Hmmm, if we replace Izzet Guildmage plus Restore with Lodestone Bauble + Mycosynth Wellspring + Walking Atlas, then we won't be able to retrieve nonbasic lands, so they can be saved until later. One way to make use of this is to put a nonbasic Forest after Lifetap, and follow that with probably card draw. If we proceed with Yawgmoth's Bargain into Boon Reflection into Spiritual Focus into Pain Magnification, we get the same number of layers, although I guess it is a little better since we are paying one life at a time rather than two. Still there are a lot of effects that draw cards, so I imagine there is a way to add layers here. Anyone see a way?
[EDIT] It looks like Farsight Mask can add a layer. Have a bunch of untapped Farsight Masks on the battlefield, and tap a hasted Gelectrode to damage ourselves. Then, before the damage ability resolves, cast Cultural Exchange to donate the Gelectrode to the opponent.
Unfortunately, we don't currently have a way to get noncreature artifact tokens. So we can either add March of the Machines, or maybe Mirrorworks.
[EDIT] And, we can add another layer if our nonbasic Forest is say Breeding Pool, and adding Amulet of Vigor to untap the land many times each time we draw and put it on the battlefield.
The Amulet of Vigor layer doesn't work since going through the Hyperstage destroys the Forest. Most of the untap triggers will fail to do anything if we try to properly increase the number of Lifetap copies in between them.
The other layer seems good, but I'm not sure how we can implement it and get a working start. With Lodestone Bauble we can refill the opponents library so we can't use Memory Jar and similar effects. But the starting sequence I suggested before won't work because we can't use Curiosity anymore.
Regarding a way to make artifact tokens: We can use Mirrorworks + Sharuum the Hegemon + Grinding Station + Mana Crypt to create an arbitrary amount of Sharuum tokens: Sharuum entering once gives a Mirrorworks trigger and if we pay for that we get a new Sharuum token. With two Sharuums entering the battlefield we can return mana crypt to pay for the token and the original sharuum to repeat the loop. So we either remove everything that convertsthis into damage or, more likely, don't use Mirrorworks. March of the Machines is an alternative. Karn, Silver Golem is another one that might be more convenient because we don't need to bounce it all the time.
Okay. Hmm, is there any alternative to Lodestone Bauble, maybe one that only takes our own lands from our graveyard into our library or into exile? I couldn't find one.
Keeping Finest Hour, but again we would have to get started with just Yawgmoth's Bargain. Even if we can't get our whole library, but can only access a few layers of our green mana stage, that would still allow us to put a whole bunch of Finest Hours onto the battlefield, and then we could access the deck during the combat stages. So I think it can be done. If worst comes to worst, we can replace Finest Hour with Thought Reflection; that should make the start easy.
Alhammarret's Archive instead of Boon Reflection might help. During the combo it's harder to use than the enchantment, but should improve the start.
EDIT: It looks like Distorting Wake can't make use of the second layer from Precursor Golem. When resolving a Precursor Golem trigger all the Wake copies are put on the stack right next to each other, with no target changes in between, so only one of them can return the Elvish Guidance to our hand.
Using something like Redirect to change the targets would allow us to trigger Psychic Battle for the new choice of Distorting Wake targets during the Hyperstage. That goes infinite, unless all our stage creatures have protection from the Wake. I don't see how we would manage that.
EDIT2: If we use Grip of Chaos instead of Psychic Battle then using Redirect should be safe. So we can save that layer.
If we have access to Redirect casts we can also use the Harness the Storm layer as long as we can put those triggers on the stack when we cast the sorcery from hand. We can do that if we use Distorting Wake as our duplicate sorcery.
But that would put us to 61 cards, without Finest Hour and questionable start capability.
EDIT3: It should be possible to use Sylvan Offering to replace both Xenograft and Hunted Phantasm. We don't have access to the X-spell everytime before an Elvish Guidance trigger resolves and the Hyperstage will wipe out the creatures, but we should be able to keep a Splinter Twin ability on the stack to put a hasty elf into play. We can then create more elves with Splinter Twin moving, resolve the elvish guidance and put the Twin ability on the stack for the next Elvish Guidance before spending all that green mana.
Removing Xenograft complicates the start a bit more.
EDIT4: Ahh, I forgot that while Redirecting a spell doesn't trigger Grip of Chaos it will still trigger Cowardice itself, which lets it bounce some creatures during the Hyperstage we don't want bounced there. So the second Precursor Goplem layer and the Harness the Storm layer can't be used this way after all.
[EDIT] I wonder if we can make hay with something like Silver Wyvern. I was hoping that Silver Wyvern would be limited because once you changed the target away from Silver Wyvern you couldn't change it again. But, with Psychic Battle, we can change the target to something like Harbinger of Spring and then change it back again with another Psychic Battle. Grip of Chaos doesn't seem to go infinite, but then Silver Wyvern doesn't seem to help out Distorting Wake.
