Tokens outside of the battlefield ceasing to exist is a state-based action; these are checked every time a player would get priority, which will happen before a spell can resolve.
You could try using something like Necromantic Selection, in which case the tokens would still be in the graveyard when the Golgari Grave-Troll is put onto the battlefield, because state-based actions are not checked in the middle of a resolving spell. However, it still would not count the tokens, because the ability is "Golgari Grave-Troll enters the battlefield with a +1/+1 counter on it for each creature card in your graveyard." (emphasis added), and tokens are not cards.
Also in the write-up for the 9-card solution, "After the first Saw, we have over 2^^^3 Doubling Season tokens" is now incorrect: 2^^^3 = 2^^2^^2 = 2^^4 = 2^2^2^2 = 65536, while the number of Doubling Seasons is 69. However, making Astral Dragon tokens with the next Saw in Half adds another exponentiation, so the result still exceeds 2^^^6.
There is an error in the write-up for the 9-card solution.
"Mystic Sanctuary enters the battlefield tapped unless you control three or more other Islands." is a replacement effect, thus it is applied before it enters the battlefield. The first time copies of it are created, they will enter tapped and not get to put a card back; we need to target Mystic Sanctuary twice with Astral Dragon to start putting Saw in Half back.
(Edit) One more thing: when you write a list of cards, it's probably better to use something other than a comma as the separator (such as a semicolon), because some card names contain commas.
I don't see how that would help. Firecat Blitz was used because, in addition to making creatures with haste, it has flashback. Kindred Charge can't replace Irenicus's Vile Duplication because the delegendarizing is neccesary.
[...]
Not sure about some of the numbers, or how to write the damage for the iterated Busy Beaver deck.
Chancellor of the Dross doesn't deal damage.
For 6 cards, we can take Parallel Lives, Astral Dragon, Mirage Phalanx and add Black Lotus, Show and Tell, Omniscience, getting (still) >2^^35.
Hmm, I've run into a problem with the Toralf hyperstage plan. In order to cast the hyperstage spell at multiple hyperstage transitions, we need to counter it, so that it isn't stuck on the stack. We can still get the benefit, if we have one copy of Swarm Intelligence, say. But, then we can just not counter the spell, and wait for both copies to resolve, getting the benefit twice and winding up ahead one resource.
I have now realised that once the power of an Astral Dragon is increased to 7+, after using Saw in Half on it, one can interleave the "draw a card" and "create copies of Mystic Sanctuary" triggers, which makes it possible to cast Saw in Half on other creatures without losing it.
No, it doesn't, because it reads "Target player draws a card." (Recent multi-modal spells are usually deliberately made hard to fizzle, by having either no modes target or all modes target.)
I think I have an 8-card deck achieving significantly more damage.
Black Lotus, sacrifice for GGG, Channel (19G available), Nature's Spiral getting back Black Lotus (18). Cast Elixir of Immortality (17) and activate it (15), gaining 5 life (20) and shuffling Channel and Nature's Spiral into the library. Recast Black Lotus and sacrifice it for blue (20UUU).
Casting Bonus Round once doubles+1 the number of active Bonus Round effects; the Jadzi triggers can cast Elixir of Immortality and Black Lotus for an adequate supply of mana.
Casting Irenicus's Vile Duplication once lets Bonus Round be cast from Jadzi triggers more times than the current Bonus Round count, for an exponentiation.
Each instant or sorcery card beyond that adds two layers, one for the Bonus Round triggers from its casting and one for the Jadzi triggers from each Bonus Round trigger. Unlike conventional layers, the cards do not have a fixed order; however, because of the way the stack works, only the cards not currently on the stack can be re-ordered, so it is still finite.
Chain Jadzi triggers into Channel, Nature's Spiral targeting Black Lotus, Irenicus's Vile Duplication, Bonus Round, and Elixir of Immortality (5R). Each time, stack the Jadzi triggers on top of the Bonus Round trigger -- except for Nature's Spiral, which should have the reverse order.
The first time Nature's Spiral is copied, refrain from activating Elixir of Immortality until the copy resolves, returning Black Lotus to hand. Discard Black Lotus to bounce the original Jadzi, then discard Jadzi to bounce one of the token copies of Jadzi -- and now, with Jadzi in the graveyard, we can add its back side, Journey to the Oracle, into the sequence.
Once everything finishes resolving, we have a big number, but unfortunately not quite big enough to show up in the final lower bound. Towards the end, use Nature's Spiral to return the Jadzi card to hand.
