Typos; in the context , after three iterations

Let’s look at the full sentence, not just the first half. “In these cases, the rules above may be applied, with the player making a different choice rather than ceasing to take an action.” First, you’re right there is ambiguity in “the rules above”, but it is directly below the section regarding non-deterministic loops, and the second half of the sentence heavily points to that specific section and its rules being the ones referenced. In the non-deterministic section directly above, it reads: “ 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. This happens most often in loops that involve shuffling a library.” So in a non-deterministic loop that results in a repeatedly unchanged game state, the person executing the loop must cease doing it, as it is not meaningfully moving the game forward; they must stop whatever loop they are executing. This is directly referenced in the second half of the sentence “In these cases, the rules above may be applied, with the player making a different choice rather than ceasing to take an action.” ; it is saying that in a choice based loop, instead of the player executing the loop being forced to cease doing so, they must instead make a different choice (this is on the context of the player who is executing the loop making a self-recursive choice, one which results in the same game state over and over). This indicates that it is directly tied to the non-deterministic loop paragraph directly above it, and therefore the “the rules above” portion of the sentence is indicating those specific rules as well.

You could try to swing the whole “different choice” bit as forcing the active player to make a different choice, but it explicitly states that the executing player is the one responsible for ending the stalemate in the referenced paragraph, meaning that this should hold true for choice based loops as well.

Your point about the iterations doesn’t seem to track either. Even if the executing player chose a certain number of iterations, say 3, and the active player said he would say no as many times as it took, say 10 million, then then the only “priority” the executing player gets is to decide what to do after three choices. The active player, in this hypothetical, has stated his intended responses for more rounds of the loop than the executing player, meaning the executing player has an earlier chance to decide what he wants to do next (play an instant, continue the loop, stop the loop, etc.). It doesn’t mean that the stalemate is ruled in favor of the executing player or that the active player must end their turn.

That’s true, if you’re advancing the board state with every round of the loop, then this would not apply and your logic would be accurate…but why not just take over the game in the first place? If krenko + intruder are already on the board, then you can just make infinite goblins. I suppose you could wait till the turn before yours to do it, but the opponents will KNOW that that’s your plan already, it’s not like waiting is doing you any favors. Similarly with your wizard method, if you have a way to untap/tap them already, why not just drain the board of permanents on your turn? Letting it go to the opponents untap step gives them free mana to perform instant speed interaction (since the earliest you are given priority to tap obeka is after their permanents untap).

You could argue that waiting puts them in a position where they have to end their turn early, but I don’t think it necessarily does. If you are in a position to dominate the game already, then the choice is really “end your turn or I do something that I am already capable of doing on my turn”. If I was a player in that position, I’d just refuse to end my turn. So either you continue the loop indefinitely and the game draws, or you eventually stop the loop after repeating if however many times you please, and I get to play the rest of my turn.

My point being, that this isn’t necessarily an obeka driven rules tweak, it seems more like a way to needlessly draw things out or toy with your opponents; either your loop doesn’t affect the board, in which case you can’t force a premature turn end, or it can affect the board, and you already have the tools to go infinite and are just choosing not to (which in the best case is just mildly annoying for the opponent, and at worst, gives them the free mana to actually try and do something about it).

A bit late to the party, but I may have an answer.

Since tournament rules supersede the comprehensive ones, we’ll use the rulings laid out there. If we take a look at MTR 4.4, the section that covers loops, we find this:

“ 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. This happens most often in loops that involve shuffling a library.

Some loops are sustained by choices rather than actions. In these cases, the rules above may be applied, with the player making a different choice rather than ceasing to take an action. The game moves to the point where the player makes that choice. If the choice involves hidden information, a judge may be needed to determine whether any choice is available that will not continue the loop.”

This loop should qualify as one dependent on choices, as it involves a series of alternating choices (you choose to tap obeka, the active player must make a choice on whether to end the turn). Therefore, it falls under the same ruling as non-deterministic loops: “ 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.“ Since you are the player executing the loop, you are responsible for stopping once it continues to reach the same game state over and over. Therefore you cannot force opponents to end their turn in this manner.