A while back, a group of us addressed the following challenge: Create a 60 card, Vintage legal deck that deals the most damage on turn 1 (assuming that you go first), given that no infinite combos are allowed. By "no infinite combos", I mean that there must be a finite upper bound to the amount of damage that the deck can deal, and the object is to make that maximum damage as large as possible. You are allowed to assume that all luck goes your way, including the ordering of the library and all coin flips.
However, there is a slight problem involving Mana Crypt and Builder's Blessing; the best fix that we've been able to find is to remove Builder's Blessing and Devout Lightcaster, and add Avacyn, Angel of Hope and Thran Dynamo, losing nine recursive layers. But, with the appearance of Gideon, Ally of Zendikar, we can use that card to replace both Avacyn and Thran Dynamo, allowing [c]Devout Lightcaster to come back in and regaining nine layers. Final damage is in excess of 2 -> 19 -> 417 damage.
This challenge originated on the Wizards forums, which have been shut down; however, an archived version appears here:
UPDATE: We have come quite a long way - the latest verified deck deals damage in excess of F_{w^3 + w13 + 5} (107), using the fast-growing hierarchy. Details can be found here, although the article is still incomplete:
For those who have not been keeping up with the thread, reading through 70+ pages is too much, so at periodic points we have been giving summaries of the progress up to that point. The latest one is this excellent breakdown by Stakfish:
This post details my discovery of the Ackermann combo, which led to all this stage madness.
This post by Iijil gave his initial thoughts on extending the deck to the hyperstage, which was refined in later posts; this is the blueprint for the stage level extensions.
4) Each Storm Herd / Caller of the Pride adds 420 creature tokens, which gets doubled 12 times for 420 * 2^12 tokens. End result: 420 * 2^15 tokens.
5) Each spell in this step doubles the number of creatures 12 times, except for Mogg Infestation which doubles it 13 times. All told there are 196 doublings, for 420 * 2^211.
6) You don't recycle Day of the Dragons, but you recycle the other 12 cards, which makes 148 doublings per Praetor's Counsel. End result: 420 * 2^803.
8) Playing another Deply / Infestation adds 25 doublings for 420 * 2^828.
9) Boros Reckoner takes 420 * 2^828 damage, which gets doubled 8 times for 420 * 2^836, then the redirect gets doubled 8 times for 420 * 2^844. Final damage: About 420 * 2^846.
Active a Mirror copy, putting Mana Crypt into the library. Cast Mnemonic Wall getting Rousing of Souls, Cast Rousing of Souls drawing Mana Crypt and bouncing Mnemonic Wall. Cast Mana crypt and make 2 mana with it. Activate a second Mirror, respond to your own activation by casting March of the Machines at instant speed, which kills Mana Crypt which triggers Mimic Vat which exiles Mana Crypt, then the Mirror ability resolves putting Mana Crypt into the library. Cast Mnemonic wall getting back Rousing of Souls, cast Rousing of Souls drawing Mana Crypt and bouncing Mnemonic Wall, March of the Machines, and Cowardice. Cast Mana Crypt, activate for 2 mana. Now, we have 4 mana.
Play Cateran Slaver. (If you thought the instant speed timing was precise so far, wait until you see this.) Activate the 3rd Mirror token, respond with the 4th mirror token, respond with March of the Machines again, killing Mana Crypt, exiling it to Mimic Vat, then resolving the 3rd mirror ability to put mana crypt in the library. Still with the 3rd Mirror of Fate ability unresolved, cast Mnemonic Wall, it enters triggering Dual Nature and its own ETB in that order. Then resolve the etb returning Rousing of Souls to your hand. With the dual nature trigger still on the stack, respond with Rousing of Souls, drawing Mana Crypt, and using the etb triggers from the spirits to target Mirror of Fate, Mnemonic Wall, March of the Machines, and Cowardice. Bounce Mirror of Fate before March of the Machines, and then recast it in response to the trigger that's bouncing March of the machines getting 4 token copies. Cast Mana Crypt also in response to the bounce trigger, cause it to die, exiling under Mimic Vat. This resolves us back to the dual nature trigger which makes mnemonic walls with last known information, which returns Rousing of Souls to our hand. Then Mirror of Fate resolves putting Mana Crypt back in the library.
Cast Rousing of Souls, draw Mana Crypt, use the etb damage triggers to kill Cateran Slaver, Exiling it onto Mimic Vat. Use the 4 mana still floating to activate Mimic Vat. Now we have a 5/5 token with haste. Cast Rite of Passage. At this point I believe the loop is ready to start.
We have 1 arbitrary mana floating.
In hand, we have Mnemonic Wall, March of the Machines, Cowardice, Mirror of Fate, and Mana Crypt.
In play, we have Clash of Realities, Omniscience, Vedalken Orerry, Rite of Passage, Opalescence, Mimic Vat, Dual Nature, 2x Doubling Season, and 5x Mirror of Fate.
In graveyard we have Rousing of Souls.
The library is empty.
We have a 5/5 token with haste.
Activate a mirror token, followed by another mirror token. Cast Mana Crypt in response, tap for 2 mana. Cast March of the Machines before mirror resolves, kill the crypt and exile to mimic vat. One Mirror resolves putting Mana Crypt into the library. Respond to the mirror on the stack with Mnemonic wall, triggering dual nature and itself. Resolve the wall trigger, getting back rousing of souls. Cast Rousing of Souls, aiming the ETB damage at the 5/5 with haste which pumps it with Rite of Passage, and drawing mana crypt. Let the dual nature trigger resolve, making wall tokens which get back Rousing of Souls. Cast mana crypt, which dies and exiles to mimic vat. Let the other mirror ability resolve, putting mana crypt back into the library. Cast Cowardice. Cast Rousing of Souls, using the etb's to bounce Mnemonic Wall, Cowardice, March of the Machines, and Mirror of Fate. Bounce Mirror of Fate before March of the Machines, and cast it again in response to the march of the machine's bounce making 4 token copies of Mirror of Fate. Allow the bouncing to resolve.
We have 3 arbitrary mana floating.
In hand, we have Mnemonic Wall, March of the Machines, Cowardice, Mirror of Fate, and Mana Crypt.
In play, we have Clash of Realities, Omniscience, Vedalken Orerry, Rite of Passage, Opalescence, Mimic Vat, Dual Nature, 2x Doubling Season, and 5x Mirror of Fate.
In graveyard we have Rousing of Souls.
The library is empty.
We have a 5/5 token with haste and 12 +1/+1 counters.
Loop forever to get infinite mana and an infinitely large hasty creature. This mess was the most efficient way that I could think of an infinite combo out of the cards listed, but an infinite combo it is, nonetheless.
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Thanks for vetting the deck! The reason Rousing of Souls does not go infinite is that it not only causes us to draw a card, but the opponent draws a card as well. Thus, we can only cast Rousing of Souls a total of 53 times before the next casting ends the game, and with it our opportunity to deal damage. Otherwise, yes, a card-drawing card that could be retrieved by Mnemonic Wall would certainly go infinite.
