Based on the metaphorical opposition between an easy life in the city and a hard life working in the outback, the Australian colloquial phrase Sydney or the bush means all or nothing—synonym: all duck or no dinner.
The most plausible origin of the phrase appeared in the Kalgoorlie Miner (Kalgoorlie, Western Australia) of Saturday 5th June 1920, which quoted the review, published in The British Australasian (London), of Digger Dialects: A Collection of Slang Phrases used by the Australian Soldiers on Active Service (1919) by Walter Hubert Downing (1893-1965); the reviewer’s final remark was that W. H. Downing
omits one of the most picturesque exclamations of the Australian soldier. It is “Well, Sydney or the bush,” when a Digger risks all on the spin of a coin.
(The hypothesis that the phrase originated in the real story of a man who gambled his fortune has all the appearances of a folk-etymological explanation.)
The earliest instance of Sydney or the bush that I have found is from The Sydney Stock and Station Journal (Sydney, New South Wales) of Friday 17th January 1902—the phrase is in inverted commas, which perhaps indicates that it was recent:
99A writes:—“Are we ever going to get our new Land Bill, as we have been waiting for it? I suppose it will be wait on! Are we going to be allowed to convert our S.L. and H.S. into C.P. and C.L. land? If not, then you will soon have plenty more loafers in your domains, for the worst land was thrown open first for lease, and every man wanted land. Some of us got it, and have been doing nothing but fighting bad seasons and improving all that time. We’ve spent our money, and now we are done if we can’t convert our S.L. into C.P., so that we can raise a few pounds to go on with. This bill is our whole trouble, for it means ‘Sydney or the bush’ with many more besides myself. I have spent between £600 and £700 on my place, and my banker (‘that was’) said that he could not give me one penny on S.L. or H.S. land. And that Relief to Settlers Bill— a man would be starved out while they are measuring the red tape. So, God help scores if we cannot convert and raise a little money, as we have prickly pear and bunny, besides wild dogs, tiger cats, and a hundred-and-one other things.”