Cranial Insertion: To Infinity and Back Again
By Thijs van Ommen on August 21st, 2005 · Filed in Cranial Insertion · Comments not available just now
To Infinity and Back Again
By Eli Shiffrin, Thijs van Ommen, and Jeff Vondruska
In today's installment of Cranial Insertion, we'll be taking a look at the rules governing infinity in Magic.
How much did you say?Q: I was playing an opponent with a strange combo deck. At one point, he had an infinite number of 1/1 Spirit tokens, as well as a Gemstone Array with an infinite number of charge counters to give him access to all the mana he wants. The turn before he is going to go for the win, I play Cut the Tethers. He wants to save his Spirits, but how many Spirits can he save, and how many charge counters from Gemstone Array would he have left? I argue that if he wants to save an infinite number of Spirits, he'd need at least infinite mana to do so, which would use up all his counters. But he responds that he could use three quarters of his mana to save one quarter of his Spirit tokens, and he'd still have an infinite number of both. Who's right?
A: Let's get right to the most important lesson in today's article: There's no such thing as "infinity" in Magic. Infinity isn't a number, so it's mathematically impossible treat it like it is and you can't do arithmetic on it like that. To find how out how the rules deal with situations like the one described above, keep reading.
The rules dealing with infinity fall under rule number 421 in the Comprehensive Rules. This is their mission statement:
So a set of actions which could be repeated forever is called a "loop." Several different types of loops and the ways to deal with them are described in this section of the rules. The first case covered is that of a loop controlled by a single player. All actions in the loop are either mandatory and happen automatically (many triggered abilities behave that way), or they rely on the decision of that player. Each time the loops get to the point where a decision has to be made, that player can choose to either stop the loop and go do something else instead, or to continue the loop one more time.
From the CompRules:
421. Handling "Infinite" Loops
421.1. Occasionally the game can get into a state in which a set of actions could be repeated forever. These rules (sometimes called the "infinity rules") govern how to break such loops.
In theory, the player might just choose to continue the loop each time, so that it would never end. But the rules don't allow that. When you control a loop, you have to get out of it at some point. More precisely, you have to choose a number and repeat the loop that many times, and then you have to end the loop. This allows you to make all the decisions you would otherwise be able to make, except for the decision to continue the loop indefinitely.
Look at them grow! But would theyQ: I'm using this combo where I use Nomads en-Kor to target a Daru Spiritualist or another Cleric for free, so that it gets +0/+2 each time. After that, I sacrifice it to Starlit Sanctum's ability to gain a lot of life. Is there a limit to the amount of life I'm allowed to gain this way?
grow if there was no one there to
look at them?
A: You're only limited by your ability to come up with large numbers. Like a googol. In this case, the loop consists of the optional action of activating the Nomads' ability, and the mandatory action of resolving the Spiritualist's trigger. (Of course, you can vary the order in which you do these things, but that won't make a difference to the outcome eventually, so the rules don't bother discussing these details.) You're completely free in your choice of a number to determine how often you go through the loop; just remember that "infinity" isn't a number.
Though there is no limit to your choice of a number, the act of choosing a number creates a limit to how often you'll go through the loop.
Q: Suppose I'm using the combo and choose to let it loop a billion times, to gain two billion and one (2,000,000,001) life. However, in response to the first trigger from the Spiritualist, my opponent plays a Shock on it. What happens now?
A: A loop can always be stopped when one of the players decides to intervene and do something that wasn't part of the set of actions that made up the loop. The interruption knocks the loop out of orbit, and the game resumes normally with the Spiritualist's ability on the stack and your opponent's Shock on top of it. However, there's nothing to stop you from initiating the loop again. Your Spiritualist won't have any trouble surviving a little Shock that way.
