4

After Theros: Beyond Death is added to standard, what will be the most mana a permanent can be tapped to produce?

Rules:

  1. Current standard sets and Theros: Beyond Death are legal

  2. No infinite combos of any sort. This INCLUDES loops that could be repeated turn after turn

  3. Your deck must contain exactly 60 cards

  4. You have set-up time limited only by decking yourself (53 turns, less or more with shenanigans)

  5. You may not use your opponent's deck at all. For the purposes of this challenge, your opponent does not have a deck.

  6. Mirror March is a card that, depending on luck, can technically get any number of mana produced. This came up when I asked a friend about this challenge, but I forgot to put it in the rules before. Any card that creates an "arbitrarily large" amount is ruled out for this challenge (Apologies Arcanist Lupus, although thanks for reminding me)

Answer with the number and the set-up required to do so. After I get a few answers, if mine is still the largest, I will post it. (Hint: I can't express it as a straight number)

  • Can we assume that the deck is stacked? – murgatroid99 Jan 12 at 17:55
  • Yes. You draw cards in whatever order is optimal for you. – CollinB Jan 12 at 18:26
  • Don't feel obligated to give a turn by turn – CollinB Jan 12 at 18:26
  • 2
    Also, can you list the set range for current standard in the question, just so that we can keep track of the exact rules for this question in the future? – murgatroid99 Jan 12 at 18:44
  • Can our solution involve repeating the same activated ability turn after turn? Not sure if this violates rule 2, as it is still limited by the number of turns until you run out of cards. – Aetherfox Jan 13 at 17:36
4

At least 3^(2^^^^39)

Decklist:

Setup for combo

The setup involves the following:

  • Drawing cards until we have Wilderness Reclamation and 7 other cards in hand, and discarding Wilderness Reclamation to hand size.

  • Drawing cards and playing lands until we have drawn and played 4 Izzet Guildgate, 3 Simic Guildgate, and 1 Boros Guildgate and all other non-land permanent cards, and drawn all of the instants and sorceries.

  • Casting Dance of the Manse with X=6 targeting Wilderness Reclamation to put it onto the battlefield as a 4/4 creature.

  • Casting Awakening of Vitu-Ghazi targeting a

This takes 14 turns to draw all of those cards, and we can finish playing them earlier than that.

Combo

We have no way to untap lands, so we can construct a "loop" that is ultimately limited by the mana that can be generated by the lands on the battlefield.

A loop iteration is as follows:

  • Cast Repeated Reverberation. Allow all Thousand-Year Storm triggers, previous Repeated Reverberation triggers, and copies to resolve, but leave the original spell on the stack. This copies the next spell to be cast a number of times equal to 2 * (2 * storm count + previous RR triggers). This costs {2}{R}{R}.

  • Cast Narset's Reversal targeting the Repeated Reverberation card. By now, the storm count is at least 1, so both of the Thousand-Year Storm triggers make at least 2 total copies of Narset's Reversal. Have 1 copy target the Repeated Reverberations card, and the other target the original Narset's Reversal card. The result is that we get 1 more copy of Repeated Reverberation, and all cards on the stack return to the hand. This costs {U}{U}.

  • Allow all of the copies of Repeated Reverberation to resolve.

This loop iteration costs 6 mana in some combination of {U} and {R}, increases the storm count by 2, and makes twices as many of the next spell to be cast. For the loop, we tap a land for {U} and a land for {R} (both modified by Nyxbloom Ancients), and repeat this loop until we have 5 mana remaining. We spend that 5 mana to cast Quasiduplicate targeting Nyxbloom Ancient, allow all of the copies to resolve, and cast Narset's Reversal to return both cards to the hand. Then we tap another two lands for much more mana, and repeat the process.

When performing this loop on a full set of untapped lands, when spending the last mana on Quasiduplicate, target the awakened Izzet Guildgate instead of Nyxbloom Ancient. When performing the loop during the main phase, target the animated Wilderness Reclamation instead

Then, in a full turn, we do the following:

  • Activate Teferi's first loyalty ability so that we can cast sorcery spells at instant speed.

