keep one's cards close to one's chest

(idiomatic) To avoid revealing one's thoughts, circumstances, or plans.

Example: 1997, Sabine Rewald, "Balthus's Magic Mountain," The Burlington Magazine, vol. 139, no. 1134, p. 626:
  Balthus has always kept his cards close to his chest. When I asked him if Summertime was a transcription of Poussin's Echo and Narcissus—a variant of his lost copy—he did not reply.
2002, Anil Netto, "Malaysia: Year of surprises and hardships," Asia Times, 25 Dec. (retrieved 25 Oct. 2008):
  Abdullah has not yet revealed his choice for the No 2 post when he takes over as prime minister, preferring to keep his cards close to his chest.