Be cautious when playing the game. These scammers may already have enough data on you before you answer the phone and all they need is to have your voice saying "Yes" and a few other key words - then they can use that to open new accounts in your name without your knowledge!
Almost everyone has at least one credit card, and that's what they are depending on. They really don't know if you, specifically, have a credit card. They are fishing, and wanting non-potential victims to hang up on the robocall.