On Saturday week, two state Labor governments will seek re-election on the same day, just as they did four years ago. Tasmania is too small and idiosyncratic to impact much on the nation’s consciousness, so South Australia is again getting most of the attention. But there are good reasons for thinking that the Tasmanian result may actually have more significance for interstate observers.

It’s true that South Australia is less predictable than it was in 2006.

Then, a Labor landslide was a foregone conclusion, and observers watched it with the morbid fascination of watching a train crash. This year, the polls are forecasting a close contest, and commentators are treating an opposition victory as a real possibility.

But a Liberal win in South Australia would go against all the precedents. None of the Labor governments in the eastern states – New South Wales in 2003, Queensland in 2004, Tasmania and Victoria in 2006 – have been seriously troubled at this point of the cycle. The Northern Territory government got a bad fright in 2008, but still managed to hold on. Only Western Australia saw a change of government, and it was starting with a narrower margin (like the Northern Territory, it had also antagonised the voters by holding an early election).

In Tasmania, however, we really have no idea who will form the next government. In 2006, voters had a clear choice: either a majority Labor government, or an unpredictable situation of minority government. Not surprisingly, they chose the former.

This time, majority government for either party seems a remote prospect.

Labor would have to hold all but one of its seats; its third seat in Franklin is gone for all money, so it would need to win three in each of Braddon, Denison and Lyons. Given anything like the swing that the polls are showing, that’s a huge task.

Despite Labor’s troubles, the Liberals are just as badly placed. They can be pretty confident of winning two seats in each electorate (a total gain of three seats), but getting beyond that will be difficult. Braddon is the only place where a third seat seems a reasonable prospect; Bass and Lyons are outside chances at best. (For all numbers, check out Antony Green’s election guide.)

That leaves the Greens, who with somewhere between three and six seats – more likely at the high end of that if the polls are right – look overwhelmingly likely to hold the balance of power. The major parties are not at all eager to talk about what they will do in that situation, but neither of them will rule out coming to terms with the Greens in some fashion.

So Tasmania will be interesting on at least two fronts. First in the result itself, because even if no-one has a majority, a great deal could turn on who comes out ahead, which could easily be decided in just one seat. But secondly in what happens afterwards.

That aftermath could have nationwide implications. For some years now, the Greens have seemed on the verge of a major breakthrough without ever quite making it. One barrier to their success is the perception that they are a party of the far left, and that when the chips are down they will always support Labor: the Liberals therefore see nothing to gain from dealing with them, and the ALP just takes them for granted.

But if Tasmania’s Greens can handle the responsibilities of power, and act as an honest broker between the two major parties, it could be a wake-up call to both the Greens and their opponents on the mainland.