1. Play Lotus, Show and Tell, put Omniscience into play, cast Enter the Infinite, draw your deck, put back Unwilling Recruit.
2. Cast Inner Fire for 54 red mana.
3. Cast Precursor Golem
4. Cast Rite of Replication with kicker 4 times. Use Regrowth effects to re-cast Rite until you're out of mana for the kicker. At this point, you have a very, very large amount of golems. Cast Battle Hymn for a very, very large amount of mana, then continue casting Regrowths into Rites. Cast Radiate on Rite.
5. Cast Might of the Masses. Cast 4x Overblaze, each time splicing for each other Overblaze still in your hand. Cast Battle Hymn for a bunch of mana.
6. Cast Praetor's Counsel
7. Repeat steps 4 and 5 for each Counsel.
8. Using all the mana you generated from each Battle Hymn, cast Unwilling Recruit for a bunch.
9. Attack for lots.
I'm genuinely interested if anyone can come up with how much damage this would deal.
That actually goes infinite. Say we have a Praetor's Counsel in the exile zone, and another Praetor's Counsel, Pull From Eternity, and Rite of Replication in our hand. Cast the Rite of Replication on a Golem, cast Pull From Eternity to put the exiled Praetor's Counsel in the graveyard, and cast the Praetor's Counsel in our hand to return all three cards in the graveyard to our hand. Our position is reset, except that there are now a lot more Golems on the board, and we can repeat this as long as we want to.
I am surprised that Radiate hasn't shown up in the lists posted here. I didn't exactly do an exhaustive search but having a modest number of animated doubling season in play (say 20) would result in an absolutely absurd number of doubling seasons if you were to cast a (kicked) rite of replication and then radiate it. Since each copy would resolve independently this alone would generate in excess 2^^^^^^^^^^^^^^^^^^^^20 (2->20 in that link I think)(that's under representing it) in play. Making the follow up radiated rite of replication generate... well a number I'm not even able to comprehend. Effectively each radiated copy spell would create a nested exponential for as many permanents as there are in play. I mean really, even after two/three resolutions of rite+radiate you are looking at numbers that make the http://www.soniccenter.org/sm/mtg/megacombo.html link look tiny. (2->20)->(2->20)
After the first Rite of Replication, there will be 6 Precursor Golems and 22 vanilla Golems. After the second Rite, there will be 279,936 Precursor Golems and about 4 million Golems total. Both numbers are between 2^^4 = 65,536 and 2^^5, which is more than 10^19728. Each additional Rite will exponentiate the number of Golems, so after the third Rite there will be between 2^^5 and 2^^6, and the fourth there will be between 2^^6 and 2^^7, and so on. The retrieval spells allow you to cast Rite of Replication 40 times, then the Praetor's Counsels repeat this four times, for 200 Rites. Finally we can flashback 4 Mystic Retrievals for 204 Rites, and between 2^^206 and 2^^207 Golems in the end.
Then there is the effect of the other cards; unfortunately, all of them combined are not enough to reach 2^^207. For example, Might of the Masses adds (X-1)Y to the power of each Golem (except one), where Y is the number of Precursor Golems and X is the total number of Golems, so the total power becomes X((X-1)Y+3) < X^3. Now X^3 sounds a lot bigger than X, but it has basically zero effect on a large power tower. For example, if X = 2^2^1000, X^3 = (2^2^1000)^3 = 2^(2^1000 * 3) < 2^2^1002. In our case we have X = 2^2^Z where Z is itself a large power tower, and we increase that to less than 2^2^(Z+2), and adding two to Z is not noticeable at all. All the other cards do less the cubing as well, so the final damage will be between 2^^206 and 2^^207.
I am surprised that Radiate hasn't shown up in the lists posted here. I didn't exactly do an exhaustive search but having a modest number of animated doubling season in play (say 20) would result in an absolutely absurd number of doubling seasons if you were to cast a (kicked) rite of replication and then radiate it. Since each copy would resolve independently this alone would generate in excess 2^^^^^^^^^^^^^^^^^^^^20 (that's under representing it) in play. Making the follow up radiated rite of replication generate... well a number I'm not even able to comprehend. Effectively each radiated copy spell would create a nested exponential for as many permanents as there are in play. I mean really, even after two resolutions of rite->radiate you are looking at numbers that make the http://www.soniccenter.org/sm/mtg/megacombo.html link look tiny.
You don't get near 2^^^^^^^^^^^^^^^^^^^^20. 2^^^^^^^^^^^^^^^^^^^^20 is not a nested exponential of 20 exponents; that's 2^^20. In general
2^^X is an exponential tower of X 2's (2^2^2...^2),
2^^^X is 2^^2^^2...^^2 with X 2's,
2^^^^X is 2^^^2^^^2...^^^2 with X 2's
and so on. Each Radiate takes X Doubling Seasons to 2^^X Doubling Seasons, so N Radiates would produce about 2^^^N Doubling Seasons in the end - nowhere near the numbers in the megacombo.
I am surprised that Radiate hasn't shown up in the lists posted here. I didn't exactly do an exhaustive search but having a modest number of animated doubling season in play (say 20) would result in an absolutely absurd number of doubling seasons if you were to cast a (kicked) rite of replication and then radiate it. Since each copy would resolve independently this alone would generate in excess 2^^^^^^^^^^^^^^^^^^^^20 (that's under representing it) in play. Making the follow up radiated rite of replication generate... well a number I'm not even able to comprehend. Effectively each radiated copy spell would create a nested exponential for as many permanents as there are in play. I mean really, even after two resolutions of rite->radiate you are looking at numbers that make the http://www.soniccenter.org/sm/mtg/megacombo.html link look tiny.
Radiate doesn't combine with Precursor Golem, since Radiates puts copies of the spell on the stack, and Precursor Golem only triggers when a spell is cast. (Which is a good thing, since otherwise it would go infinite.) Even if it worked like you thought it did, you wouldn't get anywhere near 2^^^^^^^^^^^^^^^^^^^^20. 2^^^^^^^^^^^^^^^^^^^^20 is not a nested exponential of 20 exponents; that's 2^^20. In general
2^^X is an exponential tower of X 2's (2^2^2...^2),
2^^^X is 2^^2^^2...^^2 with X 2's,
2^^^^X is 2^^^2^^^2...^^^2 with X 2's
and so on. So even if Precursor Golem triggered on every Radiate copy, each Radiate would take X Golems to 2^^X Golems, so N Radiates would produce about 2^^^N Golems in the end - nowhere near the numbers in the megacombo.
Hmm, Each Overblaze gets copied XY times where X is the number of Golems and Y is the number of Precursor Golem. So the total damage gets multiplied by 2^(10XY). This takes the damage to between 2^^207 and 2^^208.
Oh well, I figured I was misinterpreting something somewhere. Still an absurdly big number fairly simply. My mistake for misinterpreting the notation. Guess thats the problem with numbers that big, you really just cannot even wrap your head around just how big they are.
The opponent is assumed to have a deck of 60 Islands.
No, no sideboard. (Although actually, I did address the challenge where a 15 card sideboard was allowed, and I was able to obtain more than 500 Knuth arrows. But for the main challenge, no sideboard.)
