Just started DMing, and in a moment of hubris had a NPC challenge the party to a game of cards… which one of the PCs was proficient in. When asked the reasonable question of "ok what now," I realized I had no idea and a quick skim of the DM guide and PHB (and a longer look later) revealed nothing. Something that could have been fun and a nice character moment turned into a "sorry guys, let me just throw something together and move along."

Are there rules in 5e for what rolls/checks/contests are necessary or expected when using a gaming set? When and how would proficiency come into it? What other skills and proficiencies could come into play (ex: a sleight of hand check to cheat at cards)?