" that we are trying to maximize, then when we resolve down to the second group from the top, we resolve one (or a fixed number) of abilities from the second group, and that allows us to create "the number" copies of abilities for the topmost group again. When we resolve down to the third group from the top, we resolve one of the abilities from the third group, then create the top two layers with "the number" of copies.
Of course, we need some mechanism that allows us to recreate our groups of abilities back up to the topmost group, without allowing us to create any more. This is done by a "stage resource", like mana, life, or creature tokens. We spend mana for each group or pair of groups to build X or 2X groups, then as we resolve the groups, we build up mana that we can then spend to exactly recreate the missing groups without gaining any more. We keep resolving until all the group sizes go to zero.
The other way is to have ability groups intrinsically come attached with some natural number. This is what we first thought of, but with permanents using power/toughness or counters. Instead, the only implementation came recently for the stack, using Toralf abilities, with the attached number being damage.
So yeah, we will still need Toralf or some other stage implementation.
Its a bit of a shame current standard doesn't have any 0 mv spells, though we still get to go off turn 2 with exactly: untapped red land goldhound untapped land, 1mv spell + Tibalt's trickery into Wizard's Spellbook.
The "quick" overview on the current standard deck is:
Setup: get 1/1 nonlegendary copies of Jin and Orvar, and unmodified copies of our utility creatures (mage's attendant and Aberrant Mind sorcerer especially) then cast first day of class for haste, + Arlinn for creatureflash, and Sigarda's Summons for flying.
Cast (and counter!) vanquish the weak to copy our creatures, doing slightly worse than doubling the orvars for every 4 mana.
G stage
G gives X black mana by casting the pump mode of Choose your weapon on a snow covered swamp animated via Avalanche caller. This also lets us cast Skyclave shade from the graveyard.
Use most of this black to make more utility creatures, counter and return any real spells on the stack and end with making X Jins.
Skyclave shade taps for G thanks to Ashaya, Soul of the Wild.
G for the archery mode of Choose your weapon gets X copies, two of which kill skyclave shade ready for the next landfall trigger. (Use the remaining black to get choose your weapon back.)
W stage
W for thraben exorcism makes copies of an enchantment.
Path to the world tree fetches the plains, scaled herbalist puts it in play, tap for w, sac it to Roiling Regrowth
Boseiju Reaches Skyward (chapter 2 via Vorinclex, Monstrous Raider) puts it back in the library.
(we can net green mana in here by saccing the swamp and skyclave shade to roiling regrowth and getting two casts of skyclave shade each of which taps for G)
U stage
Secluded courtyard and Sparra's adjudicators work beautifully together.
U puts the citizen that makes a U on top with Bury in Books
U draws the citizen and the nonbasic land with Contact Other plane (netting white by drawing the plains too)
Toralf stage
Cabaretti charm kicks off a typical Toralf+lifelink stage
Slaughter specialist ensures the opponent has enough 1/1s
Novice occultist turns life into cards, netting U
A few layers after to round out the deck:
meeting of the five to cast the charm
tibalt's trickery to cast meeting of the five
sea gate storm caller so tibalt's trickery can cast tibalt's trickery.
Xorn for more treasures for red
Thieves' Tools for treasures
Jin gitaxias for more ETBs
Lithoform engine+spectral steel for more casts.
Many problems:
The general idea for the extra GDD ETB is to require it for some essential pupose that doesn't extend the hyperstage. I suppose if we have something that can bring it back from outside our hand, like Moggcatcher, we won't get that extra ETB.
Remind me, how do we get infinite use of Rebuild without needing expensive things like a GDD ETB or a sorcery flashback?
Suppose we have 3 usable life, without any haste resource of key artifact creature. There is Thousand-Year Storm, Psychic Battle and Verdant Succession, one of each, and one token Vedalken Orrery on board. One Centaur Safeguard on board and one in library or exile.
Play Vedalken Orrery for Mirrorworks triggers, then spend 3 life to flashback Acorn Harvest, and let Spellweaver Volute resolve to cast Smite the Monstrous. Even if we have only 1 TYS, it can still copy many instances of Smite, pushing many PB triggers on the stack. The stack looks like this:
Let the final Smite the Monstrous-PB trigger redirect the Smite, and resolve the Smite to destroy Child of Alara. The stack looks like this:
After death trigger swept out everything (and we gained 3 life from Centaur Safeguard; the other Centaur Safeguard went to board), Verdant Succession trigger bring Child of Alara back. Then Mirrorworks trigger makes a token Vedalken Orrery. Replay enchantments. Now we may play Vedalken Orrery again for next loop.
We can continue looping forever, increasing the counting number in TYS.
EDIT:
Wait... if we use Rebuild to take artifacts to hand in the final, we will leave Goblin Dark-Dwellers on board, then it will be cleaned by Child of Alara.
However, for a deck using Metallurgeon as key artifact creature, we can do more because Engineered Explosives on 2 can make its tokens.
