I know days undoing with flash doesn't exile itself but others in my play group shuffle it back into their library if it is cast on another persons turn, which to me doesn't really seem right, i could be wrong which is why i am asking here, if someone casts it on someone elses turn, does it shuffle itself into that persons deck?
No matter whose turn it is or who cast Day's Undoing, while Day's Undoing resolves and its instructions start to be followed, Day's Undoing will be on the stack, not in any player's hand or graveyard (C.R. 116.4, 608.2) — and if that spell is controlled by the player whose turn it is (C.R. 109.5), Day's Undoing will be exiled along with other spells and abilities on the stack (C.R. 716.1b).
EDIT: Correction after comment 3 was posted.
EDIT (May 10): Correct one rule citation; another rule was renumbered with Dominaria.
No matter whose turn it is or who cast Day's Undoing, while Day's Undoing resolves and its instructions start to be followed, Day's Undoing will be on the stack, not in any player's hand or graveyard (C.R. 116.4, 608.3) — and Day's Undoing will be exiled along with other spells and abilities on the stack (C.R. 715.1b).
I think you misunderstand. The turn-ending clause, which is what exiles the spell, only ends your own turn, so the OP is wondering what happens to the spell when it doesn't apply.
@OP: If you cast the spell during another player's turn, Day's Undoing will end up in your graveyard. The card will be on the stack when the hands and graveyards are shuffled into decks, so it won't be included.
608. Resolving Spells and Abilities
[...] 608.2k As the final part of an instant or sorcery spell’s resolution, the spell is put into its owner’s graveyard. As the final part of an ability’s resolution, the ability is removed from the stack and ceases to exist.
So the spell is still on the stack when it has its effects, including when the contents of the graveyard are shuffled back in as this is an effect of the spell. As it is still on the stack, the card is not yet in the graveyard and thus won't be shuffled in.
EDIT: Correction after comment 3 was posted.
EDIT (May 10): Correct one rule citation; another rule was renumbered with Dominaria.
I think you misunderstand. The turn-ending clause, which is what exiles the spell, only ends your own turn, so the OP is wondering what happens to the spell when it doesn't apply.
@OP: If you cast the spell during another player's turn, Day's Undoing will end up in your graveyard. The card will be on the stack when the hands and graveyards are shuffled into decks, so it won't be included.
So the spell is still on the stack when it has its effects, including when the contents of the graveyard are shuffled back in as this is an effect of the spell. As it is still on the stack, the card is not yet in the graveyard and thus won't be shuffled in.
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