Does a copy of a spell with X in its mana cost copy the value of X chosen by the original caster?

When a spell is copied, the copy is created with the same choices that were made for the original spell, including the value of X. This is because X, as part of the cost, becomes a defined number once the original caster announces the spell and pays mana into it. The copy inherits that defined value of X without requiring any additional mana payment.

According to CR 706.10, a copy of a spell copies all values of that spell, including choices made for it such as the value of X. The controller of the copy may then change any targets, but they do not re-choose the value of X — it remains the same as the original.

This means the copy effectively 'sees' X as a fixed number equal to whatever the original caster chose. For example, if the original caster spent 5 mana into X for a Fireball, any copy of that Fireball also has X = 5, even though no additional mana was paid for the copy.

Concrete example: Your opponent casts Rolling Thunder with X = 4. You cast Twincast to copy it. The copy also has X = 4. You choose new targets for the copy if you wish, but X stays at 4 — you do not pay any additional mana.

Note that if the copy's controller is allowed to choose a new value of X (e.g., via a specific card effect that says so), that would be an exception explicitly stated on the card. Absent such an exception, X is locked in at the original's value per CR 706.10.