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Phrase(s): play one’s cards close to one’s chest [and] play one’s cards close to one’s vest; keep one’s cards close to one’s chest; keep one’s cards close to one’s vest
Fig. to keep to oneself or be very cautious in one’s dealing with people. (As if one were playing cards and not permitting anyone to see any of the cards.) • He is very cautious. He plays his cards close to his chest. • You seem to be playing your cards close to your vest.
McGrawhill's American Idioms And Phrasal Verbs