As far as I can tell Redirect saves Harness the Storm. But to prevent it from going infinite we need to change Distorting Wake for some other instant/sorcery and I don't see one that would work. Wargate for example loses the nonbasic land layer later.
Spellskite would only trigger Psychic Battle if there is a target it can change. Otherwise there is no target choice happening.
EDIT: Derp, the Harness the Storm trigger is not a spell and changing the target of an ability is somewhat harder. Redirect doesn't work there.
We make it harder to get Elves, but the benefit is greater card drawing. From our opening hand, we can play Thought Reflection and Copy Enchantment, so our first payment to Yawgmoth's Bargain lets us draw four cards. We draw and play Alhammarret's Archive, Opalescence, Insurrection, and Splinter Twin to get two more card doublers on the battlefield, so the next Yawgmoth's Bargain draws 16 cards. Maybe with those 16 cards we can get Farsight Mask set up, along with a hasty Gelectrode, so the next damage to ourselves will get us multiple instances of card draws. I will investigate the start more later.
[EDIT 2] Hmm, I haven't been able to figure out the start yet. It seems like a reasonable start is to have Alhammarret's Archive in the opening hand, and then spend two life to draw Mirror Gallery, March of the Machines, Insurrection, and Splinter Twin, which will allow us to make a token copy of Alhammarret's Archive and draw four cards from then on. But getting sufficient mana and creature targeting from that point on seems tough.
Starting 7: Chrome Mox, Spellshift, Mana Crypt, Show and Tell, Omniscience, Yawgmoth's Bargain, Alhammarret's Archive.
Play out the hand. Pay 3 life to draw 6.
1. Grinding Station. Sacrifice Mana Crypt to mill some Artifacts. Assume that the first 2/3 sacrifices mill our artifacts and the Swamp, while the rest targets the opponent.
2. Sharuum the Hegemon. Return Mana Crypt, tap for {2}.
3. Karn, Silver Golem. Animate Alhamarret's Archive.
4. Mirror Gallery.
5. Insurrection.
6. Splinter Twin. Create a copy of Archive.
13. Backfire. Play it to bounce Sharuum twice, each time using two Bloodbond Marches. We can return 4 artifacts.
... Return Mana Crypt. Tap it. ({3})
... Return Mana Crypt. Tap it. ({5})
... Return Crown of the Ages. Animate the Archive token, move Splinter Twin to it and create another copy.
... Return Mana Crypt. Tap it. ({2})
14. Guilty Conscience. Play it to bounce Sharuum twice, each time using two Bloodbond Marches. We can return 4 artifacts.
... Return Mirror of Fate, activate it to exile our Library.
... Return Spellweaver's Helix once, imprinting Insurrection and Show and Tell.
... Return Mirror of Fate, activate it to put 7 cards into our library.
... Return Lodestone Bauble, activate it to put the Swamp back into our Library. ({1})
Pay 1 life to draw 8.
15. Opalescence.
16. Gelectrode.
17. Spiteful Shadows. Bounce Sharuum twice, return 4 artifacts: 3x Mana Crypt, 1x Chrome Mox.
18. Hardened Scales to imprint on the Chrome Mox.
19. Sylvan Offering with X=7.
20. Swamp.
21. Elvish Guidance. Tap the Swamp to get 1 black and 14 green.
22. Oversoul of Dusk.
23. Downdraft.
24. Insurrection.
... Use the green to create some Psychic Battle copies.
... When there are enough go through the green Ackermann stage with a few layers.
25. Use Crimson Acolyte to have the green stage output white and go through that stage creating copies of the enchantments.
... The last time through create a bunch of untapped Farsight Mask copies via Mimic Vat, Grinding Station and Sharuum bounces.
26. Cultural Exchange. Cast this in response to the Gelectrode targeting you. Donate that Gelectrode and get a lot of draw triggers.
If I haven't made any mistakes we are at 12 life with about 3 -> 3 -> 3 -> 10 draw triggers on the stack. Should be good enough.
Even if I missed some stuff we can probably repair it at the cost of a bit more life.
It might be better to skip creating Archive copies in the beginning. Then we wouldn't need to redraw insurrection. I used Karn, Silver Golem to animate the Archive because the Splinter Twin wouldn't survive March of the Machines bounces without moving. It might also be a mistake to go for the third Archive, but even if there are some more efficient variations, this at least gets us started.
Going to get technical for a minute: no combo can be infinite, only arbitrarily large. Therefore, Graham's Number of damage should be about the largest possible in one turn.
