Strange Loops

Sometimes, a game of Magic gets very repetitive. We'd like games to end in a reasonable amount of time, so when a loop of near-identical actions is entered, the rules allow us to shortcut to the end result.

Much like handling illegal sequences, this part of Magic is an unholy mix of game rules and tournament policy, without clear guidance as to which is supposed to take precedence when they conflict727.1c says that the MTR takes precedence over the CR, but as we'll see later, that's not actually true. And sometimes both the CR and MTR agree on something, and are both wrong!. So in order to know how to handle loops correctly, we need to be familiar with both section 727 of the Comprehensive Rules, and section 4.4 of the Magic Tournament Rules, along with the underlying philosophy and reasons why they were written this way.

Starting a loop

Any time the game gets into a repetitive state, with the same actions being taken over and over, the player(s) involved must declare it as a loop and shortcut it if possible to save time. In order to declare a loop, the player must clearly state what actions constitute the loop, along with what game variables are being incremented on each iteration.

For example, Alice could declare a loop that involves: 1) Tapping Bloom Tender for {U}{G}, 2) Activating Pemmin's Aura, paying {U} to untap Bloom Tender, 3) Resolving this ability, untapping Bloom Tender. After these three actions are executed, the game state is identical to how it started, with one variable changed: Alice's mana pool contains one additional green mana.

Once this is defined, Alice can shortcut this loop by saying "I'll execute this 1000 times". Then she doesn't need to physically move the cards around 1000 times, she just needs to adjust her mana pool to contain an extra 1000 mana.

It's customary to physically play through the loop once before shortcutting the rest of the iterations. This is not a requirement, but it's a good idea, as it helps avoid mistakes. For example in the previous situation, a player could think to themselves "Bloom Tender taps for {U}{G}, and I have infinite untaps, so I have infinite blue and green mana", without realizing that they have to spend the blue mana to untap the creature each time.

As loops get more complicated, the chance of making a mistake gets higher, and it's more and more important to be very clear about everything that's happening, ideally keeping track on a notepad for the first iteration in order to make sure you haven't missed anything. People love to jump to conclusions based on vague intuitive notions of how it feels like things should end up, and those intuitions are often wrong; you need to actually calculate it out step by step and make sure that it works the way you think it does.

(One time during the heights of KCI, a player called me over and said something like "judge, I know I can combo here, I've watched Matt Nass do it, but I'm not sure exactly how. Can you help?" No. That is not how any of this works. You need to know what legal game actions you want to execute. If you can't figure it out, skill issue.If the players think they might be in a mandatory loop, a judge can help them figure out whether that's true. But we don't assist a player with a loop that they're choosing to execute, that's a strategical decision. )

Results of a loop

Loops can end in one of two ways. Either a player breaks the loop, or no player breaks the loop.

If someone breaks the loop, then it's over; the players can't restart it unless something substantive changes about the game state. If no one breaks it, then the game is a draw.You can think of this as shortcutting ahead to when time is called in the round. ;)

In situations where a loop is broken, the ending game state needs to be legal and well-defined, though some handwaving is ok as long as it can't plausibly cause a problem. For example, if you have a loop that lets you cast Beacon of Immortality an arbitrary number of times, you probably don't need to calculate out your life total * 2^X, you can just say "I have more life than you can ever deal to me". (Be careful with this though. You'd be surprised by how much damage some decks can deal.)

Just like making sure the loop is legal, making sure the end state is legal is very important. Say for example that Alice uses the Pemmin's Aura + Bloom Tender loop from above to make infinite green mana, and she also controls Duskwatch Recruiter. She then announces that she has the ability to reorder how library however she wants, so she's just going to pick up the whole thing and put it in the order she wants.

