Learn Russian: Какая тоска, когда тебе некого позвать в кино. - What a bore when you have no one to invite to the cinema.

Некого is a special predicative negative pronoun used to say there is "no one to [do something]." It is always used in a structure with the logical subject in the dative case (here, тебе) and an infinitive verb (here, позвать). So тебе некого позвать means "you have no one to invite." If you used никого, you would need a regular nominative subject and a negated verb, like ты никого не зовёшь (you are not inviting anyone).

Which case is некого in, and why?

It is in the accusative case because it acts as the direct object of the verb позвать (to invite). Just like you would ask Кого ты хочешь позвать? (Who do you want to invite?), this negative pronoun takes the same case, combining кого with the stressed prefix не-. Note that this specific pronoun does not have a nominative form.

I thought тоска meant "sadness" or "melancholy." Why is it translated as "a bore"?

Тоска is an expressive Russian word that often means deep sadness, yearning, or depression. However, in casual, everyday speech (especially in the exclamatory phrase Какая тоска!), it is frequently used to complain about something tedious, meaning "What a bore!" or "How dull!"

Why does the sentence start with Какая?