Australia: Is it "fair shake of the sauce bottle" or "fair suck of the sauce bottle"?

The sauce bottle saga. «As an ex-Queenslander, I've heard both, but an academic, Sue Butler, whom I understand has something to do with the Macquarie Dictionary of Slang, insists the latter is correct, and patronisingly explains that Rudd has mixed two expressions ‘fair suck of the sauce bottle' and one of the following: ‘fair shake of the dice' or ‘more than one can shake a stick at'. Her subtheme was that poor Kevin has got so much going on in his head running the country, he got his expressions mixed up. »