When Eye of Doom enters, each player chooses a nonland permanent and puts a doom counter on it. , , Sacrifice Eye of Doom: Destroy each permanent with a doom counter on it.
The active player chooses a permanent first, followed by each other player in turn order. Each player will know what previous players have chosen when making their own choice. Then the doom counters are put on all the chosen permanents simultaneously.
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wotc
None of the permanents are targeted. A player can choose a permanent with protection from artifacts, for example.
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wotc
If a permanent with a doom counter isn’t destroyed by Eye of Doom’s last ability (perhaps because it has indestructible or it regenerated), the doom counter will remain on that permanent.
Random a card of Magic: The Gathering (MTG), but you can also roll the D20 dice, random a Planeswalker, have fun with the random rules and more.