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Inspired by the answer to this question about sunbeams, I realized that there may be a way to exploit Simulacrum to do basically anything an infinite number of times.

Specifically, the course of action would be this:

  1. Be Xanar, a 17th sorcerer. At level 17 you chose Simulacrum as your new spell known, and used your per-level replacement to replace one of your previous spells with Wish. You also know Dispel Magic, and took the Magic Initiate feat to pick up Eldritch Blast.

  2. Cast Simulacrum on yourself, creating a simulacrum with all of your spell slots except the 7th level one. Give it a forked, metal rod worth at least 250 gp, attuned to the Abyss.

  3. Give your simulacrum the following command: "Cast Wish to create a simulacrum of the wizard Xanar. Then immediately repeat this entire command to the new simulacrum. After doing that, take the forked rod and us it to Plane Shift to a random location within the Abyss, dropping the forked rod before you leave. Then search for the nearest demon if there is one, and cast Eldritch Blast on it. Then, cast Dispel Magic on yourself, intentionally failing the saving throw."

  4. Your simulacrum (henceforth Simulacrum A), acting on your turn, casts Wish using it's 9th-level spell slot, creating another simulacrum of Xanar, who still has a 9th-level spell slot. This new simulacrum (henceforth simulacrum B), will thus also still have a 9th-level spell slot.

Note: We aren't using Wish to cast Simulacrum using the "replicate a spell" feature, since that would require being in range of Xanar to cast it. Instead we use the second option to wish for the simulacrum to be made no matter how far away he is. This isn't asking for much beyond the basic, and so should be a valid wish. This does incur the 33% chance to not be able to cast Wish ever again, but that's for your simulacrums and thus doesn't matter.

  1. Simulacrum A, following your order, repeats said order to simulacrum B as a free action.

  2. Simulacrum B, following the order of simulacrum A, and still acting on your turn, becomes the new simulacrum A and repeats steps 4-6.

At this point, since all newly created simulacrum act on the same turn, and all cast Wish on that turn, an infinite number of simulacra are created. On the next turn, those infinite simulacra continue to follow the rest of the order they were given, leading to:

  1. The first simulacrum uses the rod to cast Plane Shift, dropping the rod just before it leaves. The next simulacrum then takes it's turn, picking up the rod (interaction), casting Plane Shift (action), and then dropping the rod as well before it leaves (free action). In this way, the rod travels along the infinite line of simulacra, allowing all of them to cast Plane Shift.

  2. Infinite simulacra of Xanar appear at every point in the Abyss, and cast an infinite number of Eldritch Blasts upon every demon there.

  3. Every demon takes an infinite amount of force damage, and dies.

  4. Every simulacra casts Dispel Magic on itself, and ceases to exist.

The important thing here is the difference between "arbitrarily large" and "infinite". Most supposedly "infinite" tricks in DnD are really just arbitrarily large, which means that they can be repeated any number of times, perhaps even over a very short period of time, but ultimately they need to stop at some point. That number can be as big as you want, but it can't be infinity.

This is important since the Abyss is both infinitely large and contains an infinite number of demons. Any spell which can simply kill an arbitrarily large number of demons would be insufficient, since no matter how many you kill, there would always be an infinite amount left.

Since this trick is recursive, however, and happens on one turn, it actually is infinite, and can therefore be used to kill all infinity demons. Since Eldritch Blast always hits on a 20, and no demon (that I could find) is immune to force damage, and there are potentially infinite Xanars ready to cast it on them, it doesn't matter how hard any given demon is to hit or how many hit points they have or whatever.

Note that this all does assume that a wished-for simulacrum can take an action immediately, on the same turn that it was created. Otherwise, it would take an infinite amount of time to create the infinite simulacra, which would defeat the whole purpose. For the purposes of this discussion, we will assume that this holds true, though a DM could obviously rule otherwise.

Aside from that issue, do you guys see any flaws in this plan? Any improvements that could be made?

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    \$\begingroup\$ I don't quite understand your distinction between infinite and arbitrarily large. If anything can continue an arbitrarily large number of times that only means that at some point, at any point actually, you have the option of stopping. If an arbitrarily large thing must stop then it simply isn't arbitrarily large. Nothing ever actually requires you to stop. Also how does one intentionally fail a saving throw, this is generally not considered an option. \$\endgroup\$ – Medix2 Jan 29 at 22:18
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    \$\begingroup\$ This question asks for flaws in the plan, that means flaws are answers. Please put those answers in an answer or in a comment-suggestion for another anwer. Please don't leave them in comments under this question. \$\endgroup\$ – Rubiksmoose Jan 30 at 13:59
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    \$\begingroup\$ Could you please add links for the Spells, etc. that you are referencing? Because the links that I am looking at have half a dozen different reasons why you can't do this, but they might be different versions? \$\endgroup\$ – RBarryYoung Jan 30 at 17:56
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    \$\begingroup\$ Out of curiosity, how is your sorcerer learning simulacrum? \$\endgroup\$ – Rubiksmoose Jan 30 at 19:26
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    \$\begingroup\$ Is the number of demons countably infinite, or uncountably infinite? This matters, because your recursion only produces a countably infinite number of copies. \$\endgroup\$ – Mark Jan 30 at 22:13
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Not necessarily, because math, and not at all in Adventure's League

