RichThesaurus
keep one's cards close to one's chest
vs
not give the game away
keep one's cards close to one's chest
verb
To avoid revealing one's thoughts, circumstances, or plans.
not give the game away
How often have the words
keep one's cards close to one's chest
and
not give the game away
occurred in a corpus of books?
(source:
Google Ngram Viewer
)