If you cast an adventurer card as an Adventure, use only its alternative characteristics to determine whether it's legal to cast that spell. For example, if Giant Killer is exiled with the last ability of Vivien, Champion of the Wilds, you can't cast it as Chop Down.
Murderous Rider // Swift End
If the target creature or planeswalker is an illegal target by the time Swift End tries to resolve, the spell won't resolve. You won't lose 2 life or exile Swift End. If the target is legal but not destroyed (most likely because it has indestructible), you do lose 2 life and exile Swift End.
Casting a card as an Adventure isn't casting it for an alternative cost. Effects that allow you to cast a spell for an alternative cost or without paying its mana cost may allow you to apply those to the Adventure.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Raluca Marinescu
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