We use Black Lotus+Show and Tell+Omniscience+Enter the Infinite, then our token makers, then Cathars' Crusade (which is really awesome), then our damage doublers, then our big token makers, then our creature pumps (Flame-Kin Zealot and the Craterhoof Behemoths), followed by our 4x Tears of Rage. Serum Visions probably isn't good, but whatever. I'm not sure exactly how much damage this is, but it's some ridiculously large number. (I've got a Python code that I think will work, but my computer can't run it, so it's probably not very efficient).
EDIT: Best-case scenario is starting with 3 Chancellor of the Forge in your opener along with the combo thing.
EDIT 2: Play your Fungal Sproutings AFTER your Craterhoofs, but before Flame-Kin Zealot (I think this is better, but I'm not sure, The sequencing here is really, really weird).
Okay, after the eight Monastery Mentors are on the board, each noncreature spell adds eight new creatures, and with four Cathar's Crusades on the board, each noncreature spell adds 32 +1/+1 counters to each creature on the board (33 if the creature has prowess). You cast 22 noncreature spells before we get to Empty the Warrens, for 176 new token creatures in addition to the 9 nontoken ones and three Goblin tokens, for 188 total. For Empty the Warrens, the storm count starts at 35, leading to 150 copies of Empty the Warrens and 300 Goblin tokens, plus 32 Monk tokens for 520 total creatures. Each Deploy to the Front adds 8 tokens and then doubles the number of creatures, so four iterations of that results in 8560 creatures. Each Chancellor of the Forge adds one creature and then doubles the number of creatures, so after four iterations we have 136,990 creatures. A Craterhoof Behomoths makes it 136,991. (It's best to alternate Craterhoof Behomoths and Fungal Sproutings.)
Next, we have to calculate the greatest power among creatures we control for Fungal Sprouting. The greatest power belongs one of the intial Monastery Mentors, which start at 2/2, and then the four Cathars' Crusades add 9,17,25, and 33 for 86 power. We cast another 26 noncreature spells, activating Prowesss 26 times for 112 power. Then, we add another 136,948 creatures, each one adding 4 power, resulting in 547,904 power. Finally, the Craterhoof Behemoths increases that to 684,895.
So when we cast the first Fungal Sprouting, we add 684,895 creatures, increasing the greatest power to 3,424,475, then the second Craterhoof Behometh adds 821,887 for 4,246,362. Second Fungal Sprouting adds 4,246,362 creatures: 5,068,250 creatures, 26,300,060 max power. Third Fungal Sporuting adds 25,300,060 creatures: 30,368,311 creatures, 161,868,611 max power. Finally the Fourth Fungal Sprouting adds 161,868,611 creatures for 192,236,922 creatures and 809,343,055 max power. Flame-Kin Zealot gives all the creatures haste, then Tears of Rage increases the max power to 1,578,290,751. So an upper bound for the amount of damage is 192,236,923 * 1,578,290,751 = 3.034 * 10^17.
1. Play Lotus, Show and Tell, put Omniscience into play, cast Enter the Infinite, draw your deck, put back Unwilling Recruit.
2. Cast Inner Fire for 54 red mana.
3. Play Rite of Replication with kicker four times. Regrowth it and continue until you run out of mana.
4. Cast Battle Hymn for a bunch of mana. Continue casting Regrowths into Rites.
5. Use either Praetor's Counsel, Feldon's Cane, Cranial Archive, or a clone on Cane or Archive to reset and do it again. (With Archive, you magically draw Enter the Infinite and start again. With Cane, you do cast Enter, then activate Cane in response).
6. Keep resetting until you're out of cards.
7. Flashback Mystic Retrival on Rite of Replication, flash it back with blue mana made by recycling Lotus over and over.
8. Cast Unwilling Recruit for all the mana you have left.
9. Attack for lots.
Begin with Opalescence, then In the Web of War to give everything a boost and haste. 4 Dual Natures (which is really 30), and then 4 Doubling Seasons (which is really approximately 2^^120 if I'm understanding that notation correctly. also, playing 4 of each may be wildly inefficient, but I admittedly don't understand the consequences here).
Get a few things in play that will start the attack power rising, namely Cathars' Crusade and Hamletback Goliath and Gratuitous Violence. (17 cards used so far)
(Side note, I now hope someday in a perfectly reasonable deck to Rite of ReplicationHamletback Goliath with Doubling Season out. 10 enter at same time, all triggering off one another, getting counters that are doubled and counted by other triggers, turning the original Goliath into a 6 million power creature with 3 cards that are all awesome in a RUG edh deck).
Then, we get more complex. We play Pyromancer Ascension, which is really an outrageous amount of them, and then Rite of Replication on something (mostly to get Rite of Replication in the graveyard). Then we play Eye of the Storm (which is close to the last permanent we play). Cast Seething Song so that we can kick every Rite of Replication forever. Cast Rite of Replication, Storm casts it again (which activates the Ascensions), kick it. Cast another Rite of Replication, kick it both in and out of the Eye because copied Seething Songs make the mana and the Rite is copied a million billion times, probably making more Doubling Seasons. With 2 Rites in the Eye, casting any instant or sorcery will be able to activate new copies of Pyromancer Ascension. Then we finally cast Radiate which copies for every Ascension, and those copy kicked Rite of Replication for every creature. Another really relevant spell is Fungal Sprouting which one copy makes tokens equal to the highest power creature times 2^(number of doubling seasons), which adds counters to your creatures equal to that number multiplied again by the number of doubling seasons, except each hamletback goliath gets that number multiplied again by the new number of tokens multiplied by 2^(number of doubling seasons) And then the Ascensions make that whole thing an ^^ for the number of ascensions. And every instant cast from here on out can radiate rite of replication equal to the number of pyromancer ascensions which makes more doubling seasons and activates makes more ascensions which are activated by the eye casting more rite of replications... (25 cards down, 35 to go, although one is still in the library)
The 26th card will be a Knowledge Pool thrown in here somewhere, which pulls the last card out of the deck and doubles the cast triggers (even though cards get eaten by Knowledge Pool, the triggers from ascensions and eye still resolve, and then resolve again once an instant or sorcery is cast out of the pool.) It might not be worth the card slot, but Moonveil Dragon seems like a nice way to spend the power of a thousand seething songs, especially when power is turning into a multiplier for raw creature count, and raw creature count ends up as an exponent.
I have no idea how this is comparing to the "mega combo," because indescribably large is hard to compare to indescribably large, but I'm pretty sure we've outstripped modern computers' ability to process these numbers either way. But without knowing the real impact of what I'm suggesting, it's hard to guess what would be the best options other than the most obvious "20 Fork effects targetting Radiate" option. All I know is that the last spell I want to resolve after spamming instants for indescribably multiplied power is Mirrorweave targetting Gratuitous Violence so that the final combat damage is whatever unbelievable amount of power has been made multiplied by 2^(whatever unbelievable amount of creatures we made).
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1. Play Lotus, Show and Tell, put Omniscience into play, cast Enter the Infinite, draw your deck, put back Unwilling Recruit.