AL problems:

(source)

The key problem is :

We aren't using Wish to cast Simulacrum using the "replicate a spell" feature, since that would require being in range of Xanar to cast it. Instead we use the second option to wish for the simulacrum to be made no matter how far away he is. This isn't asking for much beyond the basic, and so should be a valid wish. This does incur the 33% chance to not be able to cast Wish ever again, but that's for your simulacrums and thus doesn't matter.

Because:

No Copies of a Copy.

Simulacrums can’t cast simulacrum, or any spell that duplicates its effects.

and

You Are You; and So Is He.

If a simulacrum you have created casts wish, both you and your simulacrum suffer the stress associated with casting the spell — including the risk of being forever unable to cast wish again. The inability to cast wish extends to any simulacrum you create in the future. (p. 8)

Each of which is designed to deal with essential parts of this otherwise-legal plan.

General Problems:

tl;dr: ℵ1 is greater than ℵ0

Be Xanar, a 17th sorcerer. At level 17 you chose Simulacrum as your new spell known

You can't cause that's a Wizard only spell. However, you be able to do that with a permissive DM or with an appropriate homebrew sorcerous origin. You can also just cast it directly via wish, which you can cast multiple times if you have the right Epic Boon(s).

Next problem:

  1. The first simulacrum uses the rod to cast Plane Shift, dropping the rod just before it leaves. The next simulacrum then takes it's turn, picking up the rod (interaction), casting Plane Shift (action), and then dropping the rod as well before it leaves (free action). In this way, the rod travels along the infinite line of simulacra, allowing all of them to cast Plane Shift.

You almost certainly can't do this. There's no time between casting and the effects happening. You could use Contingency for this (there are ways to have more spell slots around), except Plane Shift is too high of a level. Instead, you need to be friends with or True Polymorph into a Metallic Dragon variant spellcaster that knows Plane Shift (for reasons. You can also coerce one into service with Gate+Dominate Monster or whatever), and have your simulacra using twinned wish duplicating simulacrum. Despite the fact this makes no sense (Wish-duplicated spells shouldn't be twinnable since you aren't casting them), it is legal via Sage Advice Compendium errata stuff:

Can my sorcerer use Twinned Spell on a spell duplicated by the casting of a wish spell? And if so, how many sorcery points does it cost? Yes, you can. It costs the number of sorcery points appropriate for the level of the spell you’re duplicating.

and so by spending 7 sorcery points your simulacra can duplicate both you and the dragon (or a simulacrum of her), or you and a simulacrum of you.

Assuming you take one extra day or use up your 8th level slot or have a relevant magic item or class feature to cast Simulacrum again without using up your 9th level slot, that also solves the need to be using the cheat-y wish instead of the normal one: since the first casting gets you two simulacra and they each still have wish ready, the first one can copy you and the second one, and the second one can copy two of those copies, and so on. One out of every 9 copies needs to be a dragon.

You could have done this with Gynosphinxes instead, but you can't simulacrum those because they can't turn into a beast or humanoid while retaining the ability to turn back like Metallic Dragons can. Since draconic spellcasting has no components, the dragon simulacra can warp parties of 8 Xanar simulacra to the Abyss without the need for rods.

Sidenote-- you have infinitely many Xanar in the Material Plane for a bit here, which might be uncomfortable but doesn't have any mechanical penalties and can be dealt with by having the dragons warp sooner if it is a problem for some reason. Next problem:

  1. Infinite simulacra of Xanar appear at every point in the Abyss, and cast an infinite number of Eldritch Blasts upon every demon there.

No, Infinite simulacra of Xanar appear at infinitely many points in the Abyss, and cast their infinite Eldritch Blasts upon infinitely many demons there. Your infinity and the Abyss are not guaranteed to be equal in size. In my games, for example, the Abyss is infinitely larger: you have only ℵ0 simulacra while the Abyss has ℵ0 layers with ℵ1 squares on each layer.