@Haile: I'm aware of the "no infinities" rule in Magic; I take the term "infinite combo" to refer to a combo that can be repeated an arbitrary number of times to create an arbitrary number of something. Although the term "infinite combo" may not be perfectly accurate, it's been used for years to refer to that type of combo, so I've been sticking with it. I suppose we could change the term to something like "unlimited combo", but that doesn't sound quite as natural to me.
As for Graham's Number, that number was beaten as soon as we found the Ackermann combo, way back on page 2. The latest decks far, far exceed Graham's Number.
@Iijil: Excellent start! Perhaps it could be improved a little bit, but probably not by much.
As for Graham's Number, that number was beaten as soon as we found the Ackermann combo, way back on page 2. The latest decks far, far exceed Graham's Number.
Well that's bloody impressive! Well done.
Edit: if you have indeed surpassed the previous record for largest non-infinite number ever to be used in a mathematical proof, that's kinda newsworthy.
I'm working on a Cheerios based sequence for this puzzle. My first draft swings with 197 creatures that all saw 4 Craterhoof triggers and are all copies of Wild Beastmaster. I did not calculate damage done. Cards that I think I can improve the list by working in include Resto Angel, Snapcaster, and Obstinate Familiar.
Edit: if you have indeed surpassed the previous record for largest non-infinite number ever to be used in a mathematical proof, that's kinda newsworthy.
Thank you! We've put a lot of thought into it.
Certainly larger numbers in proofs have appeared on the internet; for example, in various articles on the Googology Wiki. If we restrict to just numbers appearing in mathematical journals, then I don't know any clear cut examples that beat Graham's Number (primarily because math papers are far more likely to talk about fast growing functions than specific numbers), but then our Magic deck isn't going to appear in a mathematics journal either.
I've done some more work on the Cheerios strategy and it's going to be difficult to calculate the final number of creatures in play, let alone damage. It draws the entire library and has to use Obstinate Familiar to avoid losing by decking itself. about 3-4 slots that I still haven't figured out. There are I can probably get a list and mostly optimized play sequence done in the next few days.
Just doing those replacements would lead to infinites. If we create some Amulet of Vigor copies the Drownyard untaps multiple times producing more than the one black we can allow. To prevent this we can make creating artifact tokens more expensive. Specifically we raplace Karn, Silver Golem with Ensoul Artifact. All copies of the latter will be destroyed by Obliterate so it has the same limitations on reuse as Elvish Guidance and by using it as our method to animate artifacts and create token copies we ensure that those can only really be used in the layers after the Hyperstage.
Ensoul Artifact in turn allows Chrome Mox to exist as a creature, so we can't allow instants and sorceries that untap those anymore. We can replace Insurrection with Burst of Speed as we are no longer using Izzet Guildmage.
Excellent! With Lodestone Bauble gone, I thought that perhaps we could go back to using opponent's draw/discard as a limiter, so we could replace Thought Reflection with the higher level Bargain. Unfortunately, it looks like we can still donate Mortiphobia, Chrome Mox, and Mirror of Fate to the opponent to send a card from his hand back into his library. But, if we replace Ensoul Artifact with Animate Artifact, then Chrome Mox can no longer survive being animated, so Bargain seems safe again.
I might as well post my recent failures. First, I thought about using Cloud Cover so that we could bounce Elvish Guidance. Unfortunately, it requires the bouncing from an opponent, and if we donate Cloud Cover, the ability is not mandatory. I don't know any way to donate control of an ability.
I thought about getting another layer at the level of combat damage; the tricky part is that triggered abilities don't work well with getting that layer for Llanowar Reborn / Hardened Scales. Perhaps Quest for the Gemblades could get the +1/+1s rather than Hardened Scales, but then I am not sure how to make that work if we add another layer to combat damage.
I briefly went back to think about how to get a third stage; I would really like to make Staff of the Flame Magus and Searing Meditation work, but it seems it is not quite enough to count as a stage transition. Could there be cards added to make it work?
Talking about the start again: Iijil, do you know a good start now that we have Thought Reflection back? There is probably a way to get started using just a few life now.
With that I think we can get started after paying 3 life:
---Chrome Mox, Mana Crypt, Spellshift, Show and Tell, Omniscience, Alhammarret's Archive, Yawgmoth's Bargain.
Play the starting hand, pay 1 life, draw 2 cards.
---Thought Reflection, Copy Enchantment.
Play those, copy the Thought Reflection, pay 1 life, draw 8 cards.
---Gelectrode, Psychic Battle, Opalescence, Splinter Twin, Insurrection, Grinding Station, Spellweaver Helix, World at War.
Play the first two cards, just so they get haste and we can create copies easily later, Splinter Twin on Thought Reflection, create a copy after Insurrection.
