(UPDATE: The topic title is no longer editable, but the result is now even larger: 2^^(2^234) damage! The opponent is most certainly dead either way, but read on.)
Ever since its release,
Primal Surge 
has been one of the most centralizing cards in the game for decks that include it: useful for building around, and almost nothing else. Most of the build-around comes in the form of decks that have few or no other instants or sorceries, such that a resolved Primal Surge is a dependable way to puke the entire remainder of the deck onto the table.
Of course, it's easy to use an engine that powerful to put out something like
Laboratory Maniac 
+ card draw at that point, or one of the many combos (no matter how convoluted, since you clearly have the deck space and paying mana costs is no longer an issue) that constitute a loop which can be repeated without limit. But what if you only want to consider combos that are forced into having some known limit? How big can that limit be?
I usually pay no attention at all to the Standard card pool, but one of the assumptions I'll make here is to work only within that card pool. A couple reasons for this: the extents of general-purpose limited loops in the Vintage card pool has been pretty well explored. Also, Standard provides very little in the way of acceleration, so Primal Surge itself will play a significant role in the kickstarting process, where larger formats have the potential to explode by independent means, possibly treating the Surge as little more than an afterthought.
Another assumption I'll put in place here is a 60-card
maximum on deck size. My current plan is already compact enough to leave space for a large number of "dummy cards", cards which are completely irrelevant and fungible except for one key characteristic (in this case, being a noncreature artifact). If not for this assumption, the limit could be trivially improved simply by glutting up the deck with every single dummy card that met the requirements without also tripping the "infinite alarm". Even cards completely unrelated to the main line of attack, such as
Goblin Arsonist 
, would have to be added to squeeze out every last point of damage possible, a process diametrically opposed to the goal of finding a sleek and elegant combo.
Additionally, I have the goal of making the "critical turn" as soon as possible. Current Standard is notable for having no turn-1 activity available whatsoever, apart for the measly play of a single 1-drop, so unlike some environments past (even the most recent departure, Scars block), exploding on turn 1 will not be possible here. Turn 2 is, so that's what I'll be aiming for, though with minimal adaptation, the same result (including the same number of available card slots) can be achieved on turn 3 or 4.
Of course, the deck that follows is completely unrealistic for anyone to depend on in real Magic (for one thing, there are only three lands, and a lot of spells that are unplayable without a large stroke of luck), but for what amounts to an extreme case of theorycrafting, it's a harmless little exercise. Unless you're the monumentally unlucky opponent who has to watch in disbelief as it plays out on the other side of the table.
WARNING: The remainder of this post goes over a very complicated board state, and lots of very big numbers. Prolonged exposure may result in permanent blindness, total insanity, or worse: a desire to stock up on junk cards in hopes of living this dream. It is only a dream. Do not wake up, and do not collect 200 +1/+1 counters. That wouldn't be nearly enough counters for this sequence anyway.
Turn 1 (on the play after a mulligan to 6):
Stomping Ground 
(5),
Arbor Elf 
(4)
Turn 2 (5): Island (4),
Infernal Plunge 
(3),
Unexpected Results 
(2). Obviously, you won the lottery today so the card you flip up is Primal Surge. The two cards left in hand are
Fog 
and
Skullcrack 
, and there is a
mana floating.
Reveal 52 cards from the library:
Alchemist's Refuge 
Back from the Brink 
Death's Presence 
Druids' Repository 
Ooze Flux 
4x
Parallel Lives 
Akroma's Memorial 
Angel's Tomb 
4x
Angelic Armaments 
4x
Chromatic Lantern 
4x
Clock of Omens 
4x
Codex Shredder 
4x
Demonmail Hauberk 
4x
Illusionist's Bracers 
4x
Moonsilver Spear 
2x
Ring of Thune 
4x
Trading Post 
Gyre Sage 
1/2
Hamletback Goliath 
6/6
Master Biomancer 
2/4
Trostani, Selesnya's Voice 
4/7
Aurelia, the Warleader 
5/6
Bloodflow Connoisseur 
3/3
Bazaar Krovod 
4/7
Resolve triggers in the following order:
All Hamletback Goliath triggers (becomes 24/24)
Gyre Sage evolve from Master Biomancer (becomes 2/3)
Evolve from Bloodflow Connoisseur (3/4)
Evolve from Aurelia (4/5)
Evolve from Trostani (5/6)
Evolve from Bazaar Krovod (6/7)
Evolve from Hamletback Goliath (7/8)
One Angel's Tomb trigger will animate it into a 3/3, and the rest do nothing useful; also Trostani has some triggers now and in the future that will gain life, but life gain is meaningless in the combo so I won't bring them up again.
