I think I have a smaller deck that exceeds Graham's Number in Vintage.
The key card is the upcoming Saw in Half, which is almost perfect for this purpose (consuming one thing to make (increaseable) two smaller things), except that the rounding up means it can produce 1/1s without limit. I get around that flaw by pairing it with Temur Ascendancy, which is productive only with higher powers.
Start with Black Lotus and Show and Tell to get Omniscience onto the battlefield.
Cast Doubling Season and Temur Ascendancy, then Astral Dragon makes four copies of Temur Ascendancy and draws a card.
Next, cast Wheel of Sun and Moon on oneself, and Avabruck Caretaker, generating five "draw a card" triggers from Temur Ascendancys.
With the first three, draw Saw in Half and cast it on an Astral Dragon, and have the Astral Dragon tokens target Doubling Season. This does a tetration each time, and ends up with more than 2^^^5 copies of Doubling Season.
With the fourth trigger, draw Saw in Half again, but this time, cast it on Avabruck Caretaker, getting more than 2^^^5 copies of Avabruck Caretaker. With the fifth trigger, draw Saw in Half, and keep it in hand this time.
Proceed to the combat step; the Avabruck Caretakers trigger. Have them target each other, targeting each one once; each trigger adds lots of +1/+1 counters because of the Doubling Seasons. While there are creatures with at least 7 power, Saw in Half the lowest-powered of those, getting many Temur Ascendancy triggers that redraw Saw in Half, and after all but the last, cast Saw in Half on an Astral Dragon for more copies of Doubling Season.
EDIT: For the version where the library contains additional cards, use Feldon's Cane instead of Wheel of Sun and Moon, having to rely on luck early on (later, one can afford to draw the extra cards).
The idea was that using Lotus Blossom requires all the remaining cards to be cast in one turn. Casting Cruel Entertainment triggers Aria of Flame, which deals 2 damage because of Doubling Season, but then the opponent gets to take control for one turn, and can make Extravagant Replication target Aria of Flame, producing two copies because of Doubling Season.
The problem is that Lotus Blossom produces only one color of mana. The lands can make RG, but that still leaves 16UUB needed.
Turn X: Mercurial Transformation on Doubling Season, Progenitor Mimic copying it, using mana from Sapseep Forest and Calciform Pools
Turn X+1: In upkeep, in response to Progenitor Mimic's and Timberline Ridge's triggered abilities, tap Timberline Ridge for G, adding 4 depletion counters, to activate Sapseep Forest, going to 21 life.
Repeat once the depletion counters run out. If the number of depletion counters is N once, it will exceed 2^^N the next time. 4 = 2^^^2, then 29 more iterations, so the final delay exceeds 2^^^31.
There are some mistakes in the previous. Firstly, it is not true that the number of ordinary golems is quadrupled each time: 96*4=384, not 288. Secondly, a Precursor Golem produces two golem tokens, not three.
This is what I think is correct:
(still not counting the initially targeted Precursor Golem until the end)
Start: 8 Precursor Golems
After first copying trigger and going through its results: 8+8=16 Precursor Golems, 8*2=16 plain golems
Second one: 16+16=32 Precursor Golems, 16 + 16 (direct copies) + 16*2 (from new Precursor Golems) = 64 plain golems
Third one: 32+32=64 Precursor Golems, 64+64+32*2=192 plain golems
Fourth one: 64+64=128 Precursor Golems, 192+192+64*2=512 plain golems
Fifth one: 128+128=256 Precursor Golems, 512+512+128*2=1280 plain golems
Sixth one: 256+256=512 Precursor Golems, 1280+1280+256*2=3072 plain golems
Seventh one: 512+512=1024 Precursor Golems, 3072+3072+512*2=7168 plain golems
Eighth one: 1024+1024=2048 Precursor Golems, 7168+7168+1024*2=16384 plain golems
Ninth one: 2048+2048=4096 Precursor Golems, 16384+16384+2048*2=36864 plain golems
Finally, add the initially targeted Precursor Golem and one copy of it, for 4098.
