There is no initiative in a game until an effect instructs a player to take the initiative. Once a player is instructed to do this, they have the initiative until another player takes the initiative.
Caves of Chaos Adventurer
If you have completed a dungeon when Caves of Chaos Adventurer's last ability resolves, you can only play the exiled card without paying its mana cost. You can't choose to play it normally.
If you’re already in a dungeon when instructed to venture into Undercity, you move to the next room of that dungeon. If you are already in the last room, you will complete that dungeon and start Undercity. This is true whether you’re already in Undercity or any other dungeon.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Marcela Medeiros
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