Green’s Dictionary of Slang

(Aus., N.Z.) a phr. meaning ‘be fair, give us a chance’.

1988		McGill Dict. of Kiwi Sl. 44/2: fair shake (of the dice) [...] fair whack are some more appeals for fairness.
2003		McGill Reed Dict. of N.Z. Sl. [as cit. 1988].
2000–02		Macquarie Dict. 🌐 fair shake of the dice, an appeal for fairness or reason.