Even arbitrarily large numbersQ: I use the Daru Spiritualist loop to gain an arbitrary amount of life. I choose a number large enough to set my life total to one million. On the other side of the board, my opponent controls an Auriok Bladewarden enchanted with Rancor and Serra's Embrace, making it 5/3 with trample, flying and vigilance. He also has three Seeker of Skybreak.
sometimes have to watch out for
He attacks with the Bladewarden. After I declare no blockers, before combat damage is put on the stack, he activates the Bladewarden's ability targeting itself. In response, he plays Gerrard's Command on it. The Command resolves, untapping the Bladewarden and making it 8/6. Then the Bladewarden's own ability gives it +X/+X where X is its power, putting it at 16/14. Because the Bladewarden is still untapped, he repeats the trick and makes it 32/30. Using each of the three Seekers, he can repeat it another three times, doubling the Bladewarden's power each time (256/254). Then he plays Vitalize, and his creatures untap. Four more activations later, the Bladewarden has grown to 4096/4094, and I'm starting to worry. Another Vitalize makes it 65536/65534. A third Vitalize shows up, and the Bladewarden ends up at 1,048,576/1,048,574. That wasn't an unbounded combo, and the Bladewarden won't get any larger. Because my own combo was unbounded, can't I go back and pick a larger number for my life total? Or did I really just lose?
A: Wow, that's big.[/ambiguity] It looks like you lost a game because you chose a million when you could have chosen anything you wanted. Maybe a googol wouldn't have been such a bad idea after all....
Another type of loop that may occur is one that involves no optional actions from any player. Once the game gets in such a loop, a simple choice isn't enough to get out of it. Quite often, there won't be any way at all to break the loop. The rules state that the game ends in a draw if this occurs. If you would otherwise be able to win the game, you have to watch out for such loops, but if you're on the losing hand, you may sometimes be able to use this rule to your advantage and still pull off a draw.
Q: The only creature in play is Faceless Butcher. It has removed another Butcher from the game. Then my opponent plays a third Butcher. Does the game end in a draw?
A: When the third Butcher comes into play, its ability triggers and your opponent has to choose a target creature for it (other than the third Butcher itself). There's only one other creature available, so your opponent doesn't have any choice here: it's a mandatory action. Next, the first Butcher will be removed from the game, and its leaves-play ability triggers. When this ability resolves, it will return to play the second Butcher that had been removed from the game until now. No player has any choice in this matter, either. Now we're back at square one: one Butcher is sitting in play with another Butcher in its belly, while a third Butcher is just coming into play with its comes-into-play ability triggering. This sequence of events can repeat forever, so we're clearly dealing with a loop. Because there are no optional actions involved, the game ends in a draw as the three Butchers play musical chairs for all eternity.
Aside: If another creature had been in play, there would be a choice of which creature to target in the loop, so the loop wouldn't be completely mandatory and wouldn't draw the game. Without the "other than Faceless Butcher" part, a single Faceless Butcher coming into play while no other creatures were around would have been enough to immediatelly draw the game.
Creature - Rules Nightmare DragonQ: Could you explain how the Worldgorger Dragon + Animate Dead combo works?
A: The pull off the combo, you need the Dragon in your graveyard when you play Animate Dead. In the Oracle, Animate Dead has evolved since the days it used to be an "Enchant Dead Creature", and its first ability is now worded like this: "When Animate Dead comes into play, if it’s in play, it becomes an Aura with enchant creature. Put target creature card from a graveyard into play under your control and attach Animate Dead to it." This triggered ability will make you choose a target creature card from a graveyard. Note that if the Dragon is the only creature in any graveyard, this is a mandatory action that you don't have any choice in. When the ability resolves, it causes the Dragon to come into play (as well as doing some other nifty things like turning itself into an Aura). This in turn triggers the Dragon's comes-into-play ability, which will remove all your other stuff from the game, including your land and the enchantment that just pulled the Dragon from the graveyard. Animate Dead doesn't like that and its leaves-play ability will go on the stack, and kill the Dragon again. Finally (yes, we're almost there!), the Dragon has a leaves-play ability of its own that puts all the permanents that were removed back into play. This places the game where it was at the beginning of the loop, with a Dragon in the yard and an Animate Dead coming into play. However, one tiny detail is different: all the permanents that were removed from the game tapped will be returned untapped. This allows you to tap all your lands for mana each time, filling up your mana pool to any size you want.
Of course, all that mana will do you little good if the game is about to draw. If there is another creature card in a graveyard for Animate Dead to target, you'll be able to jump out of the loop once you have enough mana to suit your needs. If no other targets are available, you're in a mandatory loop that will draw the game unless you find another way to intervene. Because there's always some kind of triggered ability sitting on the stack while the loop is spinning, you're going to want an instant or activated ability for this job, and preferably one that wins you the game. Stroke of Genius was often used to this purpose.