No! Bad player! You don't just get to assume the outcome, you have to prove it can legally be reached. Alice needs to provide a clear explanation of what she's doing, like: "I can take the top three cards and put them on the bottom in the same order. I can do this throughout the rest of the deck until I get back where I started. This allows me to treat the deck as a circle modulo 3, accessing any point that's a multiple of 3 cards from the top, plus the next two cards down. If the last section contains 1 or 2 cards, then that section will overlap back to the top of the deck and create new sections that are one step offset from the first ones, meaning that every pair of adjacent cards exists in at least one section. I can then use Bubble sort to swap adjacent pairs until I get to the final ordering I'd like."There are of course faster algorithms that could be applied here, but it doesn't matter. When you have infinite time, why bother optimizing?

If Alice reasons through this step by step, she'll realize an important caveat; this only works if the number of cards in the deck is not divisible by three! This would be easy to miss if she were being sloppy and just assuming it worked the way she intuitively felt it would work.

Some handwaving around the number of iterations is ok, as long as that number doesn't matter. if Alice has clearly shown that she can reorder her library as she pleases, and that nothing depends on the number of times she activates the ability (e.g. there isn't a Crackdown Construct on the battlefield), then she doesn't need to figure out the exact number of times she needs to activate it, she can just say "I do it enough times". But this is only allowed as a time-saving measure after everyone is satisfied that the end state is legally-attainable.

Who must end loops?

Players are not allowed to intentionally continue a loop in order to draw the game; you can't just use Mist Dragon as a Divine Intervention.

But neither are players always required to break a loop that they don't want to. If there's a three Oblivion Ring thing happening and you have a Ray of Revelation in hand or graveyard, you're not required to cast it; you can choose to let the game end in a draw.

The distinction here is between "actions" and "choices". You're never required to take an action that you don't want to take, but you are required to change your choice if doing so would end a loop. Wizards does not provide a definition of "action" or "choice", and their usage in this context is inconsistent with their usage in other contextsIn fact it's even inconsistent within the sections on loops. The CR uses "action" as a subset of "choice", and doesn't explicitly mention choices at all, just saying that some actions don't need to be taken to break a loop. The choice/action terminology comes from the MTR, and these terms are presumably referring to the same distinction, so for simplicity in this article, I stick to the choice/action terminology., which makes it hard to know what is meant by the terms.

The intuitive definition would be that an "action" is any option where the alternative was "do nothing", and anything else is a "choice". Unfortunately, this isn't true, since Wizards has ruled that choosing to put a card in the graveyard with explore is a "choice".

So we're left with iterating special cases. We know that "actions" include casting a spell, activating an ability, conceding, and anything worded "[a player] may do [thing], if not [other thing]" or "[a player] does [thing] unless [a player] does [other thing]". We know that putting an explored card into the graveyard is a "choice", presumably along with similar things like scry and surveil. Anything that seems roughly symmetric is also probably a choice, like "sacrifice a creature", choosing modes and targets for triggered abilities, and choosing an order for them to be placed on the stack. It's unclear how we're supposed to count general "you may do [thing]" instructions, along with special actions and optional replacement effects.

At what point must the loop be broken? Well, if only one player must break the loop, they can let it continue for any finite number of iterations, but must break it individually. If both players are required to break it, then if one of them wants to break it earlier than the other, that player can do so. Otherwise, the active player must break it first.The MTR seems to be written under the assumption that loops can only ever be maintained by choices or actions, not both. Given that this is obviously wrong, I'm inclined to say it's just an error, and have written the examples below accordingly. But there's always the chance that Wizards meant something like "If a loop is maintained by both choices and actions, the choices are treated as mandatory for the purposes of determining how the loop ends", or some other unstated assumption.

Immediately-halting loops

Some loops get broken immediately by default, without any player needing to do so.

727.2a: At any point in the game, the player with priority may suggest a [loop]. It can't include conditional actions, where the outcome of a game event determines the next action a player takes.

MTR 4.4: Non-deterministic loops (loops that rely on decision trees, probability or mathematical convergence) may not be shortcut. A player attempting to execute a nondeterministic loop must stop if at any point during the process a previous game state (or one identical in all relevant ways) is reached again.

Some loops involve "decision trees", where instead of specifying "I do X", the player has to say "if [thing] occurs I do X, otherwise I do Y". These conditional loops are not allowed to be shortcut.