Grinding Station, sac Mana Crypt to mill a World at War, imprint that World at War and Insurrection on Spellweavers Helix and play the second World at War to cast another Insurrection, get another Thought Reflection copy after the untap.
---Pay 1 life, draw 32 cards.
Should be good enough, considering the earlier starting sequence. We have hasty creature targeting from auras and any instant/sorcery via Gelectrode and can easily convert that into some colorless for Sylvan Offering, which leads into Ackermann stages via Elvish Guidance.
It might be possible to create more then one card draw trigger with the third life using Farsight Mask copies. But if it works it is very complicated for only a small gain.
EDIT: Huh, I just noticed that we can't simply use Insurrection because it would steal the opponents Dismiss into Dream. Our donation combo uses Sylvan Offering which we can only cast for nonzero in later layers. Luckily we can just use Starfield of Nyx to avoid that issue.
Is there any way you can use Witch Engine to produce your black mana, instead of Vault of Whispers or Urborg, Tomb of Yawgmoth? This would let you use Rings of Brighthearth on its tap ability (since it's not a mana ability anymore), and would allow you to use a creature that only targets things your opponent controls (such as Alluring Siren or Homeward Path) for design space. And I'm reasonably certain you could get rid of all the Witch Engines your opponents control before your final attack.
EDIT: Okay, your deck has become something completely different from the one in the page. So can you explain how this latest one works, and gets multiple Conway arrows?
EDIT: Okay, your deck has become something completely different from the one in the page. So can you explain how this latest one works, and gets multiple Knuth arrows?
The Ackermann combo that allows us to get multiple Conway arrows was found and described by Deedlit11 in this post on page 2.
Essentially it allows a single card to get a variable amount of layers by seperating the layers by the amount of green mana that is available.
The key to that is that a Psychic Battle trigger that can redirect the target to Elvish Spirit Guide can be used in two different ways:
1. You can bounce the guide and then play it to get a bunch of Bloodbond March triggers.
2. You can bounce the guide and then exile it from hand to get exactly one green mana.
The exactly one in the second option is important. If it can produce more we cn go infinite since we can use a single green mana to create more psychic battle triggers.
Later we found other things that can be used to similar effect:
- Chrome Mox allows us to use any creature as a spirit guide (read from here)
- By removing support cards that create more tokens we were able to use Soul Foundry, so we can exile creatures to get exactly one token. Chosing the right creatures we are able to use one of those tokens to create the psychic battle triggers instead of mana. (read from here)
- By removing support cards that allow us to sacrifice creatures we can use something like Horobi, Death's Wail and Mimic Vat as our "one token per psychic battle trigger" option. This ensures that only the tokens have haste and opens up more options for usable creatures. (read from here)
The latest development is that we not only use mana/tokens to differentiate layers that use the same cards otherwise but go the second step and use tokens to differentiate the layers and mana to differentiate the stage. So we use the same cards for a variable amount of Ackermann stages. Some abstract thoughts on that are here, with the first ideas for implementation shortly after.
We don't really have a single post explaining the deck since the ideas tend to evolve from each other somewhat fluidly.
Is there any way you can use Witch Engine to produce your black mana, instead of Vault of Whispers or Urborg, Tomb of Yawgmoth? This would let you use Rings of Brighthearth on its tap ability (since it's not a mana ability anymore), and would allow you to use a creature that only targets things your opponent controls (such as Alluring Siren or Homeward Path) for design space. And I'm reasonably certain you could get rid of all the Witch Engines your opponents control before your final attack.
While that doesn't work in the current deck, thanks for bringing up mana abilities.
It turns out that Elvish Guidance is a triggerd mana ability and as such doesn't use the stack. Specifically we can't respond to it to increase the number of elves between different triggers, so one of the layers in the current record deck doesn't work. Before looking up the rules I didn't know triggered mana abilities were a thing, but in hindsight that makes sense.
Drat, it looks like we still need something like Patron of the Moon or Walking Atlas in order to put Overgrown Tomb or Llanowar Reborn onto the battlefield. So that squeezes out Insurrection. I'm not sure how best to start in that case. We can still draw lots of cards, but we won't be able to get anything hasted until we kill things and imprint them on Mimic Vat. This looks difficult.
We should be able to use Show and Tell for that. We can essentially cast sorceries for a black mana and that is available early enough for all the stages that need to replay those lands.
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[EDIT] It looks like Farsight Mask can add a layer. Have a bunch of untapped Farsight Masks on the battlefield, and tap a hasted Gelectrode to damage ourselves. Then, before the damage ability resolves, cast Cultural Exchange to donate the Gelectrode to the opponent.