Now that the stack is clear, the first priority is to pump up Gyre Sage. To do this, start moving a Demonmail Hauberk around, sacrificing its previous inhabitant each time, and sending all Death's Presence triggers to the Gyre Sage. You can sacrifice Hamletback Goliath, Bazaar Krovod, Master Biomancer, and Bloodflow Connoisseur for a total of 45 more +1/+1 counters, making it 56/55 (including the useless boost from the Hauberk).
Tap Gyre Sage for 51 green mana (to go along with the 1 floating red). Use
to bring Arbor Elf back from the brink, getting 16 tokens. Tap 15 of them to untap the Stomping Ground for 15 mana (the last one's mana would just be wasted, so don't bother tapping it--it'll come in handy later). Thanks to Chromatic Lantern, producing mana of colors other than red or green won't be an issue. Next up, pay 4 to bring back Master Biomancer. They're all just 2/4 since they don't boost each other, and evolve won't trigger, but that's not important.
Pay 7 to bring back Hamletback Goliath (56 mana left). Each of them comes back as a 38/38, too small to trigger evolve. They do, however, trigger off each other, and with proper cascading of the triggers, each one will end up with staggered power somewhere between 622,592 and 1,245,184 (the total power is 18,677,761, or more than 2^24).
Pay 7 to bring back Bazaar Krovod and Bloodflow Connoisseur (48 mana left), mainly just to have them as tokens. The Goliaths trigger, but not with any appreciable effect: the counters they already have are far greater than the thousand or so that'll be picked up here.
Pay 8 to equip all four Illusionist's Bracers, on Trostani. Don't tap to populate yet; it needs to be untapped when combat rolls around.
Activate Alchemist's Refuge, which will be necessary to play spells during combat later on, and play Fog now just because you have the spare mana for it. There's still 37 mana to spend before it gets wasted at the end of the main phase, and the Gyre Sage is not only tapped, it's still cardboard. Now that there's nothing else worth doing in the main phase, it's time to activate Ooze Flux, which will eventually form the largest piece of the combo (even if that point is a long way off from here). Each time you use it, remove all counters from all creatures except Master Biomancers. Right now, the Hamletback Goliaths have a combined 2^24 counters which dominate everything else. Master Biomancer's effect will be insignificant at first, but you'll get 16 tokens each with 2^24 power. 16 Hamletback Goliaths (not to mention Gyre Sage) all trigger from these. The Gyre Sage boost isn't very relevant, especially since all counters are just going to be removed, but the Goliaths each get 2^28, ensuring the supply of counters will be even bigger for next time. Go ahead and sacrifice all the Ooze tokens to one of the Bloodflow Connoisseurs, putting 16 counters on it (which doesn't really matter), and 2^28 on Master Biomancer.
With the second activation of Ooze Flux, there are about 2^32 counters to remove, each of the Oozes will have that much power, and the Goliath triggers will put them at 2^36. Every 2 mana spent on Ooze Flux will increase these exponents by 8, and you can still spare the mana to activate it 15 more times. When that's done, the largest Master Biomancer as well as all of the Hamletback Goliaths will each have power 2^156 (a gross oversimplification, but it'll do, and it's just going to get dwarfed later on).
Finally, there's 3 mana left, so sacrifice Gyre Sage to the Bloodflow Connoisseur (one counter on that, and Death's Presence puts 21 on the Biomancer, neither of which is relevant) and empty the pool to bring it back from the brink and get 16 untapped, token Sages, each with over 2^156 +1/+1 counters thanks to the huge Biomancer (and his fifteen lesser underlings). Evolve doesn't trigger, but the Goliaths do, and each of them jumps up to 2^160.
In combat, attack with everything except the Gyre Sages (yes, even the Angel's Tomb; you also have a spare Arbor Elf that's still untapped and can join the party). Fog is in effect, so none of these creatures will actually deal any combat damage, but the point is to get 16 Bazaar Krovod triggers, all targeting Trostani (plus one Aurelia trigger that untaps everything, including the noncombatants). They all have vigilance thanks to Ring of Thune and are untapped to start, and Trostani can populate 85 times for 51 mana.
