Mysterious Stranger

If a spell has {X} in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.

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. If the spell has any mandatory additional costs, those must be paid to cast the card.

If you don’t want to cast the copy, you can choose not to; the copy ceases to exist the next time state-based actions are checked.

You cast the copy while Mysterious Stranger’s last ability is resolving and still on the stack. You can’t wait to cast it later in the turn.