I'm sorry, I could not find this word anywhere, either in my Redhouse or online at Zargan sözlük. I finally found it as a song title by the late great Barış Manço.
I don't think so. I now know that the idiom is properly written as follows:
Darısı başınıza.
It means exactly what the translator translated it as: May your turn come next.
The capital letter is because it was the beginning of a new sentence. The writer (or the transcriber) just forgot to put the period (= full stop) just before it, as canaydemir said above.