2. Cast Inner Fire for 54 red mana.
3. Play Rite of Replication with kicker four times. Regrowth it and continue until you run out of mana.
4. Cast Battle Hymn for a bunch of mana. Continue casting Regrowths into Rites.
5. Use either Praetor's Counsel, Feldon's Cane, Cranial Archive, or a clone on Cane or Archive to reset and do it again. (With Archive, you magically draw Enter the Infinite and start again. With Cane, you do cast Enter, then activate Cane in response).
6. Keep resetting until you're out of cards.
7. Flashback Mystic Retrival on Rite of Replication, flash it back with blue mana made by recycling Lotus over and over.
8. Cast Unwilling Recruit for all the mana you have left.
9. Attack for lots.
Nice improvement. You cast 40 Rites of Replication, and repeat that process 13 times, for 520 Rites, then add four more at the end by flashbacking Mystic Retrieval for 524. Final damage between 2^^526 and 2^^527.
I think there's promise in the brute force Radiate method, and I can somewhat formulate a procedure, but I can't even attempt to process the numbers.
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I have no idea how this is comparing to the "mega combo," because indescribably large is hard to compare to indescribably large, but I'm pretty sure we've outstripped modern computers' ability to process these numbers either way. But without knowing the real impact of what I'm suggesting, it's hard to guess what would be the best options other than the most obvious "20 Fork effects targetting Radiate" option. All I know is that the last spell I want to resolve after spamming instants for indescribably multiplied power is Mirrorweave targetting Gratuitous Violence so that the final combat damage is whatever unbelievable amount of power has been made multiplied by 2^(whatever unbelievable amount of creatures we made).
Your 2^^120 figure is correct, however you can do better by alternating the casting of Dual Nature and Doubling Season:
1. Cast Dual Nature, getting a token copy.
2. Cast Doubling Season, get 10 tken copies for 11 total.
3. Cast Dual Nature, getting 2050 total.
4. Cast Doubling Season, getting more than 2^^2050 total.
5. Cast Dual Nature, getting more than 2^^2051.
6. Cast Doubling Season, getting more than 2^^2^^2051.
7. Cast Dual Nature, getting more than 2^^2^^2051.
8. Cast Doubling Season, getting more than 2^^2^^2^^2051, or between 2^^^5 and 2^^^6.
Most of the other cards you use don't effect the number enough to pass 2^^^6. For example, take Cathars' Crusade. Casting Cathars' Crusade gets you more than 2^^^5 copies of it, each one adding more than 2^^^5 +1/+1 counters to more than 2^^^5 creatures. So the total power increases by about X^3, where X is the number of Cathars' Crusades. That may sound a lot bigger than X when X is very large, but at this scale, the difference is unnoticeable. For example, if X = 2^2^Y, then X^3 < 2^2^(Y+2), so even for a relatively small number like X = 2^^10, cubing scarcely makes a difference, much less 2^^^5. Similarly for Hamletback Goliath, Gratuitous Violence, Fungal Sprouting, Moonveil Dragon, and Mirrorweave.
The real power comes from the Radiates. Each copy of Rite of Replication takes X Doubling Seasons to 2^X. Each copy of Radiate copies Rite of Replication for each Doubling Season on the battlefield, taking X Doubling Seasons to 2^^X Doubling Seasons. Each time you cast Radiate with X Pyromancer Ascensions with quest counters on them, you copy Radiate X times, so you generate 2^^^X Doubling Seasons. You also generate 2^^^X Pyromancer Ascensions, which would allow you to get 2^^^2^^^X Doubling Seasons on the next cast, except for the fact that the new Pyromancer Ascensions won't have quest counters on them. Fortunately, we can exile Rites of Replication to Eye of the Storm, and alternate the castings of Rite of Replication with Radiate; unfortunately, we can only exile three Rites (one is in the graveyard), so one of the Radiates won't be able to be used to full power. The best solution seems to me to have at least two copies of another spell (say Cackling Counterpart) and put one in the graveyard, and exile the other to Eye of the Storm, so we have another spell that can refresh the Pyromancer Ascensions.
So with that, we apply the function X -> 2^^^X for each casting of Radiate, so we want to maximize the number of castings. To this end, we want to exile the Radiates as soon as possible, so that they can be copied as many times as possible by the following instants/sorceries. Also, the most obvious "20 Fork effects targetting Radiate" option really does seem like the best option, although one Radiate will be "wasted" as it will have to remain on the stack for the Fork spells to copy it. Also, you do still need to alternate castings of Radiate or a spell copying it with a spell that refreshes the Pyromancer Ascensions. I believe that when you cast an exiled instant or sorcery via Knowledge Pool, it will get exiled to Eye of the Storm, so that indeed is a good way to double the number of castings. Overall, it shouldn't be too hard to generate over 500 castings of Radiate or a copy spell, so as long as we have a haste spell, we can generate about 2^^^^500 damage. This would be by far the most damage among entrants in this thread, but is still very far from the megacombo, which requires over 400 Knuth arrows to express.
One last thing: If you cast a kicked Rite of Replication on a Hamletback Goliath with Doubling Season on the battlefield, you can get much more than 6 million power! The 10 Hamletback Goliaths coming into play generate 100 triggers, so as long as you order the triggers intelligently so that each one piggybacks off the previous one, say:
1. HG#1 adds 12 +1/+1 counters to HG#2, increasing its power to 18
2. HG#2 adds 36 +1/+1 counters to HG#3, increasing its power to 42
3. HG#3 adds 84 +1/+1 counters to HG#2, increasing its power to 102
and you continue this 87 more times, forming a Hamiltonian circuit among the 10 token creatures. Each trigger will more than double the power of the largest creature, so after 87 more triggers the largest token creature will have more than 102 * 2^87 power. Finally, we resolve the 10 triggers on the original Hamletback Goliath, increasing it to more than 102 * 2^89 ~ 6.3 * 10^28 power.
That's actually very good for a three card combo. Cheers!
1. Draw your deck with Lotus into Show and Tell into Omniscience into Enter the infinite, put back Unwilling Recruit.
2. Play Precursor Golem. Play Seething Song. Play kicked Rite of Replication, then play Rite of Replication. You get 6 Precursors and 22 vanillas after the first one, and after the second one you will have 204 vanillas and 36 precursors.
3. Cast Battle Hymn for 240 red mana.
4. Play Haze of Rage. Play Spellweaver Helix, exiling Haze of Rage and Rite of Replication.
5. Play the second Haze of Rage with buyback, then play Rite of Replication with kicker. Repeat 34 times. You will have RR left in your mana pool afterwards.
6. Play 3 Isochron Scepters, exiling three Battle Hymns from your hand (which are the only targets in the deck, so as to prevent potential infinites).
7. Activate a Scepter, giving you a very, very large amount of red mana. Using all but two of that mana, cast as many Haze of Rages with buyback as possible, then casting as many kiced Rites of the Helix.
8. Once you have exhausted your red mana, activate the second Scepter. Once you've exhausted that mana, activate the third.
