Can I mill an opponent who has Emrakul, the Aeons Torn by comboing until opponent's deck is stacked in an exact way?

Question

Let's say I'm running a mill deck. I have some kind of infinite mill combo ready and available (e.g. Semblance Anvil imprinting a creature, Myr Retriever and Grinding Station - this lets me sacrifice Myr Retriever to Grinding Station, retrieve another Myr Retriever, mill opponent for 3 cards, and cast a new Myr Retriever for free). However my opponent has two copies of Emrakul, the Aeons Torn in his deck. Since Emrakul shuffles back in to the deck each time it's put into the graveyard, this means I can't actually mill him out.

However, through repeated use of the mill combo I can in principle 1) figure out every card in his deck, and then 2) mill him until the last three cards in his deck are Emrakul, Emrakul, and [irrelevant card] (I assume here the number of cards in opponent's deck before I start the mill combo is divisible by three). This means opponent must hard cast Emrakul to win, and I already know (e.g. via Thoughtseize) that he doesn't have the resources to do this. So I win anyway by milling in three turns.

This kill will take a long time to execute, for obvious reasons, because each time I mill an Emrakul it gets shuffled back into opponent's deck. I'll need the deck to be stacked in exactly such a way that the two Emrakuls + an irrelevant card are at the bottom of the deck. This will happen eventually, just probably not for a very long time.

Question: can I actually execute this kill in paper, or will standoff rules kick in first?

Answer 1

You are not allowed to execute this entire combo, either using a shortcut or playing it out explicitly.

You cannot execute this combo with a shortcut because of the way shortcuts are defined in rule 720.2a of the Taking Shortcuts rules section:

At any point in the game, the player with priority may suggest a shortcut by describing a sequence of game choices, for all players, that may be legally taken based on the current game state and the predictable results of the sequence of choices. This sequence may be a non-repetitive series of choices, a loop that repeats a specified number of times, multiple loops, or nested loops, and may even cross multiple turns. It can't include conditional actions, where the outcome of a game event determines the next action a player takes. The ending point of this sequence must be a place where a player has priority, though it need not be the player proposing the shortcut.

In the combo you describe, you determine whether to continue or stop based on which cards, and how many, are still in the deck. That in turn depends on when exactly the Emrakuls got milled and their abilities triggered, which means that your actions would fundamentally depend on those game events, making this an invalid shortcut. You can see a ruling here about a different combo that also involves an indeterminate amount of shuffling.

You also cannot execute this combo without using a shortcut. A fundamentally identical combo exists in the deck Four Horsemen, which involves milling its own library including Emrakul in order to eventually end up with a particular sequence of cards in the graveyard and the library. Previous rulings have established that this combo is slow play and it should not be played in tournaments. The basic reason for this is that the combo can take unbounded time to complete, and every time you shuffle Emrakul in you are starting all over without making any meaningful progress.

Answer 2

This falls afoul of the Slow Play rules. After the second reshuffle, you have completed a loop of actions that resulted in no change to the game state, at which point you must choose to do something different. See here for more detail on how this rule works.

Answer 3

There is a way to do this but it requires more piece to the combo.

As you are basically explaining a mix between KCI post-ban and a heartless summoning deck that already existed in the past you can do this with the following if you want.

You may want to use Heartless Summoning instead of [Grinding Station] but using your example just add:

1 - Shimmer Myr
1 - Relic of Progenitus/Tormod's Crypt/Ravenous Trap

Shimmer Myr will give your artifacts flash, so you can flash in your Myr Retrievers and leave the Emrakul shuffle triggers on the stack, when you've resolved everything to mill your to the last card you will then need to exile their graveyard with one of the 3 cards mentioned and let the triggers resolve, the library would be empty so they would "shuffle" the empty library and you could then pass turn for the win.

Using Altar of the Brood might be an idea as well to speed up the mill clock.