In the game of snooker, as you might know, the referee says "steve davis to break" to start the game.

does "steve davis to break" mean; steve davis is the one who'll(is going to) break OR steve davis will(is going to) break.

or is there another saying that means exactly same as it?

I'm trying to figure out when I can use that structure.

Many thanks..
I think it is a shortened form of something like 'Steve Davis [is designated/chosen] to break'.
Hi Mr. Micawber,
Mister MicawberI think it is

as I understood, you're not quite familiar with this form, which shows me it's not important and I don't need to learn or use it. right?

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No, I am quite familiar with the form ('Federer to serve'), but what is precisely elided is anyone's guess.
I see. what about in this sentence?

He is to arrive here tonight.

Is it the same situation, so we should understand from the conversation?

No (maybe yes-- I suppose that is one of the possible elisions: 'Federer is to serve'). However, 'be to + infinitive' is a specific future verb form. It is a bit formal and not so common, and it is used to express a future fact based on some sort of fiat-- a rigid schedule, etc.

'He is to arrive tonight' indicates that future event based on a sure schedule.
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Hmm I feel I'm getting closer to the understanding point through your explanations. Just need some more excercises.

Thanks a lot Mr. Micawber.