Except, hold on a second. Isn't that Duskwatch Recruiter situation such a loop? The decision of which cards to move depends on where they started, so the player has to define a conditional statement like "if I see this on top, I leave it there and halt the loop, otherwise I move it to the bottom".

Well that's what the policy says, but Wizards has confirmed multiple times that this sort of loop is in fact allowed.

There are two ways to resolve this seeming contradiction. One is to point out that, once the player has seen their entire library, there's no longer any hidden information. So the player can use a normal shortcut (not a loop) to quickly look at their whole library, then define a deterministic loop from that point. This this feels oddly artificial, and is not what the player is "really" doing.

The other option is to just note, as usual, that Wizards doesn't know how to write clear rules, and disregard their ban on conditional loops as an error. What Wizards probably meant to write there is that a player is not allowed to declare actions conditional on their opponent's choices, since the opponent's choices cannot be deterministically predicted in advance, meaning that a loop that includes them is effectively probabilistic. So we can ignore the "decision trees" phrase in the MTR quote above, and the only ban is on probabilistic loops.

Ok, so what happens with probabilistic loops like Four Horsemen or Wirefly Hive? These loops generally have a certain probability of successWith Four Horsemen the probability is 1, and with Wirefly Hive it's ~0.047., but there's always at least one sequence of unlucky game actions in which it would fail. Accordingly, these loops are treated as though they've already been interrupted right when they begin. The player is allowed to start executing them manually, but once an identical game state is reached, they have to stop; they're not allowed to keep trying over and over.What if the loop isn't being sustained by either player? Well, the MTR doesn't account for the existence of non-deterministic mandatory loops, but the only reasonable answer is that they're a draw. The only question would be when exactly it's a draw, and I'd say it makes the most sense to wait until the first time the game state repeats, then ask the players if either one wants to take an action to break the loop, and if neither does, the game is a draw at that point. But this isn't stated anywhere in the official documents.

(In a tournament, the exact way this works is: Once the player reaches an identical game state, they have to stop. There is no penalty for this, they just have to take a different action. If they continue anyway, then that's a violation of the rules and there's a penalty; a DQ for Cheating if they knew it was illegal, and a Warning for Slow Play if it was unintentional. But there's no penalty for continuing up to the first repetition.)

What is a "relevant difference"?

The most subjective area of the loop rules is when it comes to to deciding what differences between game states are relevant enough to make something qualify as a new loop.

For example, say Alice is executing the Wirefly combo. She hits a tails and has to destroy all her Wireflies, bringing her back to the same game state at which she started. Could she tap an Island, adding one mana to her mana pool, making the game state different, and then try again with a "new" loop?

No. The MTR calls this out explicitly:

Loops may span multiple turns if a game state is not meaningfully changing. Note that drawing cards other than the ones being used to sustain the loop is a meaningful change.

A player attempting to execute a nondeterministic loop must stop if at any point during the process a previous game state (or one identical in all relevant ways) is reached again.

The judge is the final arbiter of what constitutes a loop. A player may not make irrelevant changes between iterations in an attempt to make it appear as though there is no loop. Once a loop has been shortcut, it may not be restarted until the game has changed in a relevant way.

Here it's obvious that tapping a land is irrelevant, because Alice already had infinite mana, and even if she didn't, there's no benefit to having the mana floating instead of stored in an untapped Island. But often it's less clear whether a given difference is "relevant".

For example, let's say AP has the 3 Oblivion Ring loop ongoing. The only other nonland permanent on the battlefield is a Banishing Light that's exiling another Banishing Light. Is AP required to eventually stop targeting only Oblivion Rings and start targeting the Banishing Lights? This could be considered a new loop, since it involves different cards. But it could also be considered the same loop with an irrelevant difference; it's pretty much the same thing happening either way. Would it change if instead of 3 Oblivion Rings and 2 Banishing Lights it was 5 Oblivion Rings? Or 1 each of 5 different cards? Unclear.

