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One day, I asked my japanese friend how I could invite some friends to eat. He
said  
"一緒に食べに行くかい？"

I know that we could also say:

行きましょうか（行こうか）？  
行きませんか（行かない）？  
行きますか（行くの）？

but I got interested in why he used "kai".  
I'd like to know others situations that japanese people use "kai"
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2011-08-26T02:35:28.770
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question
usage particles register questions sentence-final-particles
In what situation can I use ~かい (for interrogative question)?
As opposed to 「か」, which is open-ended and can have any sort of answer, 「かい」
is expected to have an answer in the affirmative or negative only, that is,
yes or no, with subsequent explanation optional.

Example:

> 誰か来たのか  
>  誰か来たのかい
>
> 誰が来たのか  
>  × 誰が来たのかい
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2011-08-26T02:46:34.967
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answer
I'm not so sure about the folksiness, but it's definitely very informal. I've
mainly heard it used in speaking to children and intimates. I don't think it
would be used toward social superiors in most situations. By the way, there's
an analogous variant of the copula, だい, as in 「ママのおにぎりはどうだい？」.
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2011-08-26T03:07:41.220
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かい is used to soften the rudeness of か in informal speech. Sentences like
"見たか？" or "好きか？" are harsh to the ear, and using かい instead of か is thus nicer
to the listener.
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2011-08-26T03:46:46.393
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answer