What happens if both players have the ability to pump their creature an unlimited number of times?

Say that both players each had 2 Leaden Myr, 2 Myr Galvanizer, and a Nantuko Shade. (Or any other way to get unlimited mana, and a Nantuko Shade).

Player 1 attacks with his Nantuko Shade, and player 2 blocks with his Nantuko Shade. Before damage is assigned, each has chances to pump up their Nantuko Shade as much as they want. They can't just declare them to be "infinite," but each can always one-up the other player. What happens?

It seems there would be a loop of events, but would one player eventually be forced to break the loop as per rule 714.3? Is it considered the same game state after each player pumps their creature a bunch as it was before?

This was discussed at length on the Draw3Cards Magic Q&A site (which is no longer available), but no conclusion was reached. Some felt that the game would simply be a draw, others felt that the active player would be forced to make a different decision to break the loop. Others felt that you would just have to call a judge and see what he decides.

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This is a fragmented loop. The active player(who's turn it is) would be forced to make a decision that stops the loop.

716.3. Sometimes a loop can be fragmented, meaning that each player involved in the loop performs an independent action that results in the same game state being reached multiple times. If that happens, the active player (or, if the active player is not involved in the loop, the first player in turn order who is involved) must then make a different game choice so the loop does not continue.

Example: In a two-player game, the active player controls a creature with the ability “{0}: [This creature] gains flying,” the nonactive player controls a permanent with the ability “{0}: Target creature loses flying,” and nothing in the game cares how many times an ability has been activated. Say the active player activates his creature’s ability, it resolves, then the nonactive player activates her permanent’s ability targeting that creature, and it resolves. This returns the game to a game state it was at before. The active player must make a different game choice (in other words, anything other than activating that creature’s ability again). The creature doesn’t have flying. Note that the nonactive player could have prevented the fragmented loop simply by not activating her permanent’s ability, in which case the creature would have had flying. The nonactive player always has the final choice and is therefore able to determine whether the creature has flying.

In essence- the attacking player is screwed.

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I'm not sure this is actually applicable here - specifically, the same game state is not being reached (as the power/toughness of the relevant creatures has changed). It's not clear to me that the rules actually handle this situation cleanly, though I presume the resolution would look something like this. – Steven Stadnicki Jan 29 '14 at 1:36
@JoeW The problem is that while 'Game State' doesn't actually have a formal definition within the comprehensive rules (!), it surely must include things like the power/toughness of creatures. For instance, imagine a card that read 'creatures with power greater than 100 have Trample'. This card wants to know exactly what the P/T of every creature in play is, and so pumping a creature must yield a distinct game state. – Steven Stadnicki Jan 29 '14 at 2:23
I'm not saying that 'fragmented loop' doesn't define the concept; I'm saying that the rule specifically speaks to 'the same game state being reached multiple times' and having a different P/T on a creature than previously seems clearly to be a different game state. Their example even calls this out, where the result after a loop is explicitly the same (nothing about the game is different, other than 'an ability has been activated'). – Steven Stadnicki Jan 29 '14 at 3:01
If I were the judge called over, I would rule both shades to be destroyed. One end to a loop like this is that there is one infinity/infinity creature blocking another. Unless either player has some trick to get one of the shades out of combat, destroy the other, or do something else that would affect the loops infinite outcome, then they both should be destroyed. – Pow-Ian Jan 29 '14 at 12:29
I think the cited rule does give a subtle hint as to what constitutes game state: and nothing in the game cares how many times an ability has been activated, so as long as nothing in the game currently cares about how large a creature is, the rule should apply here. – Hackworth Jan 29 '14 at 14:59

First things first, this is a fragmented loop as defined by 716.3, the definition of pertinent game-state is left up to the discretion of the players or the judge if involved. There is plenty of precedence that repeated usage of abilities that make a minor adjustment to the game state are considered loops. Since we have a loop we by extension have a fragmented loop due to having multiple players.

Unfortunately no one is talking about the shortcut employed by the players, which is very important to how the problem gets resolved.

In these instances a shortcut is not allowed unless agreed between players or a few actions have been taken to establish how the loop will function. How the loop begins drastically changes how the overall game will be impacted.

Assuming there are no other pertinent abilities available, it would begin with the active player having the option to activate an ability on the declare blockers step.

If they choose to begin creating mana, the non-active player can bury their loop creating a non-fragmented loop, allowing "infinite pump", similarly every time the active player tried to pump they could repeat that action. An example shortcut is "every time you pump I pump 100 times", since the active player is required to break the loop, this would end with their shade dead.

If they choose to pass, the non-active player would be given the chance. The reverse of the first example would happen. Note that in this case the active player has to break the loop, however since they got to pump before the loop started, this isn't a problem. The non-active player gets an extra pump, but that doesn't matter when the active player already got lots of pumps.

If the non-active player also passes then the two 1/1's kill each other.

Thus unless I am missing something, it is a game of chicken and thus will result in two 1/1's killing each other.

EDIT:

There is one other possibility that I didn't consider. If players aren't playing perfectly (as I described here) then the judge would walk the players through moving the game forward, forcing a "number of attempts" like in 716.3. Unfortunately without a lot more detail, including knowing how the players react to this walk through, it is impossible to tell ahead of time how that will be resolved.

I have heard of something revolving around choosing numbers with restrictions but don't know offhand what it was.

However this feels a bit contrived as tournament players being nice would be odd, since the benefits of not waiting are obvious at that level of play. Similarly at kitchen table I would expect players to just let both die as a compromise.

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Any explanation for the downvote? – Guvante Feb 14 '14 at 17:56
I din't downvote, but here is a possible reason someone else did. This isn't a fragmented loop; the game state changes each time the Nantuko Shade is pumped. – Drunk Cynic Dec 11 '15 at 14:52
@DrunkCynic: You can disagree if you like but there is no meaningful way for a player with an iteration on the stack to ever pump their creature bigger than the other, since their actions are futile looking holistically it would be considered slow play to keep trying. I will note what happens with an empty stack. – Guvante Dec 11 '15 at 19:01
Counter: Every time you pump I react by pumping. – Joshua Feb 4 at 18:19

Rule 716.3 does not apply because there is not a point after any group of independent actions, or recognized shortcut, where the game state is the same as a previous game state. Every time the exercise is preformed, the Nantuko Shade power and toughness are increased by +1/+1 or black mana has been added to a players mana pool.

From that, each players could define a shortcut where they pump their Nantuko Shade at least once more than his or her opponent.

Failing the existence of an card or effect, external to these five creatures in play, that could be used to remove or disable one of them, the actions can continue unabated until one player freely decides to not pump his or her Nantuko Shade.

The further contention arises from the result of this chain of events on tournament play. Since game state changes, and each player has an interest in winning the conflict, it would be hard to call this slow play. Since it happens in the course of combat, the game won't end by going to turns. In the end, one player will have to agree to pump his Nantuko Shade less than his opponent, on the assumption that they can win the game through other means still in their deck, and that is preferential to having the match end in a draw.

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Look at the definition of slow play, it includes "Players must maintain a pace to allow the match to be finished in the announced time limit." Attempting to one up forever is the definition of not allowing the match to finish in the announced time limit. You are thinking of the quote "It is also slow play to..." (emphasis mine) which references loops where you don't know how long it will take. – Guvante Dec 11 '15 at 18:59
@Guvante - Thus the dilemma, and my conclusion regarding a player's decision to not pump further. The pace is constant, each player is just responding to the actions of the other. – Drunk Cynic Dec 11 '15 at 19:15