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play it close to one's chest

Idioms  
  1. Be secretive or cautious, give nothing away, as in We've no idea how many tickets they sold; they play it close to their chests. This expression, which is also put as play one's cards close to one's chest, alludes to holding one's cards up against one's chest, so that no one else can see them. [Slang; mid-1900s]