9. Use your five untappers (Blinkmoth Infusion, Turnabout, Reality Spasm, Toil of Night and Day, and Wild Ricochet copying a Blinkmoth Infusion) to re-use all your Scepters as many times as possible. Continue to tap scepter for lots of mana, then use that mana to buyback Haze and to kick Rites.
10. Once you've exhausted all your untappers and have a very large amount of golems, it's time to do it again! Play out all your Cane effects (and have the clones copy Archive. For Cane, you cast Alchemist's Apprentice, activate its ability, then sacrifice Cane in response). Use Cranial Archive the to shuffle your graveyard back in, then draw Enter the Infinite. Cast enter the infinite.
11. Play the fourth Scepter and exile Battle Hymn.
12. Continue to chain untappers into Battle Hymns to make absurd amounts of mana, then use that mana to cast a lot of Rites.
13. Once you've exhausted every Archive effect, every untapper, and every Battle Hymn, cast Burst of Speed. Give your legion haste. Attack for lots.
I have to say, this has been a very fun creative excersize.
You have an infinite there. Use one Cranial Archive to get Black Lotus back into the library and redraw it, so it can give you blue mana in addition to Battle Hymn's red. Now you can use the colored ability on Mizzium Transreliquat, turning it into a Precursor Golem, then make some tokens of it and use the colored ability again on one of the tokens to turn it into another Cranial Archive. Now you can reshuffle your graveyard without losing any cards, only tokens, and repeat.
Over time, we kept improving the deck to deal more and more damage. The numbers are so large, they require Conway chained arrow notation to describe. SadisticMystic recently wrote a description of the most recent deck, detailed here:
http://www.soniccenter.org/sm/mtg/megacombo.html
However, there is a slight problem involving Mana Crypt and Builder's Blessing; the best fix that we've been able to find is to remove Builder's Blessing and Devout Lightcaster, and add Avacyn, Angel of Hope and Thran Dynamo, losing nine recursive layers. But, with the appearance of Gideon, Ally of Zendikar, we can use that card to replace both Avacyn and Thran Dynamo, allowing [c]Devout Lightcaster to come back in and regaining nine layers. Final damage is in excess of 2 -> 19 -> 417 damage.
This challenge originated on the Wizards forums, which have been shut down; however, an archived version appears here:
http://web.archive.org/web/20150917153327/http://community.wizards.com/forum/cards-and-combos/threads/2230096
Any comments and suggestions are welcome.
UPDATE: We have come quite a long way - the latest verified deck deals damage in excess of F_{w^3 + w13 + 5} (107), using the fast-growing hierarchy. Details can be found here, although the article is still incomplete:
https://sites.google.com/site/deedlitsplace/ultracombo
For those who have not been keeping up with the thread, reading through 70+ pages is too much, so at periodic points we have been giving summaries of the progress up to that point. The latest one is this excellent breakdown by Stakfish:
https://www.mtgsalvation.com/forums/magic-fundamentals/magic-general/615089-most-turn-1-damage-in-a-deck-with-no-infinite?comment=1815
Here are some other useful posts in this thread:
This post details my discovery of the Ackermann combo, which led to all this stage madness.
This post by Iijil gave his initial thoughts on extending the deck to the hyperstage, which was refined in later posts; this is the blueprint for the stage level extensions.
Here's the state of the art: http://www.soniccenter.org/sm/mtg/megacombo.html
4) Each Storm Herd / Caller of the Pride adds 420 creature tokens, which gets doubled 12 times for 420 * 2^12 tokens. End result: 420 * 2^15 tokens.
5) Each spell in this step doubles the number of creatures 12 times, except for Mogg Infestation which doubles it 13 times. All told there are 196 doublings, for 420 * 2^211.
6) You don't recycle Day of the Dragons, but you recycle the other 12 cards, which makes 148 doublings per Praetor's Counsel. End result: 420 * 2^803.
8) Playing another Deply / Infestation adds 25 doublings for 420 * 2^828.
9) Boros Reckoner takes 420 * 2^828 damage, which gets doubled 8 times for 420 * 2^836, then the redirect gets doubled 8 times for 420 * 2^844. Final damage: About 420 * 2^846.
Land, Mana Crypt, Show and Tell, Omniscience.
Clash of Realities, Cowardice, Rousing of Souls, Mnemonic wall, draw half of library.
Doubling Season. Copy Enchantment -> Doubling Season. Dual Nature. Mimic Vat. Vedalken Orrery. Opalescence. March of the Machines.
Mana Crypt dies, Mimic Vat Exiles it. Play Mirror of Fate, get 4 token copies. Cast Rousing of Souls, draw a card, bounce March of the Machines and Mnemonic Wall.
Active a Mirror copy, putting Mana Crypt into the library. Cast Mnemonic Wall getting Rousing of Souls, Cast Rousing of Souls drawing Mana Crypt and bouncing Mnemonic Wall. Cast Mana crypt and make 2 mana with it. Activate a second Mirror, respond to your own activation by casting March of the Machines at instant speed, which kills Mana Crypt which triggers Mimic Vat which exiles Mana Crypt, then the Mirror ability resolves putting Mana Crypt into the library. Cast Mnemonic wall getting back Rousing of Souls, cast Rousing of Souls drawing Mana Crypt and bouncing Mnemonic Wall, March of the Machines, and Cowardice. Cast Mana Crypt, activate for 2 mana. Now, we have 4 mana.
Play Cateran Slaver. (If you thought the instant speed timing was precise so far, wait until you see this.) Activate the 3rd Mirror token, respond with the 4th mirror token, respond with March of the Machines again, killing Mana Crypt, exiling it to Mimic Vat, then resolving the 3rd mirror ability to put mana crypt in the library. Still with the 3rd Mirror of Fate ability unresolved, cast Mnemonic Wall, it enters triggering Dual Nature and its own ETB in that order. Then resolve the etb returning Rousing of Souls to your hand. With the dual nature trigger still on the stack, respond with Rousing of Souls, drawing Mana Crypt, and using the etb triggers from the spirits to target Mirror of Fate, Mnemonic Wall, March of the Machines, and Cowardice. Bounce Mirror of Fate before March of the Machines, and then recast it in response to the trigger that's bouncing March of the machines getting 4 token copies. Cast Mana Crypt also in response to the bounce trigger, cause it to die, exiling under Mimic Vat. This resolves us back to the dual nature trigger which makes mnemonic walls with last known information, which returns Rousing of Souls to our hand. Then Mirror of Fate resolves putting Mana Crypt back in the library.
Cast Rousing of Souls, draw Mana Crypt, use the etb damage triggers to kill Cateran Slaver, Exiling it onto Mimic Vat. Use the 4 mana still floating to activate Mimic Vat. Now we have a 5/5 token with haste. Cast Rite of Passage. At this point I believe the loop is ready to start.
We have 1 arbitrary mana floating.
In hand, we have Mnemonic Wall, March of the Machines, Cowardice, Mirror of Fate, and Mana Crypt.
In play, we have Clash of Realities, Omniscience, Vedalken Orerry, Rite of Passage, Opalescence, Mimic Vat, Dual Nature, 2x Doubling Season, and 5x Mirror of Fate.