Unfortunately, we don't currently have a way to get noncreature artifact tokens. So we can either add March of the Machines, or maybe Mirrorworks.
[EDIT] And, we can add another layer if our nonbasic Forest is say Breeding Pool, and adding Amulet of Vigor to untap the land many times each time we draw and put it on the battlefield.
The other layer seems good, but I'm not sure how we can implement it and get a working start. With Lodestone Bauble we can refill the opponents library so we can't use Memory Jar and similar effects. But the starting sequence I suggested before won't work because we can't use Curiosity anymore.
Regarding a way to make artifact tokens: We can use Mirrorworks + Sharuum the Hegemon + Grinding Station + Mana Crypt to create an arbitrary amount of Sharuum tokens: Sharuum entering once gives a Mirrorworks trigger and if we pay for that we get a new Sharuum token. With two Sharuums entering the battlefield we can return mana crypt to pay for the token and the original sharuum to repeat the loop. So we either remove everything that convertsthis into damage or, more likely, don't use Mirrorworks. March of the Machines is an alternative. Karn, Silver Golem is another one that might be more convenient because we don't need to bounce it all the time.
Updated deck: What I would like to use is:
2 Opalescence
3 Psychic Battle
4 Cowardice
5 Dismiss Into Dream
6 Bloodbond March
7 Cephalid Shrine
8 Mana Crypt
9 Grinding Station
10 Mimic Vat
11 Omniscience
12 Leyline of Anticipation
13 Mirror of Fate
14 Splinter Twin
15 Crown of the Ages
16 Chrome Mox
17 Mirror Gallery
18 Sharuum the Hegemon
19 Gideon, Champion of Justice
20 Karn, Silver Golem
22 Mortiphobia
23 Spellweaver Helix
24 World at War
25 World at War
26 Lodestone Bauble
27 Mycosynth Wellspring
28 Walking Atlas
29 Obliterate
30 Spellshift
31 Kaho, Minamo Historian
32 Swamp
33 Enemy of the Guildpact
34 Crimson Acolyte
35 Harbinger of Spring
36 Downdraft
37 Elvish Guidance
38 Distorting Wave
39 Night Dealings
40 Boon Reflection
41 Lifetap
42 Tropical Island
43 Farsight Mask
44 Spiritual Focus
45 Pain Magnification
46 Backfire
47 Spiteful Shadows
48 Guilty Conscience
49 Justice
50 Five-Alarm Fire
52 Cultural Exchange
53 Hunted Phantasm
54 Precursor Golem
55 Insurrection
56 Llanowar Reborn
57 Hardened Scales
58 Show and Tell
59 Yawgmoth's Bargain
60 Finest Hour
Keeping Finest Hour, but again we would have to get started with just Yawgmoth's Bargain. Even if we can't get our whole library, but can only access a few layers of our green mana stage, that would still allow us to put a whole bunch of Finest Hours onto the battlefield, and then we could access the deck during the combat stages. So I think it can be done. If worst comes to worst, we can replace Finest Hour with Thought Reflection; that should make the start easy.
EDIT: It looks like Distorting Wake can't make use of the second layer from Precursor Golem. When resolving a Precursor Golem trigger all the Wake copies are put on the stack right next to each other, with no target changes in between, so only one of them can return the Elvish Guidance to our hand.
Using something like Redirect to change the targets would allow us to trigger Psychic Battle for the new choice of Distorting Wake targets during the Hyperstage. That goes infinite, unless all our stage creatures have protection from the Wake. I don't see how we would manage that.
EDIT2: If we use Grip of Chaos instead of Psychic Battle then using Redirect should be safe. So we can save that layer.
If we have access to Redirect casts we can also use the Harness the Storm layer as long as we can put those triggers on the stack when we cast the sorcery from hand. We can do that if we use Distorting Wake as our duplicate sorcery.
But that would put us to 61 cards, without Finest Hour and questionable start capability.
EDIT3: It should be possible to use Sylvan Offering to replace both Xenograft and Hunted Phantasm. We don't have access to the X-spell everytime before an Elvish Guidance trigger resolves and the Hyperstage will wipe out the creatures, but we should be able to keep a Splinter Twin ability on the stack to put a hasty elf into play. We can then create more elves with Splinter Twin moving, resolve the elvish guidance and put the Twin ability on the stack for the next Elvish Guidance before spending all that green mana.
Removing Xenograft complicates the start a bit more.
EDIT4: Ahh, I forgot that while Redirecting a spell doesn't trigger Grip of Chaos it will still trigger Cowardice itself, which lets it bounce some creatures during the Hyperstage we don't want bounced there. So the second Precursor Goplem layer and the Harness the Storm layer can't be used this way after all.
