Angel of Serenity
Razaketh, the Foulblooded
After the Angel's ETB trigger has been put on the stack and its targets have been selected, players can respond to that trigger. If you respond by removing the Angel somehow (for example with Razaketh's sac ability), its trigger is still on the stack waiting to do its thing. But its other trigger is now put on the stack, too, and as always, it is put on top of the stack, so somewhere on top of the other trigger. This means, that the return trigger resolves first, but there is nothing to return, because nothing has been exiled yet. The exile trigger will still resolve (because abilities on the stack exist independent of their sources) and do its thing, exiling all its targets that are still legal. In order to return those cards now, the Angel has to leave the battlefield, but it's not even there anymore, so the trigger can't go off. Even if the Angel returns and then leaves again, the game considers it a new object and thus its return abilty won't refer to the previously exiled cards since they were exiled by a different Angel as far as the game is concerned.
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EDIT (Dec. 11, after comment 8 was posted): In particular, C.R. 608.3a says that as a permanent spell with no target resolves, "it becomes a permanent and enters the battlefield under the control of the spell’s controller", without stating explicitly that a particular player puts that object onto the battlefield this way.
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EDIT (Jul. 26, 2021): Edited generally, including because one rule was renumbered in the meantime.
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If you control both Rootpath Purifier and Urborg, each land you control becomes a basic Swamp in addition to its other types (C.R. 205.4b, 205.1b).
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If Angel of Sanctions leaves the battlefield before its enters-the-battlefield ability resolves, the targeted permanent won't be exiled due to that ability, since Angel of Sanctions has already left the battlefield (C.R. 610.3b). See also this thread and this thread.
EDIT (Jul. 2, 2020): The relevant part of one rule was moved in the Core Set 2021 update.
EDIT (Nov. 16, 2022): Some rules were renumbered in the meantime.
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In any case, although there are cards that care about the order of cards in a graveyard, the number of cards in that category is small. And in practice, in an unsanctioned casual game, if the players in the game agree to forbid such cards from appearing in the game, then the game would not be affected by players reordering their graveyards.
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When a permanent transforms and transforms back, are the abilities before it transforms the same "instances" as after it transforms back?
Indeed, according to the release notes, converting is another word for transforming for purposes of the game.
See also:
- https://www.reddit.com/r/mtgrules/comments/xt93ef/question_about_ratchet_field_medic_ratchet_rescue/
- https://www.reddit.com/r/mtgrules/comments/r0snor/hasnt_been_chosen_for_transformedcopied_cards/
- https://mtgsalvation.com/forums/magic-fundamentals/magic-rulings/802624-realm-razor-and-sudden-spoiling
- https://twitter.com/PeteroUPC/status/1463323874632908803
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EDIT [after comment 8 was posted]: But compare Braids with Cloudstone Curio. See also:
EDIT (Oct. 25): Edited.