With two Smite the Monstrous-PB triggers, first bounces and replay GDD, casting Rebuild, hold Metallurgeon in hand. Then second bounces GDD.
Play Metallurgeon for BM triggers. Use Engineered Explosives to kill Metallurgeon, making a haste token, then BM fetches. Engineered Explosives can come back with another play of GDD.
At the end, after we put Child of Alara in library, we use the haste Metallurgeon to bounce artifacts to hand. So we keep GDD in hand.
Replace Conclave Phalanx with Gaea's Cradle so we don't need to save the final one mana before refilling mana.
Over f3(f2(f2(f2(f2(f2(f2(2048))))))) > 2^^2^^9 damage.
We should probably move the limited card challenges to the new thread.
Thinking about using Toralf or Saw in Half in a 60-card deck... Saw in Half seems to require less setup than normal stages, but the fact that it is three mana instant that we are using at the stage level maybe means we have to use up more space early on. Possibly we could save it for an additional stage, but certainly not in the Busy Beaver deck, and the non-Busy Beaver deck has cheap additional stages.
For Toralf... the distinctiveness of the layers as damage triggers makes me wonder whether there is something interesting we can do with them. But, we do need *some* sort of destructive ability in the hyperstage transition, in order for a small payment from the lower stage to create a larger effect in the higher stage, without going infinite. I guess we have some freedom on what that could be... something produced by low damage triggers from Toralf.
Without really having concrete ideas, I was kind of hoping a different primary stage might make the hyperstage easier in the gigastage setup.
First of all, without Vedalken Orrery, you cannot cast sorcery like Twinflame if the stack is nonempty.
Now, suppose the Astral Dragon is instead an 8/8. We again create 2^(N+1) new Astral Dragons, except now these are 4/4, so we get 2^(N+1) triggers of Temur Ascendancy. (or more if we make copies of Temur Ascendancy) Each of those triggers can redraw Saw in Half, provided we use one of our Astral Dragon ETB triggers to make copies of Mystic Sanctuary, allowing us to move Saw in Half from the graveyard to on top of the library. So, before we use each of our 2^(N+1) draws, we cast Saw in Half on a 4/4 Astral Dragon, using one ETB trigger on the ensuing 2/2 Astral Dragons to copy Mystic Sanctuary and put Saw in Half on top of the library again, and the rest to copy Doubling Season, increasing the number of Doubling Seasons from X to more than 2^^X. Applying X -> 2^^X a total of 2^(N+1) times will take the number of Doubling Seasons to more than 2^^^(2^(N+1)), or better than 2^^^N. So using Saw in Half on an 8/8 Astral Dragon is better than applying pentation (triple Knuth arrows).
The pattern continues like this; using Saw in Half on a 16/16 Astral Dragon will create 2^(N+1) 8/8 Astral Dragons, each of which we can Saw in Half to apply more than triple Knuth arrows, so we wind up with more than 2^^^^(2^(N+1)) Doubling Seasons in the end. Or more generally, using Saw in Half on an Astral Dragon with 2^M power will be better than applying M Knuth arrows.
1 Coat of Arms
2 Xathrid Necromancer
3 Artificial Evolution
4 Arcbond
5 Comeuppance
6 Dralnu's Crusade
Starting a Computation
7 Opalescence
8 Wrong Turn
9 Kaervek's Spite
10 Goblin Boom Keg
11 March of the Machines
Utility: Enchantments/Artifacts
12 Vedalken Orrery
13 Dual Nature
14 Copy Enchantment
15 Mox Emerald
Utility: Spells
16 Repeated Reverberation
17 Precursor Golem
Utility: Creatures
18 Bloodbond March
19 Voracious Greatshark
Vat Stage
20 Repentant Vampire
21 Cowardice
22 Psychic Battle
23 Mimic Vat
24 Mirror of Fate
25 Tomb Robber
26 Spellweaver Volute
27 Rally the Righteous
28 Argivian Find
29 Bump in the Night
30 Mountain
31 Groundskeeper
32 Firebrand Ranger
33 Lifeforce
Helix Megastage
34 Spellweaver Helix
35 Worldpurge
36 Stone Rain
37 Hungry for More
38 Hungry for More
39 K'rrik, Son of Yawgmoth
40 Radiant Fountain
41 Panharmonicon
42 Loam Dweller
Blue Man Stage
43 Ruin Ghost
44 Archaeological Dig
45 General's Enforcer
46 Feldon of the Third Path
47 Kurkesh, Onakke Ancient
48 Flash
49 Academy Rector
50 Omniscience
51 Caress of Phyrexia
Layers
52 Smoke Spirits' Aid
53 Commune with Lava
54 Pain Seer
55 Tolarian Kraken
56 Psychic Possession
57 Floating-Dream Zubera
Misc Utility
58 Xorn
59 Harmonic Prodigy
60 Cryptic Pursuit
resulting in more than BB_{w^3 + w + 9}(12,932) damage.