In graveyard we have Rousing of Souls.
The library is empty.
We have a 5/5 token with haste.
Activate a mirror token, followed by another mirror token. Cast Mana Crypt in response, tap for 2 mana. Cast March of the Machines before mirror resolves, kill the crypt and exile to mimic vat. One Mirror resolves putting Mana Crypt into the library. Respond to the mirror on the stack with Mnemonic wall, triggering dual nature and itself. Resolve the wall trigger, getting back rousing of souls. Cast Rousing of Souls, aiming the ETB damage at the 5/5 with haste which pumps it with Rite of Passage, and drawing mana crypt. Let the dual nature trigger resolve, making wall tokens which get back Rousing of Souls. Cast mana crypt, which dies and exiles to mimic vat. Let the other mirror ability resolve, putting mana crypt back into the library. Cast Cowardice. Cast Rousing of Souls, using the etb's to bounce Mnemonic Wall, Cowardice, March of the Machines, and Mirror of Fate. Bounce Mirror of Fate before March of the Machines, and cast it again in response to the march of the machine's bounce making 4 token copies of Mirror of Fate. Allow the bouncing to resolve.
We have 3 arbitrary mana floating.
In hand, we have Mnemonic Wall, March of the Machines, Cowardice, Mirror of Fate, and Mana Crypt.
In play, we have Clash of Realities, Omniscience, Vedalken Orerry, Rite of Passage, Opalescence, Mimic Vat, Dual Nature, 2x Doubling Season, and 5x Mirror of Fate.
In graveyard we have Rousing of Souls.
The library is empty.
We have a 5/5 token with haste and 12 +1/+1 counters.
Loop forever to get infinite mana and an infinitely large hasty creature. This mess was the most efficient way that I could think of an infinite combo out of the cards listed, but an infinite combo it is, nonetheless.
1x Show and Tell
1x Omniscience
1x Enter the Infinite
1x Precursor Golem
1x Inner Fire
1x Battle Hymn
4x Call to Mind
4x Déjà vu
4x Down // Dirty
4x Elven Cache
4x Mystic Retrieval
4x Recollect
4x Regrowth
4x Relearn
4x Sage's Knowledge
3x Radiate
1x Unwilling Recruit
1x Might of the Masses
4x Overblaze
1. Play Lotus, Show and Tell, put Omniscience into play, cast Enter the Infinite, draw your deck, put back Unwilling Recruit.
2. Cast Inner Fire for 54 red mana.
3. Cast Precursor Golem
4. Cast Rite of Replication with kicker 4 times. Use Regrowth effects to re-cast Rite until you're out of mana for the kicker. At this point, you have a very, very large amount of golems. Cast Battle Hymn for a very, very large amount of mana, then continue casting Regrowths into Rites. Cast Radiate on Rite.
5. Cast Might of the Masses. Cast 4x Overblaze, each time splicing for each other Overblaze still in your hand. Cast Battle Hymn for a bunch of mana.
6. Cast Praetor's Counsel
7. Repeat steps 4 and 5 for each Counsel.
8. Using all the mana you generated from each Battle Hymn, cast Unwilling Recruit for a bunch.
9. Attack for lots.
I'm genuinely interested if anyone can come up with how much damage this would deal.
EDIT: I just realized that using Regrowth effects to re-cast Rite of Replication is much more effective than casting Cackling Counterparts. Editing the deck to account for that.
After the first Rite of Replication, there will be 6 Precursor Golems and 22 vanilla Golems. After the second Rite, there will be 279,936 Precursor Golems and about 4 million Golems total. Both numbers are between 2^^4 = 65,536 and 2^^5, which is more than 10^19728. Each additional Rite will exponentiate the number of Golems, so after the third Rite there will be between 2^^5 and 2^^6, and the fourth there will be between 2^^6 and 2^^7, and so on. The retrieval spells allow you to cast Rite of Replication 40 times, then the Praetor's Counsels repeat this four times, for 200 Rites. Finally we can flashback 4 Mystic Retrievals for 204 Rites, and between 2^^206 and 2^^207 Golems in the end.
Then there is the effect of the other cards; unfortunately, all of them combined are not enough to reach 2^^207. For example, Might of the Masses adds (X-1)Y to the power of each Golem (except one), where Y is the number of Precursor Golems and X is the total number of Golems, so the total power becomes X((X-1)Y+3) < X^3. Now X^3 sounds a lot bigger than X, but it has basically zero effect on a large power tower. For example, if X = 2^2^1000, X^3 = (2^2^1000)^3 = 2^(2^1000 * 3) < 2^2^1002. In our case we have X = 2^2^Z where Z is itself a large power tower, and we increase that to less than 2^2^(Z+2), and adding two to Z is not noticeable at all. All the other cards do less the cubing as well, so the final damage will be between 2^^206 and 2^^207.
You don't get near 2^^^^^^^^^^^^^^^^^^^^20. 2^^^^^^^^^^^^^^^^^^^^20 is not a nested exponential of 20 exponents; that's 2^^20. In general
2^^X is an exponential tower of X 2's (2^2^2...^2),
2^^^X is 2^^2^^2...^^2 with X 2's,
2^^^^X is 2^^^2^^^2...^^^2 with X 2's
and so on. Each Radiate takes X Doubling Seasons to 2^^X Doubling Seasons, so N Radiates would produce about 2^^^N Doubling Seasons in the end - nowhere near the numbers in the megacombo.
Did you account for Overblaze?
Hmm, Each Overblaze gets copied XY times where X is the number of Golems and Y is the number of Precursor Golem. So the total damage gets multiplied by 2^(10XY). This takes the damage to between 2^^207 and 2^^208.
Also, do I get a 15 card sideboard?
No, no sideboard. (Although actually, I did address the challenge where a 15 card sideboard was allowed, and I was able to obtain more than 500 Knuth arrows. But for the main challenge, no sideboard.)
1 Show and Tell
1 Omniscience
1 Enter the Infinite
4 Monastery Mentor
4 Phantasmal Image
4 Cathars' Crusade
1 Gisela, Blade of Goldnight
4 Dictate of the Twin Gods
4 Furnace of Rath
4 Bitter Feud
4 Curse of Bloodletting
1 True Conviction
2 Chancellor of the Forge
4 Deploy to the Front
4 Fungal Sprouting
1 Flame-Kin Zealot
4 Craterhoof Behemoth
4 Tears of Rage
We use Black Lotus+Show and Tell+Omniscience+Enter the Infinite, then our token makers, then Cathars' Crusade (which is really awesome), then our damage doublers, then our big token makers, then our creature pumps (Flame-Kin Zealot and the Craterhoof Behemoths), followed by our 4x Tears of Rage. Serum Visions probably isn't good, but whatever. I'm not sure exactly how much damage this is, but it's some ridiculously large number. (I've got a Python code that I think will work, but my computer can't run it, so it's probably not very efficient).
EDIT: Best-case scenario is starting with 3 Chancellor of the Forge in your opener along with the combo thing.
EDIT 2: Play your Fungal Sproutings AFTER your Craterhoofs, but before Flame-Kin Zealot (I think this is better, but I'm not sure, The sequencing here is really, really weird).