Sheltered Valley
Saprazzan Cove
Forbidden Orchard
Sandstone Needle
Doubling Season
Argent Mutation
Ensoul Artifact
Progenitor Mimic
Sparkcaster
Endgame, we cast sparkcaster 20 turns in a row. Since Sandstone Needle and Forbidden Orchard are the only lands that let us cast it, we need to get at least 20 counters on Cove. So we need at least 4 doubling seasons (2^4=16) before we play it. The first time mimic (as doubling season) triggers, it generates 4 new doubling seasons, so we're good to go at that point (playing Cove, and casting sparkcaster the first time). Each cast of sparkcaster gives the opponent several spirits. I'll just run through the number of doubling seasons, for the damage dealt. We have 6 (1), then 2^6+6 (2), then 2^{2^6+6} (3), then 2 ^2^...(19 of these)...^2^6. But we don't worry about the ones we give out when dealing leathal damage, so we get attacked by 2^^18 spirits the turn before we win. We gain enough life to ride this out over the first several turns, so this takes 2^^18 turns. (Here, if it isn't clear, ^^ is two up arrows from Knuth's up-arrow notation)
That doesn't work, for several reasons:
Progenitor Mimic can copy the Spirit tokens.
Doubling Season applies only to tokens you control. (Primal Vigor doesn't, but it comes with another restriction that makes it not work here.)
and two more cards for mana production.
The sequence with that is Quest for Ancient Secrets, Parallel Lives, Fractured Identity on Parallel Lives (1 counter on Quest for Ancient Secrets), Pull from Eternity on Parallel Lives (3 counters), Vengeful Rebirth on Pull from Eternity, Pull from Eternity on Vengeful Rebirth (5 counters), activate Quest for Ancient Secrets.
But I haven't found any choice of mana producers that makes this take many turns, and even if there is one, it still just gives a tetration of less than 20.
and something else; I'm thinking of something that requires two colored mana from Forbidden Orchard and Spire of Industry, and that can either add life or make progress towards winning.
and one more card.
This one runs into trouble with the mana requirement of Tamiyo, the Moon Sage; Soulfire Grand Master and Tasigur, the Golden Fang can also serve the same purpose, but unfortunately they can win on their own.
This results in a large number of the opponent's tokens, but does not take a long time because the main process does not use any mana!
Note that the second dependency on Coat of Arms, from Sinstriker's Will, is necessary; we cannot rely on just the dependency from the last ability of Tezzeret, Agent of Bolas, because then it would be possible to accumulate loyalty counters without Coat of Arms, only playing it after getting enough.
and probably some planeswalker; each turn, the opponent's tokens will attack the planeswalker, and one has to block those that can be blocked, and sacrifice the blocking tokens for mana and for life from Plunge into Darkness, then use Murderous Betrayal to destroy the enemy tokens that were not blocked.
and something that requires red, green or white mana multiple times, and requires Progenitor Mimic to copy Doubling Season. Sapseep Forest would work if its ability were something useful; Goblin Kaboomist would work if the tokens could deal damage to players.
Mechanized Production could also be used if there is a way to make a single permanent an artifact that doesn't last just one turn.
So, I came up with a variation of the previous Conjurer's Ban puzzle. Here's the set up:
Your opponent went infinite, capsized your board, time twistered, tormod's crypted your graveyard, played elish norn, pacifism on elish norn, cast Sphere of Safety, cast Uba Mask, cast Nevermore naming Dark Ritual, cast Liquimetal Coating, made Nevermore an artifact, cast Karn, Silver Golem, made nevermore a creature, cast Soulfire Grand Master, cast Mirror Gallery, cast Mangara of Corondor, cast rite of replication kicked targeting Mangara and bought back with Soulfire Grand Master. Then they copy Nevermore for every non-land card in the game, ending with rite of replication. Then they use Mangara to exile liquimetal coating, Karn and Soulfire Grand Master. They then pass turn, and dare you to kill them. For simplicity, assume they have 15,000 Nevermores. How quickly can you kill them? They're at 20 life, 0 poison counters, 49 cards in their deck, 7 cards in hand. You have 7 cards in hand, you can stack your deck, and have up to 4 copies of non-basic cards.
Simple version: There's an Uba Mask, a Sphere of Safety, a PacifiedElesh Norn, and a Nevermore naming every non-land card on your opponent's side, you have no cards in play, and you can stack your deck. How fast can you win? [links added for convenience]
Proof that you can win: If your deck is 30,000 Forests, your hand contains 6 forests and a Treetop Village, you can play the Treetop Village, play all the forests, then activate treetop each turn, pay for the sphere, and swing 20 turns in a row. 30,024 turns.
Can Patron of the Orochi can be avoided by using Isochron Scepter, Druid's Deliverance, Sinking Feeling, and Ethereal Armor for copies of Bloodbond March? Unfortunately, it does not work out, because Sinking Feeling alone on one of the Paragons gives two activations per token, which is unacceptable.
The latest set-up appears to go infinite: have the original Epic Experiment resolve, casting Demand and Chaos Warp, and with Demand still on the stack, use Reito Lantern on Epic Experiment and get it back with Demand, and after everything resolves, use Reito Lantern on Demand and on Chaos Warp and repeat.
