If an effect says “You may search your library . . . If you do, shuffle your library” or “You may search your library . . . then shuffle your library,” your opponents can’t choose to search, so they won’t shuffle.

Effects that instruct your opponents to reveal or look at cards from the top of their libraries will still work. Only effects that use the word “search” are affected.

If an effect says “Search your library . . . then shuffle your library,” your opponents shuffle their libraries even though they can’t search.

Spells and abilities your opponents control may cause other players to search their libraries, and spells and abilities you control may cause your opponents to search their libraries.

If Ashiok’s last ability targets an opponent, the cards put into their graveyard will be among the cards exiled by the ability. No player may take any actions between the time the cards are put into a graveyard and the time your opponents’ graveyards are all exiled.