Okay, after the eight Monastery Mentors are on the board, each noncreature spell adds eight new creatures, and with four Cathar's Crusades on the board, each noncreature spell adds 32 +1/+1 counters to each creature on the board (33 if the creature has prowess). You cast 22 noncreature spells before we get to Empty the Warrens, for 176 new token creatures in addition to the 9 nontoken ones and three Goblin tokens, for 188 total. For Empty the Warrens, the storm count starts at 35, leading to 150 copies of Empty the Warrens and 300 Goblin tokens, plus 32 Monk tokens for 520 total creatures. Each Deploy to the Front adds 8 tokens and then doubles the number of creatures, so four iterations of that results in 8560 creatures. Each Chancellor of the Forge adds one creature and then doubles the number of creatures, so after four iterations we have 136,990 creatures. A Craterhoof Behomoths makes it 136,991. (It's best to alternate Craterhoof Behomoths and Fungal Sproutings.)
Next, we have to calculate the greatest power among creatures we control for Fungal Sprouting. The greatest power belongs one of the intial Monastery Mentors, which start at 2/2, and then the four Cathars' Crusades add 9,17,25, and 33 for 86 power. We cast another 26 noncreature spells, activating Prowesss 26 times for 112 power. Then, we add another 136,948 creatures, each one adding 4 power, resulting in 547,904 power. Finally, the Craterhoof Behemoths increases that to 684,895.
So when we cast the first Fungal Sprouting, we add 684,895 creatures, increasing the greatest power to 3,424,475, then the second Craterhoof Behometh adds 821,887 for 4,246,362. Second Fungal Sprouting adds 4,246,362 creatures: 5,068,250 creatures, 26,300,060 max power. Third Fungal Sporuting adds 25,300,060 creatures: 30,368,311 creatures, 161,868,611 max power. Finally the Fourth Fungal Sprouting adds 161,868,611 creatures for 192,236,922 creatures and 809,343,055 max power. Flame-Kin Zealot gives all the creatures haste, then Tears of Rage increases the max power to 1,578,290,751. So an upper bound for the amount of damage is 192,236,923 * 1,578,290,751 = 3.034 * 10^17.
Not bad, but less than the other entrants so far.
1x Show and Tell
1x Omniscience
1x Enter the Infinite
1x Precursor Golem
1x Inner Fire
1x Battle Hymn
4x Call to Mind
4x Down // Dirty
4x Elven Cache
4x Mystic Retrieval
4x Regrowth
4x Feldon's Cane
4x Cranial Archive
4x Clever Impersonator
4x Sculpting Steel
4x Phyrexian Metamorph
1. Play Lotus, Show and Tell, put Omniscience into play, cast Enter the Infinite, draw your deck, put back Unwilling Recruit.
2. Cast Inner Fire for 54 red mana.
3. Play Rite of Replication with kicker four times. Regrowth it and continue until you run out of mana.
4. Cast Battle Hymn for a bunch of mana. Continue casting Regrowths into Rites.
5. Use either Praetor's Counsel, Feldon's Cane, Cranial Archive, or a clone on Cane or Archive to reset and do it again. (With Archive, you magically draw Enter the Infinite and start again. With Cane, you do cast Enter, then activate Cane in response).
6. Keep resetting until you're out of cards.
7. Flashback Mystic Retrival on Rite of Replication, flash it back with blue mana made by recycling Lotus over and over.
8. Cast Unwilling Recruit for all the mana you have left.
9. Attack for lots.
If we start with Black Lotus, Show and Tell, Omniscience, Enter the Infinite and work from there. (The 1 card in the library is actually useful)
Begin with Opalescence, then In the Web of War to give everything a boost and haste. 4 Dual Natures (which is really 30), and then 4 Doubling Seasons (which is really approximately 2^^120 if I'm understanding that notation correctly. also, playing 4 of each may be wildly inefficient, but I admittedly don't understand the consequences here).
Get a few things in play that will start the attack power rising, namely Cathars' Crusade and Hamletback Goliath and Gratuitous Violence. (17 cards used so far)
(Side note, I now hope someday in a perfectly reasonable deck to Rite of Replication Hamletback Goliath with Doubling Season out. 10 enter at same time, all triggering off one another, getting counters that are doubled and counted by other triggers, turning the original Goliath into a 6 million power creature with 3 cards that are all awesome in a RUG edh deck).
Then, we get more complex. We play Pyromancer Ascension, which is really an outrageous amount of them, and then Rite of Replication on something (mostly to get Rite of Replication in the graveyard). Then we play Eye of the Storm (which is close to the last permanent we play). Cast Seething Song so that we can kick every Rite of Replication forever. Cast Rite of Replication, Storm casts it again (which activates the Ascensions), kick it. Cast another Rite of Replication, kick it both in and out of the Eye because copied Seething Songs make the mana and the Rite is copied a million billion times, probably making more Doubling Seasons. With 2 Rites in the Eye, casting any instant or sorcery will be able to activate new copies of Pyromancer Ascension. Then we finally cast Radiate which copies for every Ascension, and those copy kicked Rite of Replication for every creature. Another really relevant spell is Fungal Sprouting which one copy makes tokens equal to the highest power creature times 2^(number of doubling seasons), which adds counters to your creatures equal to that number multiplied again by the number of doubling seasons, except each hamletback goliath gets that number multiplied again by the new number of tokens multiplied by 2^(number of doubling seasons) And then the Ascensions make that whole thing an ^^ for the number of ascensions. And every instant cast from here on out can radiate rite of replication equal to the number of pyromancer ascensions which makes more doubling seasons and activates makes more ascensions which are activated by the eye casting more rite of replications... (25 cards down, 35 to go, although one is still in the library)
The 26th card will be a Knowledge Pool thrown in here somewhere, which pulls the last card out of the deck and doubles the cast triggers (even though cards get eaten by Knowledge Pool, the triggers from ascensions and eye still resolve, and then resolve again once an instant or sorcery is cast out of the pool.) It might not be worth the card slot, but Moonveil Dragon seems like a nice way to spend the power of a thousand seething songs, especially when power is turning into a multiplier for raw creature count, and raw creature count ends up as an exponent.
I have no idea how this is comparing to the "mega combo," because indescribably large is hard to compare to indescribably large, but I'm pretty sure we've outstripped modern computers' ability to process these numbers either way. But without knowing the real impact of what I'm suggesting, it's hard to guess what would be the best options other than the most obvious "20 Fork effects targetting Radiate" option. All I know is that the last spell I want to resolve after spamming instants for indescribably multiplied power is Mirrorweave targetting Gratuitous Violence so that the final combat damage is whatever unbelievable amount of power has been made multiplied by 2^(whatever unbelievable amount of creatures we made).
Nice improvement. You cast 40 Rites of Replication, and repeat that process 13 times, for 520 Rites, then add four more at the end by flashbacking Mystic Retrieval for 524. Final damage between 2^^526 and 2^^527.
The rules require that there must be a finite maximum damage achievable by the deck. Mana Clash has no maximum, so is disallowed.