Is the card's converted mana cost less than or equal to the sum of all the numbers in its rules text? (Take into account any errata. Anything in brackets is not rules text. Numbers can be expressed as either numerals or words.)
My results:
4 | 6 6 2 X 6
Against #1: Use Mindbreak Traps on both creature spells and win with Beacon of Destruction.
Against #2: Use Mindbreak Traps on the Commandeers; Beacon of Destruction wins on turn 4 going first or turn 3 going second, slightly faster than Akroma, Angel of Fury.
Against #3: Use Mindbreak Trap on Progenitus, and use the second one if Last Word is cast; Time Stop cannot be cast here or else it exiles Progenitus as well. Time Stop exiles Beacon of Destruction, and this comes to a draw.
Against #5: Use Mindbreak Traps on Last Word and Iona, Shield of Emeria, and win with Beacon of Destruction.
The key card is the upcoming Saw in Half, which is almost perfect for this purpose (consuming one thing to make (increaseable) two smaller things), except that the rounding up means it can produce 1/1s without limit. I get around that flaw by pairing it with Temur Ascendancy, which is productive only with higher powers.
Start with Black Lotus and Show and Tell to get Omniscience onto the battlefield.
Cast Doubling Season and Temur Ascendancy, then Astral Dragon makes four copies of Temur Ascendancy and draws a card.
Next, cast Wheel of Sun and Moon on oneself, and Avabruck Caretaker, generating five "draw a card" triggers from Temur Ascendancys.
With the first three, draw Saw in Half and cast it on an Astral Dragon, and have the Astral Dragon tokens target Doubling Season. This does a tetration each time, and ends up with more than 2^^^5 copies of Doubling Season.
With the fourth trigger, draw Saw in Half again, but this time, cast it on Avabruck Caretaker, getting more than 2^^^5 copies of Avabruck Caretaker. With the fifth trigger, draw Saw in Half, and keep it in hand this time.
Proceed to the combat step; the Avabruck Caretakers trigger. Have them target each other, targeting each one once; each trigger adds lots of +1/+1 counters because of the Doubling Seasons. While there are creatures with at least 7 power, Saw in Half the lowest-powered of those, getting many Temur Ascendancy triggers that redraw Saw in Half, and after all but the last, cast Saw in Half on an Astral Dragon for more copies of Doubling Season.
EDIT: For the version where the library contains additional cards, use Feldon's Cane instead of Wheel of Sun and Moon, having to rely on luck early on (later, one can afford to draw the extra cards).
The idea was that using Lotus Blossom requires all the remaining cards to be cast in one turn. Casting Cruel Entertainment triggers Aria of Flame, which deals 2 damage because of Doubling Season, but then the opponent gets to take control for one turn, and can make Extravagant Replication target Aria of Flame, producing two copies because of Doubling Season.
The problem is that Lotus Blossom produces only one color of mana. The lands can make RG, but that still leaves 16UUB needed.
No, it doesn't. As in some previous versions, it is necessary to play all cards in order to enable Keldon Megaliths.
Extravagant Replication + Doubling Season + Keldon Megaliths + Timberline Ridge + Saprazzan Cove gives >2^^^21 turns in only 5 cards. Add a second Extravagant Replication and a Grip of Chaos (relying on randomness giving the slowest possibility -- is this correct?) to get hexation.
Turn X: Mercurial Transformation on Doubling Season, Progenitor Mimic copying it, using mana from Sapseep Forest and Calciform Pools
Turn X+1: In upkeep, in response to Progenitor Mimic's and Timberline Ridge's triggered abilities, tap Timberline Ridge for G, adding 4 depletion counters, to activate Sapseep Forest, going to 21 life.
Repeat once the depletion counters run out. If the number of depletion counters is N once, it will exceed 2^^N the next time. 4 = 2^^^2, then 29 more iterations, so the final delay exceeds 2^^^31.
This is what I think is correct:
(still not counting the initially targeted Precursor Golem until the end)
Start: 8 Precursor Golems
After first copying trigger and going through its results: 8+8=16 Precursor Golems, 8*2=16 plain golems
Second one: 16+16=32 Precursor Golems, 16 + 16 (direct copies) + 16*2 (from new Precursor Golems) = 64 plain golems
Third one: 32+32=64 Precursor Golems, 64+64+32*2=192 plain golems
Fourth one: 64+64=128 Precursor Golems, 192+192+64*2=512 plain golems
Fifth one: 128+128=256 Precursor Golems, 512+512+128*2=1280 plain golems
Sixth one: 256+256=512 Precursor Golems, 1280+1280+256*2=3072 plain golems
Seventh one: 512+512=1024 Precursor Golems, 3072+3072+512*2=7168 plain golems
Eighth one: 1024+1024=2048 Precursor Golems, 7168+7168+1024*2=16384 plain golems
Ninth one: 2048+2048=4096 Precursor Golems, 16384+16384+2048*2=36864 plain golems
Finally, add the initially targeted Precursor Golem and one copy of it, for 4098.
