keep one's cards close to one's chest

verb2

1. •
   To hold one's hand close to one's chest so that other players cannot see the cards.
2. •
   (figurative) To avoid revealing one's thoughts, circumstances, or plans.

   • 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. — 1997