You choose which spell to cast (if any) as Portent of Calamity resolves. If you choose to cast a spell this way, you do so as part of the resolution of Portent of Calamity. You can’t wait to cast it later in the turn. Timing restrictions based on the card’s types are ignored.
The card types that can appear on cards you reveal with Portent of Calamity are artifact, battle, creature, enchantment, instant, kindred, land, planeswalker, and sorcery. Legendary, basic, and snow are supertypes, not card types. Raccoon and Scout are subtypes, not card types.
If the spell you cast has {X} in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Justine Mara Andersen
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If you cast a spell “without paying its mana cost,” you can’t choose to cast it for any alternative costs. You can, however, pay additional costs, such as kicker costs. If the card has any mandatory additional costs, those must be paid to cast the spell.
