The player who controls the triggered ability chooses which opponent separates the cards into two piles. This choice is made after revealing those cards.
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That opponent may choose to put all of the cards into one pile and leave the other pile empty. In that case, the ability’s controller chooses whether to put the revealed cards into their hand or into their graveyard.
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Domain abilities count the number of basic land types among lands you control, not how many lands you control or how many of any type.
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The basic land types are Plains, Island, Swamp, Mountain, and Forest. Land types other than basic land types (such as Desert) don’t contribute to domain abilities.
Flying, ward
Domain — Whenever this creature deals combat damage to a player, reveal the top X cards of your library, where X is the number of basic land types among lands you control. An opponent separates those cards into two piles. Put one pile into your hand and the other into your graveyard. (Piles can be empty.)
