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

Question

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.

Answer 1

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

719.3. 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.

Answer 2

I would like to make the case for "Nothing happens. Both creatures will die as 1/1 or 2/2." in this special case. I think this would happen due to how the stack works.

Let's say Alice decides to start the pumping process. She taps both Leaden Myrs to get two black Mana, spends one to pump her Shade and the other to activate the untap ability of one of her Galvanizers. Bob does the same in response. Now we have two 2/2 Shades posed to fight each other and one tapped Galvanizer on both sides.

After Galvanizer's ability resolves, Alice receives priority. She taps a Myr for a third black mana and then uses it to activate the untap ability of her second Galvanizer. Bob decides to seize the opportunity and activates his second Galvanizer's ability in response. It goes to the top of the stack and since Alice has nothing to respond herself (aside from maybe giving the Shade one further +1/+1), it resolves first. Now Bob's Myrs untap and Alice's untap ability is still on the stack. Bob won't let that ability resolve until he has used the combo to +10/+10 his Shade.

Now Alice can try to pump her Shade as often as she wants, but Bob will always respond with +10/+10 for every +1/+1 she can muster. So, Bob informs her that he will respond this way every time and asks Alice how often she wants to pump her Shade. Whatever she says, her Shade will be weaker and thus die.

Conversely, if Alice passes priority without doing anything, and Bob starts to pump his Shade, Alice will be able to always respond with a +10/+10 for each of Bob's +1/+1. Then, Bob's Shade will die.

Knowing this, Alice will pass priority, as will Bob, without doing anything and both Shades die as 1/1.

Answer 3

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.

Answer 4

This situation used to be covered in a different way by the Comprehensive rules. According to this Mark Rosewater article, the following rule existed in 2002.

421.5. If the loop contains at least one optional action controlled by each player and these actions don’t depend on one another, the active player chooses a number. The nonactive player can either agree to that number or choose a higher number. Note that this rule applies even if the actions could exist in separate loops rather than in a single loop.

So this situation could be handled by Player A saying "I propose that we both pump the Nuntako Shades to 9000/9000". Player B either accepts that number, or proposes a higher number. (That higher number would be final.)

Now the loop "sequence" rules have been rewritten.

719.2a 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 nonrepetitive 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.

So the player with priority proposes the shortcut. "I propose that our shades are pumped to 9000/9000 and then you have priority." Note that they could propose that they have priority. (Perhaps to threaten a trick?)

Next Player B has a decision:

719.2b Each other player, in turn order starting after the player who suggested the shortcut, may either accept the proposed sequence, or shorten it by naming a place where he or she will make a game choice that’s different than what’s been proposed. (The player doesn’t need to specify at this time what the new choice will be.) This place becomes the new ending point of the proposed sequence.

So Player B can either say "Stop the loop when our Nuntakos reach 8000/8000" (and they must make a different decision that will break the loop) or "I accept that proposal, I get priority when our Nuntako's reach 9000/9000 and the loop ends."

Note that this situation contains 3 loops (or 4 depending on how you define it). Loop A: Player A pumps their shade an arbitrary number of times, Loop B: Player B pumps their shade an arbitrary number of times, and Loop C: priority is passed an arbitrary number of times.

719.2a states "This sequence may be a nonrepetitive series of choices, a loop that repeats a specified number of times, multiple loops, or nested loops, and may even cross multiple turns."

So theoretically player A could propose a shortcut like "I will hold priority while pumping my creature by 10, pass priority and you pump yours by 10, until both creatures are 90/90" for whatever reason.

IN SHORT: The active player proposes a shortcut which defines the number of times loop(s) are repeated and the ending game state, the other player may then accept this shortcut, or shorten the loop(s) at some other arbitrary point and make a different game choice that doesn't result in the same loop(s).

Result: Both Nuntakos will die at X/X power/toughness where X is chosen by the active player, unless the non-active player can make a decision (a card or ability to play) and chooses to break the loop earlier.

Answer 5

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.

Answer 6

The game doesn't end in a draw

This is true in any case, and I haven't seen it mentioned in here before. Here's the rule for games ending because of a loop of actions:

104.4b. If a game (...) somehow enters a "loop" of mandatory actions, repeating a sequence of events with no way to stop, the game is a draw. Loops that contain an optional action don’t result in a draw.

Since nothing about this interaction is mandatory, there's no way this would end in a draw.

This situation isn't a fragmented loop

Note: The following rule's number used to be 716.3, which is widely referenced in other answers

719.3. 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 (...)

The rules don't give a specific definition for "game state", but the only possible interpretation without breaking the rules is that it includes all information required to reconstruct the game from scratch, should you attempt to do so. Static buffs would have to be part of the game state, just like counters or whether a creature is tapped or not, or even on the battlefield. A 1/1 is simply not the same as a 1/1 that has +10/+10 - if you disagree, imagine the same game state with a Elesh Norn, Grand Cenobite in play for only one of the players. Game state should not be confused with relative board presence.
Further, the IPG mentions "triggered abilities that affects the game state in non-visible ways", which precisely applies to static buffs and granted abilities such as Flying in the example of 719.3.

Due to the game state changing after each execution of the loop, 719.3 doesn't apply.

How this plays out (in a tournament scenario)

From what's stated in the question, it would simply result in two equally sized Nantuko Shades at any point that would kill each other.