Other people run the Abyss as only having ℵ0 or some smaller number of points or spaces on each layer. In that case, this might be a larger number than the number of demons. Even so, there's no guarantee that your ℵ0 is the same size as their ℵ0. It might be bigger, smaller, or something else entirely-- the game does not in any way define the superstructure of the Abyss. Comparing infinities is not easy, that's why ∞ - ∞ is undefined, not 0.

To solve this problem for sure, you would need a system to generate an uncountable number of simulacra. That is, you would need the demons to not be able to apply Cantor Diagonalization to your onslaught and, in so doing, show that at least one demon wasn't attacked. I am not sure if this can be done or how you would do it.

Even if you did it, your sets would each be ℵ1 large, and you'd still have an ∞ - ∞ situation for your DM to define the result of. To get around that, you'd need to incorporate the source of the demons into your simulacrum creation, so that the number of simulacra can be shown to be greater than the number of demons at infinity and the result of the subtraction can be medium-well-defined.

You also need a mapping function to get your simulacra to not all be bunched onto the same points, but that's a smaller problem likely solved by assuming a 1-to-1 correspondence between Material Plane spaces and Abyss spaces, somewhat supported by the explanation of how planes work in the DMG.

Even then you are gonna miss infinitely many demons, though because of the next problem:

  1. Every demon takes an infinite amount of force damage, and dies.

Not necessarily. Demons in antimagic fields won't, and, in fact, no, Xanars can't warp into such spaces! So that's infinitely many demons this won't kill.

Also, you're rolling initiative and even with infinitely many rolls you won't beat any creature who rolls higher than it is possible for you to roll or who has special abilities allowing it to go first. Any creature who goes before you might take actions to elude your army, for example by casting antimagic field or plane shift or wall of force or meld into stone or doing anything else that negates infinitely many eldritch blasts. And any creature who doesn't go before you still might escape with reactions unless they are surprised (which, admittedly, seems likely, but is still not guaranteed). And those who don't might, like with antimagic field residents, be immune anyway for some other reason.

That said, this will still kill infinitely many demons, so it may well still be worth a try. Just watch out for the infinitely many survivors who immediately plane shift in on your position and give you a bad day.

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    \$\begingroup\$ This is exactly the kind of answer I was looking for, thanks. Though now I'm wondering what it would actually take to be sure to kill all infinitely many demons. \$\endgroup\$ – AgentPaper Jan 30 at 6:03
  • \$\begingroup\$ Comments are not for extended discussion; this conversation has been moved to chat. \$\endgroup\$ – Rubiksmoose Feb 2 at 1:00
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    \$\begingroup\$ Note that even if you have the same infinite number of Xanars as there are demons, you still don't necessarily kill them all. Indeed, you almost surely (that is: with probability 100% (and that's not rounded!)) don't! The probability of having an empty space of at least any given finite radius in a random distribution of countably infinitely many points on the plane is 1, so in particular there is almost surely a Xanar-less circle of radius at least, say, 1 mile, in which there are no Xanars, and so no Eldrich blasts, and so all of the demons in there are fine. \$\endgroup\$ – user3482749 Feb 6 at 0:36
  • \$\begingroup\$ @user3482749 Yes, that is part of why I choose to mostly focus on spaces rather than demons-- if 'an infinite number of Xanars appear at every point in the Abyss' were true, you'd in fact be able to kill all the demons (assuming they have only finite demons per space), and if not you (for a variety of reasons) can't, at least generally. The mapping function I touch briefly was an attempt to address your point, though maybe it would be good to examine it in detail. My concern is keeping this easily comprehensible for RPGers with only a casual understanding and little interest in math. \$\endgroup\$ – Please stop being evil Feb 6 at 1:16
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At a glance...

  1. Infinite series lead to infinite problems. This plan will not, and cannot, be completed, because the existence of infinite demons means that they will never run out. Even if this plan ran for eternity, it would never finish and therefore never achieve the stated goal

  2. Infinite simulacra themselves pose infinite problems. They would, collectively, need an infinite amount of space to occupy before they could move on to step 7 (when they start disappearing from their initial plane)

  3. The order of events is such that no simulacrum will ever actually travel to the Abyss (they need to complete the task of creating infinite simulacra first, which by definition will never occur)

  4. Because an infinite amount of space is required to accommodate infinite simulacra, the position of the tuning fork can't accommodate all of them at once. At least some simulacra will be too far away to get to it and pick it up to use in a single turn. And, once again, infinity means that an infinite number of those simulacra will be an infinite distance away from the fork

  5. If the effect of Plane Shift is instantaneous it may not be possible to drop the fork used to cast it before shifting to another plane. If this is true, then a fork would be needed for each simulacrum (though Wish might be able to provide that)