Don't populate after the last trigger resolves, because it needs to be untapped at the start of the next combat to attack again there (remember, Krovod can only target attacking creatures, which is an easy restriction to overlook if it's not a card you're familiar with).
Populating costs white mana, which Gyre Sage doesn't provide. Fortunately, Druids' Repository gets a counter (and thus a mana) for every attacking creature. This will always be enough to cover the white mana portion of the populate costs--for instance, there are currently 84 attacking creatures, and the total populate cost is 17 white, 17 green, and 17 of any color. You'll also use Druids' Repository counters to produce a few more mana (including at least 2 white and 2 red) to help create additional combat phases, but your army is guaranteed to be large enough to cover that cost too. A single Gyre Sage taps for 2^156 mana (and that number's only going to get bigger in the future), which is enough to cover all the green and colorless without even leaving a dent in its supply. Populate into 1360 more Bazaar Krovod tokens, which the Gyre Sages don't care about, while Hamletback Goliaths each go to 2^166 (certainly this is visible progress, but it's unnoticeable in the long run).
Before Aurelia untaps everything, tap all the Gyre Sages for about 2^160 mana, which is enough to do the Ooze Flux loop 2^159 times. This allows Master Biomancer and Hamletback Goliath to shoot way up to 2^(2^162), while the Sages get a more modest upgrade to 2^163.
Of course, stopping here wouldn't make those numbers anywhere near big enough. That's why...you don't stop here! Sacrifice Aurelia to Bloodflow Connoisseur, sacrifice Codex Shredder to bring back Aurelia, and replay her immediately using the spare Druids' Repository mana that was set aside, now with a reset object identity and 2^(2^162) +1/+1 counters.
In combat 2, again attack with everything but the Gyre Sages (including 1376 Bazaar Krovods). The goal is to accumulate more and more Krovods in every combat phase but the last, to set up for an absolutely huge explosion in the last one. The Gyre Sages, Hamletback Goliaths, and Ooze Flux all do their thing, but what's important is that the supply of Krovods increases slightly more than 81-fold each time. Between Sages and Repository, mana will never be an issue, so you should never populate for anything except Krovod until the final combat.
After combat 2, there will be 111,536 Krovods, and so on. Because Master Biomancer is so huge, all incoming creatures will be big enough to make the existing Gyre Sages evolve, but for only 16 counters at a whack...purely a drop in the bucket. With over 2^166 loops through Ooze Flux, Biomancer and Goliaths will go to 2^(2^169), and Sages go to 2^170, a +7 gain on each of their topmost exponents each time (which can be explained as +4 because Parallel Lives causes the production of 2^4 tokens with each activation, +4 because there are 2^4 Hamletback Goliaths that trigger on each token, and -1 because each activation costs 2 mana).
The deck is designed to maximize the number of combat phases available while still making room for the rest of the combo. This requires resetting Aurelia each time, and there's a lot of time for that:
Combat 1-4: Sacrifice Codex Shredder, bringing Aurelia back in a straightforward manner.
Combat 5-8: Activate Trading Post, sacrificing a creature to bring back Codex Shredder, then replay Codex Shredder and use that to reset Aurelia. The 15 spare Bloodflow Connoisseurs and the 16 Arbor Elves are the most expendable creatures available. All Death's Presence triggers go to Master Biomancer, of course.
Combat 9+: Use Clock of Omens to untap Trading Post, then proceed as before. Angel's Tomb is a creature and will be untapped by each of Aurelia's attack triggers, so tap it plus one of the other artifacts each time (if you do so before Aurelia's trigger resolves, it will be untapped and ready to attack for a Druids' Repository counter in the next combat, what with vigilance and all that):
9 Akroma's Memorial
10-13 Angelic Armaments
14-17 Chromatic Lantern
18-21 Clock of Omens
22-25 Demonmail Hauberk
26-29 Illusionist's Bracers
30-33 Moonsilver Spear
34-35 Ring of Thune
This calls for 31 sacrifices, which neatly coincides with the number of expendable creatures mentioned above. Aurelia will get an attack trigger in combat 36, and untap Angel's Tomb, but this time there will be no second artifact that can be tapped to pay the cost for Clock of Omens. So 36 will be the last Krovod-gathering combat, and 37 will be the last combat, period. After N combats, the Krovod count will be slightly more than 16*(81^N): in this case N=36, or about 2^232. Also after combat 36, the Biomancer and the Goliaths will have power near 2^(2^407), and the Gyre Sages will have around 2^408.