Can Redirect really save the Harness the Storm layer? If so, it would make sense to give up Distorting Wake to get that layer.
[EDIT] I wonder if we can make hay with something like Silver Wyvern. I was hoping that Silver Wyvern would be limited because once you changed the target away from Silver Wyvern you couldn't change it again. But, with Psychic Battle, we can change the target to something like Harbinger of Spring and then change it back again with another Psychic Battle. Grip of Chaos doesn't seem to go infinite, but then Silver Wyvern doesn't seem to help out Distorting Wake.
What about Spellskite? We could activate it for Harness the Storm's triggered ability, and it would do nothing. Would the attempt trigger Psychic Battle?
Spellskite would only trigger Psychic Battle if there is a target it can change. Otherwise there is no target choice happening.
EDIT: Derp, the Harness the Storm trigger is not a spell and changing the target of an ability is somewhat harder. Redirect doesn't work there.
We make it harder to get Elves, but the benefit is greater card drawing. From our opening hand, we can play Thought Reflection and Copy Enchantment, so our first payment to Yawgmoth's Bargain lets us draw four cards. We draw and play Alhammarret's Archive, Opalescence, Insurrection, and Splinter Twin to get two more card doublers on the battlefield, so the next Yawgmoth's Bargain draws 16 cards. Maybe with those 16 cards we can get Farsight Mask set up, along with a hasty Gelectrode, so the next damage to ourselves will get us multiple instances of card draws. I will investigate the start more later.
[EDIT] I believe that we can save the Amulet of Vigor layer by adding Consecrate Land, which will preserve the Forest from getting destroyed by Obliterate. That uses up two more cards, so we would have to give up Finest Hour and Thought Reflection. So we have to get started with just Yawgmoth's Bargain and Alhammarret's Archive, making it hard again.
[EDIT 2] Hmm, I haven't been able to figure out the start yet. It seems like a reasonable start is to have Alhammarret's Archive in the opening hand, and then spend two life to draw Mirror Gallery, March of the Machines, Insurrection, and Splinter Twin, which will allow us to make a token copy of Alhammarret's Archive and draw four cards from then on. But getting sufficient mana and creature targeting from that point on seems tough.
Starting 7: Chrome Mox, Spellshift, Mana Crypt, Show and Tell, Omniscience, Yawgmoth's Bargain, Alhammarret's Archive.
Play out the hand. Pay 3 life to draw 6.
1. Grinding Station. Sacrifice Mana Crypt to mill some Artifacts. Assume that the first 2/3 sacrifices mill our artifacts and the Swamp, while the rest targets the opponent.
2. Sharuum the Hegemon. Return Mana Crypt, tap for {2}.
3. Karn, Silver Golem. Animate Alhamarret's Archive.
4. Mirror Gallery.
5. Insurrection.
6. Splinter Twin. Create a copy of Archive.
Pay 3 life to draw 12.
7. Bloodbond March.
8. Copy Enchantment, copying Bloodbond March.
9. Cephalid Shrine.
10. Cowardice.
11. Psychic Battle.
12. Leyline of Anticipation.
13. Backfire. Play it to bounce Sharuum twice, each time using two Bloodbond Marches. We can return 4 artifacts.
... Return Mana Crypt. Tap it. ({3})
... Return Mana Crypt. Tap it. ({5})
... Return Crown of the Ages. Animate the Archive token, move Splinter Twin to it and create another copy.
... Return Mana Crypt. Tap it. ({2})
14. Guilty Conscience. Play it to bounce Sharuum twice, each time using two Bloodbond Marches. We can return 4 artifacts.
... Return Mirror of Fate, activate it to exile our Library.
... Return Spellweaver's Helix once, imprinting Insurrection and Show and Tell.
... Return Mirror of Fate, activate it to put 7 cards into our library.
... Return Lodestone Bauble, activate it to put the Swamp back into our Library. ({1})
Pay 1 life to draw 8.
15. Opalescence.
16. Gelectrode.
17. Spiteful Shadows. Bounce Sharuum twice, return 4 artifacts: 3x Mana Crypt, 1x Chrome Mox.
18. Hardened Scales to imprint on the Chrome Mox.
19. Sylvan Offering with X=7.
20. Swamp.
21. Elvish Guidance. Tap the Swamp to get 1 black and 14 green.
22. Oversoul of Dusk.
23. Downdraft.
24. Insurrection.
... Use the green to create some Psychic Battle copies.
... When there are enough go through the green Ackermann stage with a few layers.
25. Use Crimson Acolyte to have the green stage output white and go through that stage creating copies of the enchantments.
... The last time through create a bunch of untapped Farsight Mask copies via Mimic Vat, Grinding Station and Sharuum bounces.
