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Yes, the Mario Kart Tour game is available as a free download.
You must link your game to a Nintendo Account in order to play. You can register for a Nintendo Account for free at the following link:
https://accounts.nintendo.com
You can purchase in-game currency (called rubies) using real money (optional; not required). You can also acquire rubies for free. There is a paid service that provides various benefits for a monthly fee. For more information on Gold Pass, please see the About the Gold Pass section of this FAQ.
Note: Persistent Internet and compatible smartphone required to play game. Data charges may apply.