In combat 37, attack with the usual suspects. Get about 2^232 Bazaar Krovod triggers, or more than 2^234 populates (2^238 tokens). This time, the populate target of choice should be Gyre Sage. Before each populate resolves (and remember, thanks to Illusionist's Bracers, one activation of the "populate" ability really gives you five things to respond to), tap all available Sages for mana and run the Ooze Flux loop as much as you can, until all that's left is the supply of white (plus one red for reasons that will be clear later, and if necessary, two more green to pay for the next populate activation in turn).
Observe what the Ooze Flux loop does: for example, in combat 2, Gyre Sages were able to produce 2^167 mana, which could be spent to give the Master Biomancer and Hamletback Goliath a power boost up to 2^(2^169)--basically, whatever mana Gyre Sage inputs (call it X), those creatures can use it to obtain a power higher than 2^X. Gyre Sage itself only grows by a multiplicative factor of 128 each time, which is why it was still only at a simple exponential expression--2^408 to begin combat 35. The steps could have been rearranged to make Gyre Sage much larger by this point, but the goal isn't to maximize damage at a certain midway point; the goal is to maximize damage by the end. That first populate into Gyre Sage brings the mana production up to 2^(2^417)--not only catching up to the Biomancer's figure, but exceeding it, and doing the Ooze Flux loop at this point causes the Biomancer to take 2 to
that power. In summary, every populate step from now on allows the Sages and the Biomancer, in turn, to each add a "2^" to the beginning of their power towers.
Of course, Sage was almost completely ignored through all 36 prior combat phases, to focus on Bazaar Krovod instead. That decision actually results in the greatest number of untap triggers, and thus as many populate steps as possible. By going all-in on this final combat phase, Trostani can now populate over 2^234 times...and
every single one of them adds a new term to the power towers. Forget numbers that can be described by twelve-digit exponents, or even triple or quadruple nested exponents. This is way,
way past that. In order to describe the power or toughness of the Biomancer and Goliaths at the end, it would take an ongoing chain of 2^(2^(2^(2^(2^(...))))) where if you tried to use single atoms to represent each "2", you could use up
all the atoms in the solar system, and still only have 0.000000005% of the expression completed. Or you could just thank Donald Knuth, write
2^^(2^234), and save yourself all that trouble. Oh yeah, one more thing: after the last populate step, and the creation and sacrifice of all those Ooze tokens in the final batch, make sure to stop when you get down to
in the mana pool. You'll need it.
At this point, you can use the Bloodflow Connoisseur's sacrifice ability to start capturing everything else in a giant snowball, putting counters on itself both from its own ability and from the Death's Presence triggers. The difference this makes is absolutely undetectable compared to the power that already existed on the board, but nonetheless the goal is "maximum damage", and this really does increase the damage. When the snowball comes to a screeching halt, Connoisseur will be the only creature you have left, in the 37th and final combat phase of this second turn, so it had better count for something.
And with 2 mana left, play the only card remaining in your hand: Skullcrack, to ensure it
does count for something. In addition to nugging the opponent for 3, it also turns off Fog, allowing your Bloodflow Connoisseur--who certainly puts the "power" in "power tower"--to
finally get through for some damage. Hopefully, the sheer amount of damage makes it worth the wait.
If you've read all the way through this monster of a post, feel free to doublecheck all the growth rates, or (if you want to drive yourself completely insane) look to see if there's a more efficient way to use these cards. It's unfortunate that there's absolutely no enchantment animation in the environment, because being able to populate token copies of Parallel Lives (even if the first one has to be made by a
Cackling Counterpart 
) would have opened up a completely new monster: as big as the numbers here are, token Parallel Lives would still run roughshod over them.
And if you just skipped all the way to the end of the post instead, you might not want to look behind you. I wouldn't want to piss off someone as powerful as is demonstrated here, especially not when they look so thirsty.
