か vs かい - What's the nuance?

So, usually when asking a question. The particle at the end is か
like: 大丈夫ですか - are you alright?

However, for a fandom I’m in, I was looking at line stickers of all things and found this

大丈夫かい?
Idk how much context I need to give
but the sticker is taken from a music video, in it this woman has had a bit too much to drink and has drunkenly fell asleep on him

Which is probably why in the sticker he’s asking if she’s ok

Now this is part grammar lesson and part dragging you guys into my mystery solving, because we never figure out what these two’s relationship is (strangers, friends, siblings, extramarital affair ect ect)

My dictionary says かい is familiar language

But I couldn’t find any good examples of what this means in context
Do you only use it with people you know/are on good terms with?
Is it just casual/friendly?
Does it have something to do with age (the character loves playing up how middled aged/おじさん he is) or gender, or dialect? (this series doesn’t really have regional dialects in it, but the character is from Yokohama for what its worth)

Ultimately, even if you don’t care about my mystery, I do also just want a straight grammar lesson:
Just how is かい used?

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かい is a bit more casual and softer than か, and as I understand it exclusively for yes/no questions. From what I gather it’s fairly masculine, and mostly used in Kanto.

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lol this is a really succinct summary, thank you

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what I would add to this is that かい is much more casual than か.
So you would only use it with very close friends and even then it is not used often.

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Important to note that while this may be true for real Japanese, かい is a common component of yakuwarigo and as such you’ll encounter it a lot in things like manga, videogames and anime.

Here’s bunpro’s entry for かい: かい (日本語能力試験 N4) | Bunpro – 日本語の文法解説

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The Dictionary of Basic Japanese Grammar has an entry for it. As well as what others have said here, the equivalent for how much/when/who/etc open questions is だい.

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What kind of role does it have in yakuwarigo?

Make the character look a bit rough and impolite I’d say.

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From my understanding かい is a “yes or no question.”

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