Note that Worldgorger Dragon is banned in Legacy due to the broken power of this combo.
So far, we've looked at loops where one player or no players had any optional actions in the loop. What if several players all have optional actions? Such loops rely on all involved players to want to continue the loop. If even one of them decides that they don't want to continue, the loop comes to a halt.
So how does this work in practice? The active player gets to choose a number of times he wants to execute the loop. (If you're in a multiplayer game and the active player isn't involved in the loop, go around the players in turn order, starting with the active player. The first player you run into who is involved in the loop will be the one to pick the number.) Now, in turn order, the other players may either decide to fully cooperate with the first player until that point, or they may decide to stop cooperating at some earlier point. Obviously, they have to pick a point where they got to take an optional action. This way, all players involved in the loop either go with the loop as it stands, or decrease the length of the loop by some amount. Finally, the loop gets executed for that length. Let's have a look at some examples:
Sorry Mr. Butcher, I already made theQ: In a two player game, I control a Grizzly Bears and a Faceless Butcher that has eaten my opponent's Butcher. My opponent also controls Angelic Chorus. Then he plays his second Butcher, and chooses for it to eat my Butcher. How do we determine how much life he gains from the Chorus?
A: This is a loop that consists of optional actions for both players, because either player could decide to have a Butcher remove your Bear instead of another Butcher. Your opponent is the active player, so he gets to pick a number. He'll probably pick something really large, because he's gaining life while you gain nothing. (This is presuming your opponent's only goal is to gain as much life as possible; otherwise, there might be a better play for him.) You will get the choice to break the loop at some earlier point. Let's see what your earliest opportunity is. Your opponent's Butcher comes into play and removes yours. Then, his other Butcher (that was previously removed by yours) comes back and removes the newly played Butcher (which is the only one in play at this point). Now your Butcher comes back, and you get to choose a target for its ability; picking the Bears now will break the loop. If you play it this way, two creatures will have come into play for your opponent, gaining him 6 life from the Chorus's triggered ability. After all this, both you and your opponent will have a Butcher in play. Yours has removed your Bears, while your opponent's has removed his other Butcher.
If you had been the active player and your opponent had somehow played his Butcher as an instant, the outcome would have been the same. You could have chosen to only continue the loop as far as described above, and your opponent could either agree or make it run even shorter.
Another example, where it does matter who the active player is, comes straight from the rulebook:
Obviously, it wouldn't do any good for the active player to try again to enter the loop: the outcome would be the same, because the opponent has final say in this situation. Trying to repeatedly enter the loop would be considered stalling.
From the CompRules:
Example: In a two-player game, one player controls a creature with the ability ": [This creature] gains flying," and another player controls a permanent with the ability ": Target creature loses flying." The "infinity rule" ensures that regardless of which player initiated the gain/lose flying ability, the nonactive player will always have the final choice and therefore be able to determine whether the creature has flying. (Note that this assumes that the first player attempted to give the creature flying at least once.)
We've covered all possible loops now. Something else that might happen hasn't been covered yet, though: what if at some point in the game, several loops are available?
Q: Both me and my opponent have access to arbitrarily large amounts of mana. My opponent attacks me with Flailing Manticore. How much damage am I going to take?
A: There are two independent loops going on here: you can use whatever trick it is you're using to get , then use that mana to play the Manticore's -1/-1 ability, while your opponent can do the same for the +1/+1 ability. In such a situation, the active player must choose first how often he wants to go through his loop. Then the other player decides, and then the loops are executed. The exact order in which the abilities go on the stack is irrelevant in this case, as you can simply choose a number at least three larger than your opponent, and the Manticore will end up at 0/0. It will go to the graveyard, and you won't take any damage from it.
-Thijs van Ommen, The Netherlands
By Thijs van Ommen on August 21st, 2005 · Filed in Cranial Insertion · Comments not available just now
About Thijs van Ommen
Even though I'm not a judge, my interest in the rules of the game is the main reason for me to play. You'll usually find me answering questions in the rulings forum. I'm mostly a casual player: the only tournaments I visit are prereleases.