play murders close to the vest

ChandlerのThe Big Sleep を読んでいます。
There's a couple more deaths involved, Ohls said, pinching the soft flesh at the end of his chin.
Cronjager stiffened visibly. His surly eyes became points of steely light.
Ohls said: You heard about a car being lifted out of the Pacific Ocean off Lido pier this a.m. with a dead guy in it?
Cronjager said: No, and kept on looking nasty.
The dead guy in the car was chauffeur to a rich family, Ohls said. The family was being blackmailed on account of one of the daughters. Mr. Wilde recommended Marlowe to the family, through me. Marlowe played it kind of close to the vest.
I love private dicks that play murders close to the vest, Cronjager snarled. You don't have to be so goddamned coy about it.
"played it kind of close to the vest" の個所が分かりません。慣用句が使われている様です。辞書で調べます。 二つの辞書に次の説明がありました。
play (it) close to the vest:
・Webster’s New World College Dictionary: to be reserved, secretive, etc.; keep (one's plans, thoughts, etc.) to oneself
close to:
・Urban Dictionay: keep something secret, to hold something close so no one else can see it: Though it was just a friendly game of Go-Fish, Henry kept his cards close to the vest, not letting anyone else see which cards he held.