Your 2^^120 figure is correct, however you can do better by alternating the casting of Dual Nature and Doubling Season:
1. Cast Dual Nature, getting a token copy.
2. Cast Doubling Season, get 10 tken copies for 11 total.
3. Cast Dual Nature, getting 2050 total.
4. Cast Doubling Season, getting more than 2^^2050 total.
5. Cast Dual Nature, getting more than 2^^2051.
6. Cast Doubling Season, getting more than 2^^2^^2051.
7. Cast Dual Nature, getting more than 2^^2^^2051.
8. Cast Doubling Season, getting more than 2^^2^^2^^2051, or between 2^^^5 and 2^^^6.
Most of the other cards you use don't effect the number enough to pass 2^^^6. For example, take Cathars' Crusade. Casting Cathars' Crusade gets you more than 2^^^5 copies of it, each one adding more than 2^^^5 +1/+1 counters to more than 2^^^5 creatures. So the total power increases by about X^3, where X is the number of Cathars' Crusades. That may sound a lot bigger than X when X is very large, but at this scale, the difference is unnoticeable. For example, if X = 2^2^Y, then X^3 < 2^2^(Y+2), so even for a relatively small number like X = 2^^10, cubing scarcely makes a difference, much less 2^^^5. Similarly for Hamletback Goliath, Gratuitous Violence, Fungal Sprouting, Moonveil Dragon, and Mirrorweave.
The real power comes from the Radiates. Each copy of Rite of Replication takes X Doubling Seasons to 2^X. Each copy of Radiate copies Rite of Replication for each Doubling Season on the battlefield, taking X Doubling Seasons to 2^^X Doubling Seasons. Each time you cast Radiate with X Pyromancer Ascensions with quest counters on them, you copy Radiate X times, so you generate 2^^^X Doubling Seasons. You also generate 2^^^X Pyromancer Ascensions, which would allow you to get 2^^^2^^^X Doubling Seasons on the next cast, except for the fact that the new Pyromancer Ascensions won't have quest counters on them. Fortunately, we can exile Rites of Replication to Eye of the Storm, and alternate the castings of Rite of Replication with Radiate; unfortunately, we can only exile three Rites (one is in the graveyard), so one of the Radiates won't be able to be used to full power. The best solution seems to me to have at least two copies of another spell (say Cackling Counterpart) and put one in the graveyard, and exile the other to Eye of the Storm, so we have another spell that can refresh the Pyromancer Ascensions.
So with that, we apply the function X -> 2^^^X for each casting of Radiate, so we want to maximize the number of castings. To this end, we want to exile the Radiates as soon as possible, so that they can be copied as many times as possible by the following instants/sorceries. Also, the most obvious "20 Fork effects targetting Radiate" option really does seem like the best option, although one Radiate will be "wasted" as it will have to remain on the stack for the Fork spells to copy it. Also, you do still need to alternate castings of Radiate or a spell copying it with a spell that refreshes the Pyromancer Ascensions. I believe that when you cast an exiled instant or sorcery via Knowledge Pool, it will get exiled to Eye of the Storm, so that indeed is a good way to double the number of castings. Overall, it shouldn't be too hard to generate over 500 castings of Radiate or a copy spell, so as long as we have a haste spell, we can generate about 2^^^^500 damage. This would be by far the most damage among entrants in this thread, but is still very far from the megacombo, which requires over 400 Knuth arrows to express.
One last thing: If you cast a kicked Rite of Replication on a Hamletback Goliath with Doubling Season on the battlefield, you can get much more than 6 million power! The 10 Hamletback Goliaths coming into play generate 100 triggers, so as long as you order the triggers intelligently so that each one piggybacks off the previous one, say:
1. HG#1 adds 12 +1/+1 counters to HG#2, increasing its power to 18
2. HG#2 adds 36 +1/+1 counters to HG#3, increasing its power to 42
3. HG#3 adds 84 +1/+1 counters to HG#2, increasing its power to 102
and you continue this 87 more times, forming a Hamiltonian circuit among the 10 token creatures. Each trigger will more than double the power of the largest creature, so after 87 more triggers the largest token creature will have more than 102 * 2^87 power. Finally, we resolve the 10 triggers on the original Hamletback Goliath, increasing it to more than 102 * 2^89 ~ 6.3 * 10^28 power.
That's actually very good for a three card combo. Cheers!
1x Show and Tell
1x Omniscience
1x Enter the Infinite
1x Precursor Golem
1x Seething Song
4x Isochron Scepter
4x Battle Hymn
1x Spellweaver Helix
2x Haze of Rage
4x Blinkmoth Infusion
4x Turnabout
4x Reality Spasm
4x Toils of Night and Day
4x Wild Ricochet
4x Clever Impersonator
4x Sculpting Steel
4x Phyrexian Metamorph
3x Feldon's Cane
1x Alchemist's Apprentice
1x Burst of Speed
Okay, this gets pretty big.
1. Draw your deck with Lotus into Show and Tell into Omniscience into Enter the infinite, put back Unwilling Recruit.
2. Play Precursor Golem. Play Seething Song. Play kicked Rite of Replication, then play Rite of Replication. You get 6 Precursors and 22 vanillas after the first one, and after the second one you will have 204 vanillas and 36 precursors.
3. Cast Battle Hymn for 240 red mana.
4. Play Haze of Rage. Play Spellweaver Helix, exiling Haze of Rage and Rite of Replication.
5. Play the second Haze of Rage with buyback, then play Rite of Replication with kicker. Repeat 34 times. You will have RR left in your mana pool afterwards.
6. Play 3 Isochron Scepters, exiling three Battle Hymns from your hand (which are the only targets in the deck, so as to prevent potential infinites).
7. Activate a Scepter, giving you a very, very large amount of red mana. Using all but two of that mana, cast as many Haze of Rages with buyback as possible, then casting as many kiced Rites of the Helix.
8. Once you have exhausted your red mana, activate the second Scepter. Once you've exhausted that mana, activate the third.
9. Use your five untappers (Blinkmoth Infusion, Turnabout, Reality Spasm, Toil of Night and Day, and Wild Ricochet copying a Blinkmoth Infusion) to re-use all your Scepters as many times as possible. Continue to tap scepter for lots of mana, then use that mana to buyback Haze and to kick Rites.
10. Once you've exhausted all your untappers and have a very large amount of golems, it's time to do it again! Play out all your Cane effects (and have the clones copy Archive. For Cane, you cast Alchemist's Apprentice, activate its ability, then sacrifice Cane in response). Use Cranial Archive the to shuffle your graveyard back in, then draw Enter the Infinite. Cast enter the infinite.
11. Play the fourth Scepter and exile Battle Hymn.
12. Continue to chain untappers into Battle Hymns to make absurd amounts of mana, then use that mana to cast a lot of Rites.
13. Once you've exhausted every Archive effect, every untapper, and every Battle Hymn, cast Burst of Speed. Give your legion haste. Attack for lots.
I have to say, this has been a very fun creative excersize.
EDIT: It doesn't, but adding Alchemist's Apprentice makes it work.