You actually get more than 240 Golems after the second Rite of Replication. Remember, you get 6 triggers of Precursor Golem when you cast the Rite, and when each trigger resolves, it copies Rite of Replication for each Golem currently on the battlefield, not just the ones on the battlefield when you cast the Rite. I count 384 Precursor Golems and 3650 vanilla Golems, 4034 total.

It's actually better to cast unkicked Rite of Replications than kicked ones when you use Spellweaver Helix. Even though kicked Rites are putatively more powerful, casting N unkicked Rites will result in between 2^^(N+3) and 2^^(N+4) Golems, and the same result will be true if you cast kicked Rites. So you can either cast 576 kicked Rites and get between 2^^579 and 2^^580 Golems, or cast 2016 unkicked Rites and get between 2^^2019 and 2^^2020 Golems.

Each tapping of an Isochron Scepter will allow you to cast X Rites, resulting in 2^^X Golems. I don't see why we should save the fourth Isochron Scepter for later, so I will assume it is activated along with the first three. Each Blinkmoth Infusion, Turnabout, and Wild Ricochet will allow another four tappings of an Isochron Scepter, and Toils of Night and Day will allow two more. Reality Spasm is problematic; casting it with Omniscience is useless, since X will be defined to be 0. So we need blue mana, and there currently is no source for that. So I count 56 additional tappings of Isochron Scepter from our untapping spells. When we use Cranial Archive to reshuffle and redraw everything, we do get a blue mana source, namely Black Lotus, which we can copy a couple of times to cast all four Reality Spasms. So we get 72 untappings on the following go-arounds. When we are down to say one Cranial Archive and two Phyrexian metamorphs, we need to use one of the Metamorphs to copy Cranial Archive, so we can make one copy of Black Lotus, allowing for three Reality Spasms. Then for the last three go-arounds we have just the one Black Lotus for one Reality Spasm. All told I count 1388 tappings of Isochron Scepter. Since we start with 2016 Rites, which is between 2^^^2 and 2^^^3, we wind up with a final damage of between 2^^^1390 and 2^^^1391.

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.

<snip>

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!

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.

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.)

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.

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.

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.

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.

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.

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.

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.

Hmm, I would to post the contents of a spreadsheet, but it didn't work. Anyone know how?

It's actually better to cast unkicked Rite of Replications than kicked ones when you use Spellweaver Helix. Even though kicked Rites are putatively more powerful, casting N unkicked Rites will result in between 2^^(N+3) and 2^^(N+4) Golems, and the same result will be true if you cast kicked Rites. So you can either cast 576 kicked Rites and get between 2^^579 and 2^^580 Golems, or cast 2016 unkicked Rites and get between 2^^2019 and 2^^2020 Golems.

Each tapping of an Isochron Scepter will allow you to cast X Rites, resulting in 2^^X Golems. I don't see why we should save the fourth Isochron Scepter for later, so I will assume it is activated along with the first three. Each Blinkmoth Infusion, Turnabout, and Wild Ricochet will allow another four tappings of an Isochron Scepter, and Toils of Night and Day will allow two more. Reality Spasm is problematic; casting it with Omniscience is useless, since X will be defined to be 0. So we need blue mana, and there currently is no source for that. So I count 56 additional tappings of Isochron Scepter from our untapping spells. When we use Cranial Archive to reshuffle and redraw everything, we do get a blue mana source, namely Black Lotus, which we can copy a couple of times to cast all four Reality Spasms. So we get 72 untappings on the following go-arounds. When we are down to say one Cranial Archive and two Phyrexian metamorphs, we need to use one of the Metamorphs to copy Cranial Archive, so we can make one copy of Black Lotus, allowing for three Reality Spasms. Then for the last three go-arounds we have just the one Black Lotus for one Reality Spasm. All told I count 1388 tappings of Isochron Scepter. Since we start with 2016 Rites, which is between 2^^^2 and 2^^^3, we wind up with a final damage of between 2^^^1390 and 2^^^1391.

I'm glad you had fun with this challenge!

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!

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.

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.)

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.

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.

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.

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.

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.