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Can a Tarfire kill a Tarmogoyf when both players' graveyards are empty?

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No. State based actions are checked after a spell is completely resolved. By that time, Tarfire is already in the graveyard. Tarfire counts as both a Tribal and an Instant, and so Tarmagoyf is a 2/3.

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    The comprehensive rule to back up this answer is too long to fit in a comment, but the relevant portion is, "704.3. Whenever a player would get priority (see rule 116, “Timing and Priority”), the game checks for any of the listed conditions for state-based actions, then performs all applicable state-based actions simultaneously as a single event."
    – Rainbolt
    Dec 7 '15 at 14:12
  • Why is it a 2/3? If both graveyards are empty then after the spell resolves there should only be cards of the type instant in the graveyard which would make Goyf a 1/2. Is there something I'm missing? Dec 7 '15 at 14:16
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    @RobertWertz Tarfire isn't just an instant, it's also a tribal. And yes tribal is a card type, not a supertype Dec 7 '15 at 14:16
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    @IvoBeckers maybe you could incorporate that as part or your answer.
    – Colin D
    Dec 7 '15 at 14:47
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    Note that if can kill if the Tarfire fails to go to the graveyard, such as if it was cast using flashback granted by Snapcaster Mage, or if there's an effect preventing card from going to the graveyard, such as Rest in Peace
    – VolleyJosh
    Dec 7 '15 at 17:41

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