New Zealand are still dreaming big but wet weather remains their best chance of staving of defeat in the first Test against Australia at the Gabba.
Steve Smith's men need seven wickets on day five to win the three-Test series opener, while the tourists are 3-142 and require a further 362 runs on Monday.
"I certainly think we're in with a chance," optimistic NZ opener Tom Latham said.
"If we have a solid start and the two boys (Brendon McCullum and Ross Taylor) can set a platform for us then hopefully good things will happen late in the day."
A Kiwi win would set all manner of records, most notably bettering the 7-418 scored by West Indies in 2003 - the highest successful fourth-innings chase is Test history.
"There's definitely a chance but I'd like to say the odds are more in Australia's favour," Nathan Lyon said, having claimed the key scalp of Kane Williamson on day four.
"If we bowl well then we win this Test match."
Wet weather is the wildcard.
Rain resulted in an extended lunch break on Sunday, when Smith declared overnight to set NZ a victory target of 504 runs.
No play was possible in the final session due to another downpour then bad light.
There is a 50 per cent chance of rain on Monday according to the Bureau of Meteorology.
"Disappointing but ... if we could control the weather we'd be millionaires," Australia coach Darren Lehmann told ABC radio.
"We've got 98 overs.
"We'll get enough play in to create the chances."
"We've created a couple of extra chances, we've got to take them."
Martin Guptill was dropped on zero and seven on Sunday, Smith slapping his hands in frustration after the second life.
Australia's new captain was rarely a happy camper on day four, when Australia managed only 53 overs.
Smith was clearly stroppy when umpires ordered players off the field due to light rain in the morning.
Former Australia skipper Mark Taylor felt the 26-year-old had a point.
"If it was drizzling like this on day one you wouldn't go off," Taylor opined on the Nine Network.
"They've played in heavier rain than this in this Test match."
Smith then had a long discussion with officials when Australia were waiting for play to resume after the downpour at lunch.
He was even tetchy after snaffling an edge at slip to dismiss Guptill, who was undone by Lyon.
Smith hurled the ball away and seemed to point to a spot on the pitch after the catch, having talked tactics with his offspinner during Guptill's stonewall.
"I didn't really see it. A few of the boys were talking about it, but he seemed pretty happy in the group," Lyon said.
"He's a very good captain."
Guptill scored 23 runs during a 133-ball stay at the crease.
Williamson, who scored 140 in the first dig, offered spirited resistance in a knock of 59.
He was trapped lbw by Lyon in the penultimate over of the second session.
Williamson reviewed the decision but ball-tracking technology suggested it was 'umpire's call' by the barest of margins.
"To get his wicket was pretty big for us," Lyon said.
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