26. Cultural Exchange. Cast this in response to the Gelectrode targeting you. Donate that Gelectrode and get a lot of draw triggers.
If I haven't made any mistakes we are at 12 life with about 3 -> 3 -> 3 -> 10 draw triggers on the stack. Should be good enough.
Even if I missed some stuff we can probably repair it at the cost of a bit more life.
It might be better to skip creating Archive copies in the beginning. Then we wouldn't need to redraw insurrection. I used Karn, Silver Golem to animate the Archive because the Splinter Twin wouldn't survive March of the Machines bounces without moving. It might also be a mistake to go for the third Archive, but even if there are some more efficient variations, this at least gets us started.
You had me on the edge of my seat when you went for 3 archives and used Mirror of Fate, but you made it work. What a nail-biter! lol
As for Graham's Number, that number was beaten as soon as we found the Ackermann combo, way back on page 2. The latest decks far, far exceed Graham's Number.
@Iijil: Excellent start! Perhaps it could be improved a little bit, but probably not by much.
Well that's bloody impressive! Well done.
Edit: if you have indeed surpassed the previous record for largest non-infinite number ever to be used in a mathematical proof, that's kinda newsworthy.
Pauper: Burn
Modern: Burn
Legacy: Burn
EDH: Marath, Will of the Wild - Ramp/Combo | Anafenza the Foremost - French | Uril, the Miststalker - Voltron | Freyalise, Llanowar's Fury - Goodstuff
Ghost Council of Orzhov - Tokens | Lazav, Dimir Mastermind - Control | Isamaru, Hound of Konda - Tiny Leaders
Thank you! We've put a lot of thought into it.
Certainly larger numbers in proofs have appeared on the internet; for example, in various articles on the Googology Wiki. If we restrict to just numbers appearing in mathematical journals, then I don't know any clear cut examples that beat Graham's Number (primarily because math papers are far more likely to talk about fast growing functions than specific numbers), but then our Magic deck isn't going to appear in a mathematics journal either.
Pauper: Burn
Modern: Burn
Legacy: Burn
EDH: Marath, Will of the Wild - Ramp/Combo | Anafenza the Foremost - French | Uril, the Miststalker - Voltron | Freyalise, Llanowar's Fury - Goodstuff
Ghost Council of Orzhov - Tokens | Lazav, Dimir Mastermind - Control | Isamaru, Hound of Konda - Tiny Leaders
Replace the Swamp, Walking Atlas, Lodestone Bauble and Mycosynth Wellspring with Drownyard Temple and Urborg, Tomb of Yawgmoth. The Drownyard Temple can come back from the graveyard using ots own ability and untap with the Amulet of Vigor we are running anyway. It can then tap for black thanks to Urborg, which is staying on the battlefield thanks to Consecrate Land.
Just doing those replacements would lead to infinites. If we create some Amulet of Vigor copies the Drownyard untaps multiple times producing more than the one black we can allow. To prevent this we can make creating artifact tokens more expensive. Specifically we raplace Karn, Silver Golem with Ensoul Artifact. All copies of the latter will be destroyed by Obliterate so it has the same limitations on reuse as Elvish Guidance and by using it as our method to animate artifacts and create token copies we ensure that those can only really be used in the layers after the Hyperstage.
Ensoul Artifact in turn allows Chrome Mox to exist as a creature, so we can't allow instants and sorceries that untap those anymore. We can replace Insurrection with Burst of Speed as we are no longer using Izzet Guildmage.
With those changes the deck now looks like this:
2 Opalescence
3 Psychic Battle
4 Cowardice
5 Dismiss Into Dream
6 Bloodbond March
7 Cephalid Shrine
8 Mana Crypt
9 Grinding Station
10 Mimic Vat
11 Omniscience
12 Leyline of Anticipation
13 Mirror of Fate
14 Splinter Twin
15 Crown of the Ages
16 Chrome Mox
17 Mirror Gallery
18 Sharuum the Hegemon
19 Gideon, Champion of Justice
20 Gelectrode
22 Spellweaver Helix
23 World at War
24 World at War
25 Urborg, Tomb of Yawgmoth
26 Consecrate Land
27 Obliterate
28 Spellshift
29 Kaho, Minamo Historian
30 Drownyard Temple
31 Enemy of the Guildpact
32 Crimson Acolyte
33 Harbinger of Spring
34 Downdraft
35 Elvish Guidance
36 Distorting Wake
37 Night Dealings
38 Alhammarret's Archive
39 Lifetap
40 Amulet of Vigor
41 Overgrown Tomb
42 Farsight Mask
43 Spiritual Focus
44 Pain Magnification
45 Backfire
46 Spiteful Shadows
47 Guilty Conscience
48 Justice
49 Five-Alarm Fire
51 Cultural Exchange
52 Ensoul Artifact
53 Precursor Golem
54 Burst of Speed
55 Llanowar Reborn
56 Hardened Scales
57 Show and Tell
58 Yawgmoth's Bargain
59 Thought Reflection
60 Finest Hour
I might as well post my recent failures. First, I thought about using Cloud Cover so that we could bounce Elvish Guidance. Unfortunately, it requires the bouncing from an opponent, and if we donate Cloud Cover, the ability is not mandatory. I don't know any way to donate control of an ability.
