First month in Bologna, I kept hearing "dai" in conversations where it clearly wasn't "come on." Someone would tell a story about their brother getting a job, and their friend would respond with "ma dai!" like they didn't believe it. The barista would say it as she handed me my espresso, kind of a sign-off. Two kids arguing on the bus used it like they were begging each other to stop. My textbook had one entry: "dai, come on (encouragement)." That covered maybe 20% of what I was hearing.
Technically "dai" is the second person singular imperative of "dare" (to give). Literally, "give!" But nobody actually uses it like that. If you want someone to hand you something, you'd say "dammelo" or "passami." The bare "dai" has drifted into doing something else entirely.
Here's what I pieced together after enough listening:
"Dai, andiamo." Come on, let's go. This is the textbook one.
"Ma dai, non ci credo!" Come off it, no way. Used when someone tells you something surprising, whether it's true or a joke. Often positive. If your coworker says they got the promotion, "ma dai!" is how you react, and it means something like "no way, that's amazing."
"Dai, smettila." Come on, cut it out. Mild reproach. Tone does the work. A parent uses this on a kid who won't stop whining.
"Dai, ti prego." Please, come on. Begging, pleading. Kids use it constantly.
"Bello, dai." It's nice, right? Sentence-final tag, like a soft "innit." This one took me forever to hear because it's not pushing for anything, it's just closing the sentence with a shared vibe.
"Dai su." Come on now. Often used to give someone a gentle push when they're tired, down, or dragging. "Su" is literally "up" and does that lifting.
Once I noticed the pattern, "dai" is almost always doing pragmatic work rather than lexical work. Most of the time it's a softener or a response marker. English doesn't have a single word that covers all this. You end up translating it as "come on" or "come off it" or "right?" or "please" depending on the slice.
What finally helped was making a rule for myself: whenever I heard a "dai" I couldn't parse, I'd send a voice note to a language partner on HelloTalk and ask her what the speaker was actually doing. She'd usually reply with a couple of similar contexts from her own life. Two months of that and my ear started catching the intonation on its own.But, where I still get it wrong: overusing it. Because I noticed how often Italians tag "dai" at the end of sentences, I started doing it in my own speech and a friend eventually told me I was sounding mildly annoyed at her. Apparently the intonation was doing something I hadn't picked up on yet.
One thing I still can't figure out: whether "dai" as a full standalone response (someone tells you something, you just say "dai," end of turn) is more of a Northern habit. I hear it constantly here in Emilia-Romagna, but a Roman friend told me she doesn't use it that way.