The only meager guidance we have here is this article about Four Horsemen, which tells us that making the opponent lose a life counts as a relevant change. Combining this with the MTR's mention that drawing a card is a meaningful change, I think we can reasonably extrapolate this to any game variable changing, so a player gaining life or adding mana to their mana pool would also be a relevant change as long as the new value is likely to matter. (e.g. if the player has only 8 mana value worth of cards in their hand and no way to draw more cards, adding mana past the eighth becomes irrelevant.Plus an extra few if the opponent could reasonably be playing Daze or Mana Leak.)

But this interpretation leads to some unintuitive results, like it allowing a player to "slow-roll" mana production in order to squeeze our more iterations of a non-deterministic loop that can optionally produce mana.

As for what counts as two different loops, we have even less guidance. In the Oblivion Ring/Banishing Light scenario above, treating them as different loops results in a meta-loop where the player is required to break one loop only to start a new one, then break that one in order to start a third, etc. ad infinitum. CR 727.2a does specifically mention "nested loops" as an option, implying that something like this could be intended. But if we take this to its logical conclusion, players will be required to try out every possible "variant" of a loop just in case that causes the opponent to want to break it, which doesn't seem like something they should have to do.

So as much as it bothers me not to have a comprehensive system for handling this, I think I have to just throw up my hands and admit that Wizards has not given us enough to work with here. Any time this comes up, it's going to be a very subjective judgement call from that tournament's head judge, different head judges are going to rule different ways, there's going to be lots of inconsistency between tournaments, and there's nothing to be done about it unless Wizards deigns to clarify their rules.

(As an example of just how bad this can get, question #11 below came up before RC Atlanta 2023. Lots of players were asking about it, as it informed their deckbuilding and strategical decisions. I asked around among various L5 judges along with the head judges for the RC, and there was near-unanimous consent that it worked one way. Then I emailed Wizards just to be sure, and Wizards said it works the other way.)

Example questions

Let's try some practice questions to help you make sure you understand the details. For each question, take a moment to consider how you think it works first, and then check the answer to see if you misunderstood anything.

Question #1

Nathan controls Lethal Vapors. Alice controls Collective Blessing and Aura Shards, and has Gurgling Anointer in her graveyard. She plays another Gurgling Anointer. Who's required to break the loop, and how?

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Question #2

Alice casts Illicit Auction, targeting Nathan's Platinum Angel. Both players pay increasing amounts of life, going past their life total, and neither wants to stop bidding. What happens?

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Question #3

Alice controls Obstinate Familiar and Panoptic Mirror imprinting Time Warp. If she doesn't have any way to win with her infinite turns, what happens?

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Alice is the only player maintaining the loop by choosing to cast Time Warp, so she has to stop eventually.

Question #4

Nathan controls Zndrsplt, Eye of Wisdom. Alice plays Frenetic Efreet and activates it a million times. What happens?

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Question #5

Alice controls Platinum Angel, and Nathan's deck contains no removal for it, so it is impossible for Nathan to win the game. However, Nathan's deck contains Emrakul, the Aeons Torn. Nathan plans to discard it to hand size over and over, preventing him from milling out and making the game a draw. Is this allowed?

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No. After the first time Nathan reaches an identical game state, he must choose to discard a different card. (Unless his entire hand and library is just Emrakuls, in which case it is a draw.)

Question #6

Nathan has infinite mana, and controls High Alert and Obeka, Brute Chronologist. In Alice's upkeep, he continues to tap Obeka over and over. Alice doesn't want to end her turn. What happens?

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Question #7

Alice controls Mondrak, Glory Dominus, and casts Quantum Misalignment twice to get 11 Mondraks in total. She then casts a kicked Rite of Replication targeting Meddling Mage, creating 10,240 more Meddling Mages. How does she go about choosing cards to name?

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Question #8

Using a very convoluted sequence of cards, Alice donates Door to Nothingness to Nathan, and exiles all of the rest of his deck except the mana needed to activate Door to Nothingness. Alice has Leyline of Sanctity and Omen Machine, and neither player has any cards in their library. Does Nathan have to activate Door to Nothingness targeting himself, or can me make the game be a draw?