Assuming the players wouldn't be satisfied with that, they would call a Judge. As I stated in a comment to M.Herzkamp's answer, it's not the Judge's job to come up with other possibilities to what could have been done (and in fact should refrain from doing so, or at least telling the players about it), but to handle the presented situation. Now, there's a number of ways in which this could be presented (and keep in mind that the Judge's responses are what I deem to be applicable, and that actual Judge calls may differ in result):

1. The active player is complaining that every time they activate their Nantuko Shade's ability, their opponent does the same. This has been going on for a while.
   This sounds like a perfect example of Slow Play (for both players), and might result in a Warning, or at least a remark about it.
2. The active player has proposed a shortcut of pumping his Nantuko Shade a set number of times with the combo described in the question, and the opponent agreed, however adding that each time the active player would activate it, they would activate their own Nantuko Shade in response.
   All the judge can reasonably do here is confirm that everything's done by the rules, and that the shortcut proposed is legal, even knowing that after it's handled, situation 1 would likely occur, unless a player comes up with one of the different ways to play this scenario.

In other words, this might result in some Slow Play warnings, however if no player figures out a way to break the cycle, will likely result in equally proportioned Nantuko Shades that will kill each other.

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I would also like to highlight something that the user Pow-Ian suggested this in the comments above:

If I were the judge called over, I would rule both [Nantuko 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.

This would be very harmful for the game in progress, and very much outside of the job description of a Judge. The comment suggests that you take control out of the player's hands by deciding how they will act (pumping the creatures to the same level) as opposed to judging what effects their actions have. Furthermore, you advance the game to the combat damage step by ruling that both creatures get destroyed, preventing both players from casting additional spells or activating abilities. Furthermore, you suggest to only do this if they don't have a means to break this non-mandatory loop, which allows for the interpretation of forcing them to cast a spell in their hand that they may cast or revealing the existance of such, even though the player never intended to do so. On top of that, suggesting to the players that "infinite" P/T exists is one of the less recommendable actions in this situation.

How this plays out in any non-tournament scenario

Without the problem/feature of Slow Play issues, and without the prohibited outside assistance, players are more likely to figure out a different solution, such as the one proposed by M.Herzkamp, and continue the game from that point. They might also just eventually put both Nantuko Shades in their graveyards, or agree on a draw, or yell at each other and never formally finish the game...

Answer 7

Short Answer: The active player proposes a number of times they go back and forth doing this, and the non-active player either accepts it or proposes a larger number. (This is a change from what I wrote previously; the "on-high" ruling on this has to be adjusted to the new shortcut rules.)

Either way, they're going to wind up balancing out 1-for-1, equal number of pumps unless one of them voluntarily does fewer than their opponent.

Current Comp Rules:

719.1b Occasionally the game gets into a state in which a set of actions could be repeated indefinitely (thus creating a “loop”). In that case, the shortcut rules can be used to determine how many times those actions are repeated without having to actually perform them, and how the loop is broken.

719.2. Taking a shortcut follows the following procedure.

719.2a 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. Example: A player controls a creature enchanted by Presence of Gond, which grants the creature the ability “{T}: Create a 1/1 green Elf Warrior creature token,” and another player controls Intruder Alarm, which reads, in part, “Whenever a creature enters the battlefield, untap all creatures.” When the player has priority, he or she may suggest “I’ll create a million tokens,” indicating the sequence of activating the creature’s ability, all players passing priority, letting the creature’s ability resolve and create a token (which causes Intruder Alarm’s ability to trigger), Intruder Alarm’s controller putting that triggered ability on the stack, all players passing priority, Intruder Alarm’s triggered ability resolving, all players passing priority until the player proposing the shortcut has priority, and repeating that sequence 999,999 more times, ending just after the last token-creating ability resolves.

719.2b Each other player, in turn order starting after the player who suggested the shortcut, may either accept the proposed sequence, or shorten it by naming a place where he or she will make a game choice that’s different than what’s been proposed. (The player doesn’t need to specify at this time what the new choice will be.) This place becomes the new ending point of the proposed sequence. Example: The active player draws a card during her draw step, then says, “Go.” The nonactive player is holding Into the Fray (an instant that says “Target creature attacks this turn if able”) and says, “I’d like to cast a spell during your beginning of combat step.” The current proposed shortcut is that all players pass priority at all opportunities during the turn until the nonactive player has priority during the beginning of combat step.

719.2c Once the last player has either accepted or shortened the shortcut proposal, the shortcut is taken. The game advances to the last proposed ending point, with all game choices contained in the shortcut proposal having been taken. If the shortcut was shortened from the original proposal, the player who now has priority must make a different game choice than what was originally proposed for that player.

719.3. 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.

Full Explanation:

Case 1) Player A(ctive) is reasonable and suggests that they pump 1 for 1, and proposes a finite number N, responding to each other in turn and then stopping at that number. Player B is also reasonable and accepts. The game moves forward after each creature gets pumped that many times.

Case 2) Player A as above, Player B says a different number M, smaller (he changes the sequence at that point, but his only option to change it is to not pump his own creature). Result: A will pump +N, B will pump +M. Not optimal for B in most cases, so this will almost never happen.

Case 3) Player A as above, Player B says that after that shortcut, he wants to pump another P times. A will of course respond to those, forming a new suggested shortcut, the end result will be (eliding shortcut negotiation) P+N pumps to both creatures. (If A chooses not to respond in kind, A will have a smaller pump, again, rarely happens.)

Case 4) Player A suggests a shortcut that has only themselves pumping, but B will not accept the shortcut, because they will interrupt after the first by pumping, geting us back into Case 1.

Case 5) Neither player understands or accepts the simple shortcut of even pumping, and so they try to go back and forth forever. Slow play warning and explanation of why they are stuck with Case 1.

So, short answer: Player A names a number. Player B accepts or names a bigger number, and they both get pumped that many times. If player B wants to pump less, they can stop A's shortcut early, but this will only happen if B has a rare trick.