That doesn't work, for several reasons:
I did have a look at that too, but the exiling makes it difficult. The best I could come up with is
- Parallel Lives
- Quest for Ancient Secrets
- Fractured Identity
- Pull from Eternity
- Vengeful Rebirth
and two more cards for mana production.The sequence with that is Quest for Ancient Secrets, Parallel Lives, Fractured Identity on Parallel Lives (1 counter on Quest for Ancient Secrets), Pull from Eternity on Parallel Lives (3 counters), Vengeful Rebirth on Pull from Eternity, Pull from Eternity on Vengeful Rebirth (5 counters), activate Quest for Ancient Secrets.
But I haven't found any choice of mana producers that makes this take many turns, and even if there is one, it still just gives a tetration of less than 20.
Still trying to exponentiate the opponent's creatures every turn:
A small change to a previous deck:
- Forbidden Orchard
- Spire of Industry
- Rushwood Grove
- Coat of Arms
- Tamiyo, the Moon Sage
- Mercy Killing
and something else; I'm thinking of something that requires two colored mana from Forbidden Orchard and Spire of Industry, and that can either add life or make progress towards winning.- Forbidden Orchard
- Rushwood Grove
- Tamiyo, the Moon Sage
- Parallel Evolution
- Quiet Contemplation
- Leyline of Anticipation
and one more card.This one runs into trouble with the mana requirement of Tamiyo, the Moon Sage; Soulfire Grand Master and Tasigur, the Golden Fang can also serve the same purpose, but unfortunately they can win on their own.
- Forbidden Orchard
- Calciform Pools
- Tidewater Minion
- Intruder Alarm
- Coat of Arms
- Sinstriker's Will
- Tezzeret, Agent of Bolas
This results in a large number of the opponent's tokens, but does not take a long time because the main process does not use any mana!Note that the second dependency on Coat of Arms, from Sinstriker's Will, is necessary; we cannot rely on just the dependency from the last ability of Tezzeret, Agent of Bolas, because then it would be possible to accumulate loyalty counters without Coat of Arms, only playing it after getting enough.
- Fountain of Cho
- Alliance of Arms
- Phyrexian Altar
- Murderous Betrayal
- Plunge into Darkness
- Seasons Past
and probably some planeswalker; each turn, the opponent's tokens will attack the planeswalker, and one has to block those that can be blocked, and sacrifice the blocking tokens for mana and for life from Plunge into Darkness, then use Murderous Betrayal to destroy the enemy tokens that were not blocked.Taking a different direction:
- Saprazzan Cove
- Doubling Season
- Argent Mutation
- March of the Machines
- Progenitor Mimic
and something that requires red, green or white mana multiple times, and requires Progenitor Mimic to copy Doubling Season. Sapseep Forest would work if its ability were something useful; Goblin Kaboomist would work if the tokens could deal damage to players.Mechanized Production could also be used if there is a way to make a single permanent an artifact that doesn't last just one turn.
– and add a few more permanents: Anafenza, the Foremost enchanted with a second Pacifism, and Kira, Great Glass-Spinner enchanted with a third Pacifism. How fast can you win now?
The latest set-up appears to go infinite: have the original Epic Experiment resolve, casting Demand and Chaos Warp, and with Demand still on the stack, use Reito Lantern on Epic Experiment and get it back with Demand, and after everything resolves, use Reito Lantern on Demand and on Chaos Warp and repeat.
4 | 6 6 2 X 6
Against #1: Use Mindbreak Traps on both creature spells and win with Beacon of Destruction.
Against #2: Use Mindbreak Traps on the Commandeers; Beacon of Destruction wins on turn 4 going first or turn 3 going second, slightly faster than Akroma, Angel of Fury.
Against #3: Use Mindbreak Trap on Progenitus, and use the second one if Last Word is cast; Time Stop cannot be cast here or else it exiles Progenitus as well. Time Stop exiles Beacon of Destruction, and this comes to a draw.
Against #5: Use Mindbreak Traps on Last Word and Iona, Shield of Emeria, and win with Beacon of Destruction.