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In short, no, Modern Warfare 3's Zombies experience is not free-to-play. Players have to purchase the full version of Modern Warfare 3 in order to access the game mode, even if they have no interest in the campaign or multiplayer. If you're an experienced CoD player, this shouldn't exactly come as a surprise.

OPERATION DEADBOLT: AN ALL-NEW OPEN-WORLD ZOMBIES EXPERIENCE\n\n For the first time, team up with other squads to survive and fight massive hordes of the undead in the largest Call of Duty Zombies map ever.