Cast Journey to the Oracle from hand, starting the process again, which increases the number to more than 2^^^^^^^^^^3. (Journey to the Oracle cannot be retrieved if it is the first card cast, keeping it finite.)
Cast Firecat Blitz by flashback with X=0, starting the process again, which increases the number to more than 2^^^^^^^^^^4.
Again, return the Jadzi card to hand with Nature's Spiral and cast it as Journey to the Oracle. However, because Firecat Blitz is now exiled, it's less effective. The last time Irenicus's Vile Duplication is cast, target one of the Cat tokens with haste with it and with all the copies, making more than 2^^^^^^^^^^4 more Cat tokens with haste, which finally attack.
Black Lotus, then Channel: 19+G
Aetherflux Reservoir: 15+G
Cogwork Assembler (+4): 16+G
Pay 7 to make a copy of Aetherflux Reservoir: 9+G
Parallel Lives (+5*2): 16
Pay 7 to make 2 copies of Aetherflux Reservoir: 9
Mycosynth Lattice (+6*4): 27
Pay 7 to make 2 copies of Parallel Lives: 20
Pay 7 to make 8 copies of Parallel Lives: 13
Pay 7 to make 2048 copies of Aetherflux Reservoir: 6
Creeping Renaissance (+7*2052): 14365
In response, make lots of copies of Parallel Lives, but also make some copies of Cogwork Assembler, and pay 50 life to Aetherflux Reservoir to destroy the nontoken Cogwork Assembler, so that Creeping Renaissance can return both Cogwork Assembler and Black Lotus.
Each spell cast gives a tetration, and there are 5 more that can be cast (Cogwork Assembler and Black Lotus, then Creeping Renaissance again, and Cogwork Assembler and Black Lotus again).
If there are extra cards in the library, replace Creeping Renaissance with Whispers of the Muse to get >2^^^55.
Mystic Sanctuary can do the restricted retrieval (in place of Wheel of Sun and Moon), but it doesn't allow Saw in Half to be gotten back after casting it on Avabruck Caretaker.
...Aha! I think Dromoka, the Eternal in place of Avabruck Caretaker works; it allows for always targeting Astral Dragon with Saw in Half, which as a bonus increases the number of triggers from >2^^^5 to >2^^^6 (because the copies of Doubling Season made by Astral Dragon are also Dragons).
(Having to target Mystic Sanctuary twice with Astral Dragons after the first Saw in Half makes it a bit worse, but it looks like it still ends up >2^^^6: with the first Saw in Half, there remain two Astral Dragons that can target Doubling Season, producing 4 copies (making 5), then 64 (making 69), and then the second Saw in Half produces 2^70 > 2^16 = 2^^^3 Astral Dragons.)
EDIT: We have to be careful to ensure that the final bolster can go to an attacking creature, but that can be done easily, as there will be plenty of 1/1 Astral Dragons that can attack, and many more will be created throughout the process.
Tokens outside of the battlefield ceasing to exist is a state-based action; these are checked every time a player would get priority, which will happen before a spell can resolve.
You could try using something like Necromantic Selection, in which case the tokens would still be in the graveyard when the Golgari Grave-Troll is put onto the battlefield, because state-based actions are not checked in the middle of a resolving spell. However, it still would not count the tokens, because the ability is "Golgari Grave-Troll enters the battlefield with a +1/+1 counter on it for each creature card in your graveyard." (emphasis added), and tokens are not cards.
For 5 cards, Sparkcaster in place of Storm Herd can be cast 38 times before having to kill a player.
A 4-card solution that is close but not quite best: Black Lotus, Channel, Uktabi Drake, Bronze Cudgels for 38 damage.
"Mystic Sanctuary enters the battlefield tapped unless you control three or more other Islands." is a replacement effect, thus it is applied before it enters the battlefield. The first time copies of it are created, they will enter tapped and not get to put a card back; we need to target Mystic Sanctuary twice with Astral Dragon to start putting Saw in Half back.
(Edit) One more thing: when you write a list of cards, it's probably better to use something other than a comma as the separator (such as a semicolon), because some card names contain commas.
I don't see how that would help. Firecat Blitz was used because, in addition to making creatures with haste, it has flashback. Kindred Charge can't replace Irenicus's Vile Duplication because the delegendarizing is neccesary.
Chancellor of the Dross doesn't deal damage.
