Starting with you, each player separates all permanents they control into three piles. Then each player chooses one of their piles at random and sacrifices those permanents.
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If you put all permanents you control into one pile, you'll have a two-thirds chance of not having to sacrifice any permanents, but a one-third chance of having to sacrifice all of them.
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To choose a pile at random, each pile must have an equal chance of being chosen. There are many ways to do this, including assigning each pile a number and rolling a die.
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You may put Auras or Equipment into one pile and the creatures they were attached to into a different pile.