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A. The Problem of Indeterminate Loops.
The best example of such a loop occurs (and comes up frequently on Magic forums) in the context of the much-maligned “Four Horseman” deck. You can see a copy of this deck performing well in Legacy recently if you look up Jeff Liu’s deck, which came in 17th place at the September 16, 2012 Star City Games Legacy Open. The deck functions by resolving Basalt Monolith and Mesmeric Orb. Since you can tap the Monolith for 3 mana, and spend that mana to untap the Monolith again, you can trigger the Orb as many times as you like.
The deck’s goal is to mill a Blasting Station, at least three Narcomeboas, Sharuum the Hegemon, and a Dread Return. Once it does that, it puts the Narcomebias into play, sacrifices them to Dread Return to return Sharuum, who brings back the Blasting Station. This leaves you with a bunch of Narcomebias in the yard. No problem; just keep tapping your Monolith and keep milling yourself until you hit an Emrakul, the Aeons Torn. When she hits the yard, you will shuffle those lovely Narcobmebias back into your library, where you can mill them back into play and start feeding them to the Blasting Station to ping your opponent to death.
There’s a random element to all of these moving parts, however: the order of cards in your shuffled library. Consider what happens if the Four Horseman player mills an Emrakul before the other half-dozen cards it needs to be in the yard. Emrakul’s shuffle trigger will go on the stack next time the player has priority. The player can keep milling in response, certainly, but the stack will never be empty until Emrakul’s trigger finally resolves. That’s a problem, because Dread Return in a Sorcery, and you cannot cast Sorceries until the stack is empty. The upshot is that player shuffles the yard back into the library and try again from scratch if Emrakul arrives early.
In theory, the player could keep doing this as much as they like, just as someone could keep rolling a twenty-sided dice until they hit a 1. But, since the outcome of each roll or shuffle is based on chance, there’s no way to pick a specific number of iterations around the loop that will be required in order to accomplish the desired graveyard order. Worse still, there’s no way to know, in advance, exactly what will be in the graveyard or in the library when the win condition finally comes up.
B. Winning Eventually Is Not Enough For a Shortcut.
Fans of the Four Horseman will be quick to point out that, if the deck was given infinite time, then it eventually would reach the necessary conditions to win. Put more precisely: for any arbitrarily small probability X, you could calculate a number of iterations around the Four Horseman loop that would bring the probability of failure after that many iterations below X. Since the deck will eventually win, given enough time, the player should be allowed to propose a shortcut without specifying the particular finite number of iterations or the particular board states passed through to get there, or so the argument often goes.
This suggestion fails for two reasons. First, the shortcut rules do not allow you to shortcut where you can prove there is a vanishingly small chance of getting the result you want. The mathematical concept of a “limit” is not contained in the Rules. Since you cannot specify a number of iterations that will precisely get you to a specific board state, you cannot use the shortcut Rules.
The second flaw with this argument is that it ignores the second part of the shortcut rule: the opponent’s option to shorten it. Perhaps, by way of illustration, the opponent wishes to stop the combo when the last two cards in the pilot’s library are the two Emrakuls and then attempt to exile them to deck the opponent. It is impossible for the players to know how many iterations will occur before this state is reached. It is also impossible to know whether this state will happen before or after the Four Horseman pilot hits his win condition.
This is why it is so critical that a shortcut involve both a finite, specified number of iterations and a definite, predictable board state during and after the loop. Without both, you cannot use the shortcut rules. Instead, you just have to go through the actions that would make up your loop, action after action, just like you were playing on Magic: The Gathering Online. Except that, if you do this in a tournament setting, you might get warned by a judge for Slow Play and told to stop trying to win with your combo. We will discuss that in more detail below.
..and this section explains why you can't just do it without a shortcut, either:
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Slow Play
To understand Slow Play, we must leave the realm of the Comprehensive Rules and enter the domain of the Infraction Procedure Guide, or IPG. The IPG does not apply to all Magic tournaments, only those “held at a Competitive or Professional Rules Enforcement Level.” I.P.G. at Introduction (July 22, 2016). At your kitchen table, or at Regular R.E.L., you may very well be allowed to execute your Indeterminate Loop to your heart’s content. Remember, check with your local judge beforehand!
Slow Play is a tournament error that results in a Warning. I.P.G. § 3 and 3.3. When players think of Slow Play, the usual thing that springs to mind is someone taking longer than normal to move the game along. Slow Play does indeed occur when “[a] player takes longer than is reasonably necessary to complete game actions.” I.P.G. § 3.3. Tucked away behind this definition, however, is a subsidiary definition that appears to be included here mostly because it does not really fit anywhere else. The Guide says: “It is also slow play if a player continues to execute a loop without being able to provide an exact number of iterations and the expected resulting game state.” Id.
This short statement is packed with meaning. It applies when someone is trying to “execute” a loop. The term “execute” is not defined by either the Comprehensive Rules or the I.P.G., but it appears to be intended to include both shortcutting a loop or carrying out the actions involved in a loop. The Slow Play definition also specifically calls out the type of loop we have defined as an Indeterminate Loop above; one for which the player cannot provide both a specific number of iterations and a specific resulting game state.
This all means that, in practice, you cannot execute - carry out - the actions of your Indeterminate Loop. But, as we already explored above, you cannot propose a shortcut of such a loop, either. The result is that you simply cannot win with an Indeterminate Loop! As it applies to the Four Horseman in particular, Head Judge Josh Stansfield had this to say about Mr. Liu’s deck at the Star City Open:
"During Round 3 of the tournament, I was made aware of a Four Horsemen player on the feature match table. I went over to watch the match, knowing that I was likely to see a problematic line of play according to the IPG. When the player started to flip cards from the Basalt Monolith/Mesmeric Orb combination, he quickly ran into Emrakul, and was forced to shuffle his library. After doing this again, he was left in an identical game state: An empty graveyard and no other change to the game state. By performing the same loop of actions without changing the game, he was violating the shortcut policy outlined in the Magic Tournament Rules and the Slow Play policy in the Infraction Procedure Guide.
Put another way: Mr. Liu would violate the shortcut rule if he proposed a shortcut, but he would violate the Slow Play rule if he did not, and as a result, he is barred from trying to win.
This is little unusual. It is not often in Magic that a player is told they may not take an otherwise legal game action, even though the action is clearly designed to win. This strange rules interaction makes the option of bringing Four Horseman to a tournament impossible or at least wildly unwise. That strikes many people as unfair. People also rankle, understandably, at the suggestion that fast-paced play with the goal of winning can be defined as Slow Play, the same tournament error that applies to someone who is simply wasting time.
There is a logic behind this rule, however. The shortcut rules are already complicated, and it is not at all clear whether any change to accommodate Indeterminate Loops would be good for the game, or even possible. Once shortcuts are off the table, infinite loops present a massive challenge the Magic Tournament Rules. Sure, your deck may be able to win given an infinite amount of time. Magic Tournaments do not occur over an infinite amount of time (even if it seems like they do on some occasions).
Under the Tournament Rules, tournament matches are given a time limit, which must be at least forty minutes. Magic Tournament Rules at Appendix B (July 22, 2016). Once the time for a match has expired, “the player whose turn it is finishes his or her turn and five additional turns are played in total” at which point the game ends in a draw. Id. § 2.5. There is nothing in the Tournament Rules allowing a judge to stop a player from continuing to act but not actually ending his or her turn. A player executing an infinite loop could simply keep doing so and the tournament would grind to a halt. That situation is not good for anyone involved.
The Slow Play rules give judges a way to avoid this scenario, to the benefit of all players.
