My opponent has 0 cards in hand, no permanents in play, all lands tapped. No action possible from their side (for the sake of the example).
I have a Felidar Guardian and cast Restoration Angel, it resolves. RA trigger resolves targeting FG, its trigger resolves targeting RA. This generates the possibility for an infinite loop, can I force a draw with it?
In case this example results in a 'no', is it possible to enter an infinite loop and force a draw in MTG? I strongly dislike the idea that could do such a thing (as it's very anti-magic), but I'm curious to know to be prepared for it happening on the other side of the table, should the occasion arise.
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No, the loop involving Felidar Guardian and Restoration Angel, as you described, won't necessarily lead to a draw because the loop contains optional actions ("you may exile...") (C.R. 603.5, 104.4b). Moreover, carrying out the actions you mentioned manually is generally useless, since it generally leads to the same relevant game state as though the loop weren't taken at all.
In general, the only time a loop results in a draw is if it contains only mandatory actions (C.R. 720.4; see also C.R. 104.4b).
EDIT (Mar. 30, 2019): One rule was renumbered with Dominaria. Correctness edit.
No, for several reasons. Both creatures' triggers are a "may" meaning you have a choice to not use the effect and thus stoppong the loop with objects involved in it. Also, it is very unlikely, that you have no other permanents around to target with the Guardian's trigger, since your lands are viable targets, and thus another choice about an involved object can end the loop.
Yes, there are mandatory infinite loops, and if the game ever enters one, it ends in a draw. One example of such a loop are three Oblivion Rings exiling each other over and over with no other nonland permanents on the field. These triggers are mandatory and the only possible choice for them is the other O-Ring currently on the field. There is no way out with just the objects involved. If a player has the means and the will to stop the loop (like a Naturalize in hand with the mana to cast it), he can opt to stop the loop, but he is not forced to as those means aren't part of the loop.
For the case you described, no. Both Felidar Guardian and Restoration Angel say that you may exile the targeted permanent and return it to the battlefield, which means that you always have the option not to do that when one of the abilities resolves. The game only enters an infinite loop that causes a draw if a sequence of events occurs where no player is given a choice that could cause the loop to end.
A simple example of a case that would cause an infinite loop is if the battlefield has an Oblivion Ring which has another Oblivion Ring exiled to it, there are no other nonland permanents, and someone plays a third Oblivion Ring. The new Ring has to target and exile the current one, which triggers the ability that returns the other exiled Oblivion Ring to the battlefield, which has to target and exile the other one on the battlefield, which causes the other exiled Ring to come back... and there's no choice anywhere to stop it.
No, you can't do that Cat / Angel loop just for the sake of it, because it's not a loop of mandatory actions. Since you have the possibility of not using either effect, you can't do that loop if it doesn't have any result other than wasting time. A loop will make the game end in a draw only if it's comprised solely of mandatory actions. For example, three Oblivion Rings exiling each other with no other nonland permanents on the battlefield to target, actually causes the game to be stuck in the mandatory loop and end in a draw as soon as it's recognized as such.
719.4. If a loop contains only mandatory actions, the game is a draw. (See rules 104.4b and 104.4f.)
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I'm a former judge (lapsed), who keeps up to date on rules and policy. Keep in mind that judges' answers aren't necessarily more valid than those of people who aren't judges; what matters is we can quote the rules to back up our answers. When in doubt, ask for such quotes.
My opponent has 0 cards in hand, no permanents in play, all lands tapped. No action possible from their side (for the sake of the example).
I have a Felidar Guardian and cast Restoration Angel, it resolves. RA trigger resolves targeting FG, its trigger resolves targeting RA. This generates the possibility for an infinite loop, can I force a draw with it?
In case this example results in a 'no', is it possible to enter an infinite loop and force a draw in MTG? I strongly dislike the idea that could do such a thing (as it's very anti-magic), but I'm curious to know to be prepared for it happening on the other side of the table, should the occasion arise.
As to an actual infinite loop that creates a draw, yes there are some, the most notable being 3 oblivion rings with no other legal permanents.
In general, the only time a loop results in a draw is if it contains only mandatory actions (C.R. 720.4; see also C.R. 104.4b).
EDIT (Mar. 30, 2019): One rule was renumbered with Dominaria. Correctness edit.
Yes, there are mandatory infinite loops, and if the game ever enters one, it ends in a draw. One example of such a loop are three Oblivion Rings exiling each other over and over with no other nonland permanents on the field. These triggers are mandatory and the only possible choice for them is the other O-Ring currently on the field. There is no way out with just the objects involved. If a player has the means and the will to stop the loop (like a Naturalize in hand with the mana to cast it), he can opt to stop the loop, but he is not forced to as those means aren't part of the loop.
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A simple example of a case that would cause an infinite loop is if the battlefield has an Oblivion Ring which has another Oblivion Ring exiled to it, there are no other nonland permanents, and someone plays a third Oblivion Ring. The new Ring has to target and exile the current one, which triggers the ability that returns the other exiled Oblivion Ring to the battlefield, which has to target and exile the other one on the battlefield, which causes the other exiled Ring to come back... and there's no choice anywhere to stop it.