cross palm with silver
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cross (one's) palm with silver
To pay someone, often as a bribe. Well, if you cross my palm with silver, I might remember a few details about the people you're asking about. I crossed her palm with silver to make sure she won't come after us.
cross someone's palm with silver
Fig. to pay money to someone in payment for a service. (A fortune-teller might ask for a potential customer to cross her palm with silver. Used in that sense or jocularly for something like tipping a porter.) I crossed his palm with silver, but he still stood there. You will find that things happen much faster in hotels if you cross the staff's palms with silver fairly often.