  • Perform the loop described above, copying Nyxbloom Ancient, and with the last lands, Wilderness Reclamation

  • For each Wilderness Reclamation trigger, perform the same loop, copying Nyxbloom Ancient, and with the last lands, Izzet Guildgate

In the long run, the doubling from Repeated Reverberation far outpaces the storm copies from Thousand-Year Storm, so we can approximately say that each loop iteration doubles the number of copies 8 times. So, after we tap a pair of lands for M = 2 * 3^N mana, where N is the number of copies of Nyxbloom Ancient on the battlefield, we can make approximately 2^((M-5)/6) copies of Nyxbloom Ancient. In the longer run, the multiplicative factors don't even matter that much, so we can say that the number of Nyxbloom Ancients we get from tapping one land is about 2^(3^N), where N is the number we previously had.

2^(3^N) is much greater than 2^(2^N), so we can say that every time we untap our lands, we get more than 2^...^K Nyxbloom Ancients and Izzet Guildgates or Wilderness Reclamations, where K is the number of Nyxbloom Ancients we untapped with and the number of 2s is equal to the number of Izzet Guildgates we untapped with. In Knuth's up-arrow notation, this is much greater than 2^^N, where N is the number of Izzet Guildgates. So, each turn we get 2^^N Wilderness Reclamations and repeat that process in response to each Wilderness Reclamation trigger. That gives us 2^^^(2^^N) Izzet Guildgates.

We repeat that process for the 39 turns it takes to draw the rest of the library, getting more than 2^^^^39 Guildgates, Nyxbloom Ancients, and Wilderness Reclamations. In the end, we tap the last land for more than 3^(2^^^^39) mana.


This cannot go infinite because every land in the decklist unconditionally enters the battlefield tapped, and we can only untap lands during the untap step and a bounded number of times each end step because of Wilderness Reclamation. So, creating more lands can only increase the amount of mana available the next time we untap lands, and the number of times we can untap lands each turn is bounded.


Credit to Arcanist Lupus's answer for the idea of using Wilderness Reclamation, and using Dance of the Manse to be able to copy it with Quasiduplicate.

  • I think that you're right that Wilderness Reclamation is worth duplicating, but Thousand-Year Storm is not. Why is Folio of Fancies in your decklist? I don't see you using it. Also, why 4 copies of Nyxbloom Ancient? Wouldn't it be more efficient to use the mana spent playing the three extra copies on duplicating it? – Arcanist Lupus Jan 12 at 21:03
  • The loop I described uses 10 cards. The Folio is there so that I can keep them all in my hand every turn. And the 4 Nyxbloom Ancients are in there to ensure that I can do a full loop iteration the first time around. They're not strictly necessary but they make the algorithm simpler. I'm sure you can optimize things here and make that last number 50 or more, but there's already so many approximations that it doesn't really matter. The way I see it, the only real improvement would be to add another layer, increasing the number of up arrows. – murgatroid99 Jan 12 at 21:07
  • Still, looking at it again, the benefits of having several of those cards kind of disappear when doing all of those approximations, so I can definitely edit to make it simpler. – murgatroid99 Jan 12 at 21:19
  • Ah, that makes sense. – Arcanist Lupus Jan 12 at 21:26
  • I did not think of using Wilderness reclamation at all! My own first solution was only 10369*3^3455, which I am relatively sure is smaller than 3^(2^^^41) – CollinB Jan 13 at 0:03
1

Pretty big

I'm not going to do the math on this, and there may be more optimal configurations, but here's the basic idea:

Ingredients
Dance of the Manse
Thousand-Year Storm
Nyxbloom Ancient
Quasiduplicate
Narset's Reversal
Lotus Field
54 Islands

Gameplan
Go second. Skip the first land play, and discard Thousand-Year Storm (TYS) Play 2 Islands
Play Lotus Field, saccing the two Islands
Play 2 land each turn. Upon playing your 7th land, play Nyxbloom Ancient (NBA).

