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Casting a spell for its surge cost doesn't change its mana cost or its mana value.

For some cards, surge represents only an alternative cost, a discount that applies if you or a teammate has cast another spell this turn. Other cards, like Reckless Bushwhacker, have additional abilities or effects if you paid the surge cost to cast the spell.

If an instant or sorcery spell cast for its surge cost is copied, the copy is also considered to have had its surge cost paid.

The other spell that you or a teammate cast can be one that's resolved, one that was countered, or (for instants with surge) one that's still on the stack.