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If I have a Jace's Erasure (Whenever you draw a card, you may have target player mill 1) out and cast Prosperity (Each player draws X cards), since we both draw at the same time, for each card drawn would it be

I draw, I can make opponent mill, opponent draws

or

Opponent draws, I draw, I can make opponent mill

Also, if I have Jace's Erasure and instead my opponent casts Prosperity, does the outcome change?

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The order of events in this case is as follows:

  1. Prosperity resolves
  2. Resolve the text on the card in its entirety, so each player draws X cards.
  3. Jace's Erasure's ability is triggered once for each card drawn, but we wait until the resolution of Prosperity is complete before putting the triggers on the stack.
  4. The triggered abilities of Jace's Erasure resolve one at a time, and you mill cards from your opponent's library one at a time as they do.

Summary: You both draw, then you mill the cards from your opponent's library. Changing whoever cast the spell does not affect this outcome.

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    Your point 3 isn't exactly right. During the resolution of Prosperity, Jace's Erasure's triggered ability triggers, but it doesn't go on the stack until after Prosperity has finished resolving.
    – murgatroid99 ♦
    Jan 20, 2020 at 1:24
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    Also, there will be a separate trigger for each card drawn.
    – Arcanist Lupus
    Jan 20, 2020 at 2:25
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    Jace's Erasure puts cards in opponent's graveyard. It doesn't exile them.
    – Aulis Ronkainen
    Jan 20, 2020 at 4:06

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