何さ、いやな人たちだね。こんな家に生まれてきたのが運のツキだよ。
What!? I'm an unpleasant person am I? To be born in a house such as this ...
Bit confused by the part in bold. 運 means "luck" and ツキ can also mean "luck". So is this "luck of lucks"? Is it a sarcastic comment "Lucky me, to be born in a house such as this"?
If so, do Japanese people tend to use sarcasm often?