For 6 cards, we can take Parallel Lives, Astral Dragon, Mirage Phalanx and add Black Lotus, Show and Tell, Omniscience, getting (still) >2^^35.
Psychic Rebuttal?
That part fails because you don't control three or more other Islands.
No, it doesn't, because it reads "Target player draws a card." (Recent multi-modal spells are usually deliberately made hard to fizzle, by having either no modes target or all modes target.)
Black Lotus, sacrifice for GGG, Channel (19G available), Nature's Spiral getting back Black Lotus (18). Cast Elixir of Immortality (17) and activate it (15), gaining 5 life (20) and shuffling Channel and Nature's Spiral into the library. Recast Black Lotus and sacrifice it for blue (20UUU).
Jadzi, Oracle of Arcavios (14U). Cast Irenicus's Vile Duplication (11) targeting Jadzi, chaining Jadzi triggers to cast Nature's Spiral targeting Black Lotus, Bonus Round, and Elixir of Immortality (8). Let them all resolve.
Activate Elixir of Immortality (6); gain 5 life (11) and shuffle the graveyard back in. Cast Black Lotus and sacrifice it for red (11RRR).
Cast Firecat Blitz with X=1 (10R)...
The first time Nature's Spiral is copied, refrain from activating Elixir of Immortality until the copy resolves, returning Black Lotus to hand. Discard Black Lotus to bounce the original Jadzi, then discard Jadzi to bounce one of the token copies of Jadzi -- and now, with Jadzi in the graveyard, we can add its back side, Journey to the Oracle, into the sequence.
Once everything finishes resolving, we have a big number, but unfortunately not quite big enough to show up in the final lower bound. Towards the end, use Nature's Spiral to return the Jadzi card to hand.
Cast Journey to the Oracle from hand, starting the process again, which increases the number to more than 2^^^^^^^^^^3. (Journey to the Oracle cannot be retrieved if it is the first card cast, keeping it finite.)
Cast Firecat Blitz by flashback with X=0, starting the process again, which increases the number to more than 2^^^^^^^^^^4.
Again, return the Jadzi card to hand with Nature's Spiral and cast it as Journey to the Oracle. However, because Firecat Blitz is now exiled, it's less effective. The last time Irenicus's Vile Duplication is cast, target one of the Cat tokens with haste with it and with all the copies, making more than 2^^^^^^^^^^4 more Cat tokens with haste, which finally attack.
Aetherflux Reservoir: 15+G
Cogwork Assembler (+4): 16+G
Pay 7 to make a copy of Aetherflux Reservoir: 9+G
Parallel Lives (+5*2): 16
Pay 7 to make 2 copies of Aetherflux Reservoir: 9
Mycosynth Lattice (+6*4): 27
Pay 7 to make 2 copies of Parallel Lives: 20
Pay 7 to make 8 copies of Parallel Lives: 13
Pay 7 to make 2048 copies of Aetherflux Reservoir: 6
Creeping Renaissance (+7*2052): 14365
In response, make lots of copies of Parallel Lives, but also make some copies of Cogwork Assembler, and pay 50 life to Aetherflux Reservoir to destroy the nontoken Cogwork Assembler, so that Creeping Renaissance can return both Cogwork Assembler and Black Lotus.
Each spell cast gives a tetration, and there are 5 more that can be cast (Cogwork Assembler and Black Lotus, then Creeping Renaissance again, and Cogwork Assembler and Black Lotus again).
>2^^^^(2^^2^^35)>2^^^^(2^^34), unfortunately not benefiting from the extra copies of Restoration Angel because it targets....Aha! I think Dromoka, the Eternal in place of Avabruck Caretaker works; it allows for always targeting Astral Dragon with Saw in Half, which as a bonus increases the number of triggers from >2^^^5 to >2^^^6 (because the copies of Doubling Season made by Astral Dragon are also Dragons).
(Having to target Mystic Sanctuary twice with Astral Dragons after the first Saw in Half makes it a bit worse, but it looks like it still ends up >2^^^6: with the first Saw in Half, there remain two Astral Dragons that can target Doubling Season, producing 4 copies (making 5), then 64 (making 69), and then the second Saw in Half produces 2^70 > 2^16 = 2^^^3 Astral Dragons.)
EDIT: We have to be careful to ensure that the final bolster can go to an attacking creature, but that can be done easily, as there will be plenty of 1/1 Astral Dragons that can attack, and many more will be created throughout the process.