I am trying to make sentences with give the game away and new to the game as follow.
1. May's colleagues look her down because she has just joined the company and she's new to the game.
2. Dave and Jo do not want to disclose an intimacy has grown between them to their friends, however, Jo's mum gave the game away.
Are my sentences OK?
Is "give the game away" a way to say "let the cat out of the bag"? It's not one I know.
I would have thought it meant "threw" the game - deliberately did something to cause a failure.
.give the game away
to spoil a surprise or a joke by telling someone something that should have been kept secret It's a secret, so don't give the game away, will you?
Cambridge Advanced Learner's Dictionary & Thesaurus © Cambridge University Press)
I think it may need a "Chiefly British" citation, but it's Cambridge, so that may be implied.
Is this a commonly used expression?
Yes - it's very common.
We use 'throw the game' for the other meaning.
"Throwing a game" is deliberate. "Giving the game away" need not be.