You canâ€™t choose to pay any additional costs for the copy. However, effects based on any additional or alternative costs paid for the targeted spell are copied as though those same costs were paid for the copy.
The copy will have the same targets as the spell itâ€™s copying unless you choose new ones. You may change any number of the targets, including all of them or none of them. If, for one of the targets, you canâ€™t choose a new legal target, then it remains unchanged (even if the current target is illegal).
If the spell is modal (that is, it says â€œChoose one â€”â€ or the like), the copy will have the same mode. You canâ€™t choose a different one.
If the spell has an X whose value was determined as it was cast (like Earthquake does), the copy has the same value of X.
If the copy says that it affects â€œyou,â€ it affects the controller of the copy, not the controller of the original spell. Similarly, if the copy says that it affects an â€œopponent,â€ it affects an opponent of the copyâ€™s controller, not an opponent of the original spellâ€™s controller.
Dualcaster Mageâ€™s triggered ability can target (and copy) any instant or sorcery spell, not just one with targets. It doesnâ€™t matter who controls it.
As Dualcaster Mageâ€™s triggered ability resolves, it creates a copy of a spell on the stack. The copy isnâ€™t cast, so abilities that trigger when a player casts a spell wonâ€™t trigger.
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