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This is a loop of "do nothing forever", and Nathan has the ability to break this loop by activating Door to Nothingness. But players are never required to take an action like activating an ability to break a loop, so Nathan can choose to continue doing nothing, making the game a draw.

Question #9

Alice controls Vexing Puzzlebox, two Mana Reflections, and Filigree Sages. Nathan controls Solemnity. If Alice wants to create infinite mana, does she have to roll a d20 every time?

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The d20 does nothing, so it's irrelevant to the loop, and doesn't make this count as a non-deterministic loop. Alice can simply declare how many times she's tapping it and add that much mana to her mana pool. (If the Solemnity weren't there though, she would have to actually roll the die.)

Question #10

Alice controls Horizon Chimera, Drogskul Reaver, Wheel of Sun and Moon, and Obstinate Familiar. Nathan controls Chains of Mephistopheles. Alice gains 1 life, starting this loop. She doesn't have any way to win, so she wants to let it continue forever and draw the game. Is that allowed, or does she have to eventually skip a draw with Obstinate Familiar, ending the loop?

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Question #11

Alice controls Wildgrowth Walker and Amalia Benavides Aguirre. She gains a life to start the loop, and Nathan gives Wildgrowth Walker indestructible with Adamant Will. Nathan has an Otawara, Soaring City in hand. What happens?

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Wizards has ruled that "having a different card on top of the library" is a relevant enough difference to warrant saying that the loop ends as soon as Alice removes one card from the top of her library, and a new loop begins. Since milling a card counts as a "choice" rather than an "action", Alice has the ability to end each loop by milling the nonland card, and she must eventually do so. Another loop promptly begins with the next card down, etc. Once her library is empty, there are no more choices she can make and the game will be a draw unless Nathan decides to use his Otawara.

Question #12

Alice controls Altar of Dementia and two Lotus Petals. She can sacrifice the Petals, cast Animate Dead on Saprazzan Bailiff, then immediately sacrifice it to Altar of Dementia, getting back the Lotus Petals and Animate Dead to her hand. Nathan has 1 life, and his deck contains Triskelion and 4 Gaea's Blessings. What are Alice's options?This actually comes up in premodern.

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Question #13

Alice controls Altar of Dementia and three Lotus Petals. She can sacrifice the Petals, cast Animate Dead on Saprazzan Bailiff, then immediately sacrifice it to Altar of Dementia, getting back the Lotus Petals and Animate Dead to her hand. Nathan has 1 life, and his deck contains Triskelion and 4 Gaea's Blessings. What are Alice's options?

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Question #14

Alice and Nathan are deep in the middle of a game. Alice Doom Blade's Nathan's Kozilek, Butcher of Truth, then activates Elixir of Immortality and passes the turn. Several turns later, Alice notices that they've arrived back at the same position. What happens?

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If all the cards in Alice's and Nathan's hands are the same, and Alice lost 5 life in the mean time, and all the cards in the graveyard are the same, then this is a non-deterministic loop. Alice must make a different play.

Question #15

Alice was on the play, and many turns into the game, she restarts it with Karn Liberated, with no cards exiled underneath it. While starting the new game, she happens to draw the same 7 opening hand that she had in the first game. Nathan also draws the same opening hand that he had in the original game. Is this a non-determinstic loop?

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Question #16

Alice controls Life and Limb and a Charismatic Conqueror that's had "Vampire" replaced with "Saproling" by Artificial Evolution. Nathan has enchanted Alice with Curse of the Restless Dead. If Nathan plays a creature, is he eventually required to tap a Zombie in order to halt the loop?

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No. Anything phrased as "a player may do X, otherwise do Y" counts as an action, not a choice, so Nathan is never required to tap a creature if he doens't want to. He can let the game be a draw.

Question #17

Alice uses several Xathrid Necromancers and Artificial Evolutions along with a few other cards to emulate the Waterfall Model of computation, creating a board state that implements Adam Yedidia's 7918 state Turing machine, with behavior independent of the axioms of Zermelo-Fraenkel set theory with the axiom of choice. What should the judge do in this situation?

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