I thought about getting another layer at the level of combat damage; the tricky part is that triggered abilities don't work well with getting that layer for Llanowar Reborn / Hardened Scales. Perhaps Quest for the Gemblades could get the +1/+1s rather than Hardened Scales, but then I am not sure how to make that work if we add another layer to combat damage.
I briefly went back to think about how to get a third stage; I would really like to make Staff of the Flame Magus and Searing Meditation work, but it seems it is not quite enough to count as a stage transition. Could there be cards added to make it work?
Talking about the start again: Iijil, do you know a good start now that we have Thought Reflection back? There is probably a way to get started using just a few life now.
With that I think we can get started after paying 3 life:
---Chrome Mox, Mana Crypt, Spellshift, Show and Tell, Omniscience, Alhammarret's Archive, Yawgmoth's Bargain.
Play the starting hand, pay 1 life, draw 2 cards.
---Thought Reflection, Copy Enchantment.
Play those, copy the Thought Reflection, pay 1 life, draw 8 cards.
---Gelectrode, Psychic Battle, Opalescence, Splinter Twin, Insurrection, Grinding Station, Spellweaver Helix, World at War.
Play the first two cards, just so they get haste and we can create copies easily later, Splinter Twin on Thought Reflection, create a copy after Insurrection.
Grinding Station, sac Mana Crypt to mill a World at War, imprint that World at War and Insurrection on Spellweavers Helix and play the second World at War to cast another Insurrection, get another Thought Reflection copy after the untap.
---Pay 1 life, draw 32 cards.
Should be good enough, considering the earlier starting sequence. We have hasty creature targeting from auras and any instant/sorcery via Gelectrode and can easily convert that into some colorless for Sylvan Offering, which leads into Ackermann stages via Elvish Guidance.
It might be possible to create more then one card draw trigger with the third life using Farsight Mask copies. But if it works it is very complicated for only a small gain.
EDIT: Huh, I just noticed that we can't simply use Insurrection because it would steal the opponents Dismiss into Dream. Our donation combo uses Sylvan Offering which we can only cast for nonzero in later layers. Luckily we can just use Starfield of Nyx to avoid that issue.
EDIT: Okay, your deck has become something completely different from the one in the page. So can you explain how this latest one works, and gets multiple Conway arrows?
Essentially it allows a single card to get a variable amount of layers by seperating the layers by the amount of green mana that is available.
The key to that is that a Psychic Battle trigger that can redirect the target to Elvish Spirit Guide can be used in two different ways:
1. You can bounce the guide and then play it to get a bunch of Bloodbond March triggers.
2. You can bounce the guide and then exile it from hand to get exactly one green mana.
The exactly one in the second option is important. If it can produce more we cn go infinite since we can use a single green mana to create more psychic battle triggers.
Later we found other things that can be used to similar effect:
- Chrome Mox allows us to use any creature as a spirit guide (read from here)
- By removing support cards that create more tokens we were able to use Soul Foundry, so we can exile creatures to get exactly one token. Chosing the right creatures we are able to use one of those tokens to create the psychic battle triggers instead of mana. (read from here)
- By removing support cards that allow us to sacrifice creatures we can use something like Horobi, Death's Wail and Mimic Vat as our "one token per psychic battle trigger" option. This ensures that only the tokens have haste and opens up more options for usable creatures. (read from here)
The latest development is that we not only use mana/tokens to differentiate layers that use the same cards otherwise but go the second step and use tokens to differentiate the layers and mana to differentiate the stage. So we use the same cards for a variable amount of Ackermann stages. Some abstract thoughts on that are here, with the first ideas for implementation shortly after.
We don't really have a single post explaining the deck since the ideas tend to evolve from each other somewhat fluidly.
While that doesn't work in the current deck, thanks for bringing up mana abilities.
It turns out that Elvish Guidance is a triggerd mana ability and as such doesn't use the stack. Specifically we can't respond to it to increase the number of elves between different triggers, so one of the layers in the current record deck doesn't work. Before looking up the rules I didn't know triggered mana abilities were a thing, but in hindsight that makes sense.
I guess with three spare card slots, there is certainly space to add another layer, but I can't think of one right now.