  6. Wish is unstable when used for purposes other than replicating spells, which is the case here. If a casting of Wish fails at any point (and, given the infinite recursion, as long as there is a nonzero chance of failure at least one failure will occur), the cycle breaks down short of infinity

  7. A GM will almost certainly bend the effects of Wish in some way which would invalidate or seriously complicate the plan. If you're trying to evaluate this exclusively in-universe, then reality or the Weave or a deity (or something) will almost certainly frustrate the scheme

  8. This seriously bends the way that time is represented in-game by relying on an abstraction of time (turns). Wish takes an Action to cast, roughly six seconds. Since a simulacrum created in this way will only come into being at the end of the casting, and therefore the end of a turn, I'm not sure it's sound to say that these effects would be instantaneous. There should be six seconds' worth of casting time for each simulacrum casting Wish, even if you want to say it's all the same turn

  9. Characters can't choose to fail saving throws, though that part of the plan seems irrelevant (it doesn't matter if a simulacrum continues to exist or not after its initial Eldritch Blast). Further, Dispel Magic involves a spellcasting check, which can fail, further complicating matters

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    \$\begingroup\$ You explained it better than I did. You can also add "Plane Shift is "Instantaneous" so there is no dropping the tuning fork for the next guy. Everyone would need their own. That in itself would break the cycle (unless you also have infinite forks)." \$\endgroup\$ – MivaScott Jan 29 at 22:45
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    \$\begingroup\$ For #9, it's also worth noting that dispel magic involves a spellcasting ability check by the caster, not a saving throw by the target. \$\endgroup\$ – V2Blast Jan 29 at 23:33
  • \$\begingroup\$ 2, 3 and 4 don't really make sense since the new simulacrum acts after the old one, so there is never a space problem and the first one begins blasting 6 seconds later regardless of whether infinite simulacrum were created yet. \$\endgroup\$ – gszavae Jan 30 at 0:16
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    \$\begingroup\$ @jgn I'm not sure that's true. The OP clearly indicates that each simulacrum acts on the same turn as the creature that created it, and so that turn can't end until all simulacra have been created. Plane Shift is a spell, and so needs a second turn anyhow (because casting Wish consumes the Action of the first turn). I didn't see a step suggesting that a simulacrum can cast a second spell on the same turn it casts Wish, though Wish itself offers lots of ways to fiddle with rules. But the OP is explicit that each phase takes place in a single turn. The first turn never ends. \$\endgroup\$ – Upper_Case Jan 30 at 0:27
  • \$\begingroup\$ 1 and 3 aren't valid - a process with infinite steps can be completed in finite time. To run a race, you first have to run the first half, then the next quarter, then the next eighth, and so on - infinite steps. And yet even I, as unfit as I am, can complete such a task in finite time. See Zeno's paradox. In this case, there are other concerns (such as where to fit all those copies, which you address), but RAW the timing works. \$\endgroup\$ – Sirv Feb 5 at 5:53
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Suppose wishes don't fail and all simulacra are created in a neat line (so that they can pass the fork) in a likewise infinite plane, sequentially but within the 6-second turn.

Also suppose (I'm not too confident that there's any time in between the spell being cast and having an effect) that it is possible to take a free item-drop action before being planeshifted away, and that letting go the fork before the spell has any effect does not ruin the spell.

You get infinite simulacra in the Abyss at the same time, each occupying their own spot in space, but only a finite number of them can actually be in range of any specific demon, unless they have no volume.

This finite number is not large enough to guarantee that they manage to kill their target demon. They might all miss.

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Another problem in step 5 is that you can talk without an action, but only:

through brief utterances and gestures

It definitely takes a benevolent DM to rule that:

"Cast Wish to create a simulacrum of the wizard Xanar. Then immediately repeat this entire command to the new simulacrum. After doing that, take the forked rod and us it to Plane Shift to a random location within the Abyss, dropping the forked rod before you leave. Then search for the nearest demon if there is one, and cast Eldritch Blast on it. Then, cast Dispel Magic on yourself, intentionally failing the saving throw."

is "brief".

It probably requires 2 turns of actions to say that much.

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  • \$\begingroup\$ You could potentially Wish for the new simulacrum to already know the plan? But even then, the time to speak the verbal component of Wish is non-zero, and you can't justify this entire chain of casts rounding down to fit in the span of 1 round. (Unless each Wish is for the new Sim to have already appeared a few seconds ago...) So at best you can get linear growth with time, or exponential with Twinned Spell, but still finite for any finite amount of time. \$\endgroup\$ – Peter Cordes Jan 31 at 6:56

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