Turn 9: Play a 6th land (8th land drop, minus Lotus Field sacs) Tap Lotus Field for 9 W, 1 island for 3 U Cast Dance of the Manse with X=6, returning TYS to the battlefield as a creature (2W2U remaining)

Cast Quasiduplicate (QD), targeting TYS. TYS copies QD, the copy targets NBA. Let the copy resolve, then tap an island for 9 U (1W9U remaining) Cast Narset's Reversal* (NR) on QD. The two copies of NR both target NR. The first will bounce it, and the second will fissile. The copy of QD created by the copy of NR will create a copy of TYS.

Cast QD again, this time getting 6 copies. Then cast NR, getting 8 copies which all target NR.

I think you can see where this is going. For 5 mana, you get to play Quasiduplicate with Buyback, and tick up your storm counter twice. This is not an infinite combo, because you can only get mana from your lands, and each land can only be tapped once. But each land generates a ton of mana (3^N, where N is the number of Nyxbloom Ancients in play).

You can repeat this every turn until you run out of cards in your deck (see, still not infinite). At the very end, tap your Lotus Field for ungodly gobs of mana.

*For our purposes, when Narset's Reversal creates a copy of a spell, that copy will always target the original target. There's no benefit to switching targets, so I'm not going to bother to mention it in the main description.


Possible Deck Adjustments
I'm not sure what the optimal ratio of Nyxbloom Ancients to Thousand-Year Storms is for targeting with Quasiduplicate is. It's possible that Nyxbloom Ancient is always the better target, in which case you can drop Dance of the Manse entirely and replace it with a 55th land. I'm pretty sure that that isn't the case, though.

There will be 2 (or 3 if you drop Dance of the Manse) islands left in your hand at the end of the game when you deck yourself. You can replace those with Firemind Vessels (which will speed up your engine a turn, and give you more mana on the board), but this is a bit of a tricky point in the rules of the challenge, since if you discard a Vessel the way you discarded the Thousand-Year Storm and then reanimate both of them, the deck goes infinite. Does it disqualify a deck if the deck is capable of going infinite even if you play it in such a way that you never reach that capability?

Obviously, if you cut Dance of the Manse (as mentioned in the first possible adjustment), then the Vessels are safe to include.

You can also replace one of the islands with Dryad of the Ilysian Grove, which will let you play the other island a turn early.

Another possible substitute for the last land is Repeated Reverberation, which combines with Narset's Reversal to be two Quasiduplicates for the cost of [3RRUU]. This is a better rate than 1 QD for 1UUUU, but it means you have to juggle your mana sources between R and U, and each land can only tap for 1 color at a time (even if its a multicolored land, the tripling will copy the color being produced), so I'm not sure it actually works out as more effective.

You can also include a mana dork (such as Paradise Druid as the last card. These can be copied by Quasiduplicate, but because they don't have haste they can't be used for mana the turn you create them and you still don't go infinite. I'm pretty sure that you're better off copying Nyxbloom Ancient over a dork every time, though.

Wilderness Reclamation may also be a valuable addition when combined with Teferi, Time Raveler to give Quasiduplicate flash. You're effectively doubling the number of lands you have, and if you Dance of the Manse it you can start ratcheting up that multiplicative factor. This isn't an infinite combo because the untap triggers only happen once per turn, but I'm still not sure if the extra untaps are worth giving up copying Nyxbloom Ancient (My gut says yes, but you also lose a turn to pitching Wilderness Reclamation into the graveyard, so it's hard to judge).

  • Sorry, I should specify in my answer – CollinB Jan 12 at 17:36
  • I think I can use your Wilderness Reclamation idea to massively improve the number in my answer. – murgatroid99 Jan 12 at 20:05

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