Both have played with house money after saving match points to reach their third slam final, where there is so much more on the line than the world No 1 spot and the A$4m winner’s prize

Consistency has been the hallmark of Caroline Wozniacki’s career, so it might come as something of a surprise to learn that between her matches at the Australian Open over the past two weeks the Dane has been popping into the Crown Casino here. It could yet be a metaphor for Saturday’s final, when she takes on the world No 1, Simona Halep, when both women will be trying to win their first grand slam title. She who dares may just win.

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“We’ve been at the casino a couple of times, won a couple of hundred dollars,” Wozniacki said as she prepared for her third grand slam final, having lost at the US Open in 2009 and 2014. “I’m on a plus so far. We may go in and play a couple hundred again, see how it goes.”

Like a gambler down to her last dollar, Wozniacki looked down and out in the second round when she trailed Jana Fett of Croatia 5-1, 40-15 in the final set. As Fett blinked, Wozniacki saved the two match points and battled back to clinch a victory that probably only she had believed possible. Given a second chance, she has not looked back.

The No 1 ranking, which Wozniacki held at the end of 2010 and 2011, is also on the line in the final, with the winner taking home A$4m (£2.27m) in prize money. But winning their first grand slam title is the real prize.

“I always believed in myself,” Wozniacki said. “I had a tough period where I had a few injuries. That was kind of hard and tough mentally. But once I got past that, I knew that if I can stay healthy and I work hard my game is good enough for it [to win a grand slam].

“I’m really happy and proud of how I’ve managed to turn things around when things weren’t going my way and keep it up whenever it was going my way. I’m just excited. It’s another final. It’s another great two weeks. Regardless of what happens now, I’ve done my best. When you go out there, you have everything to win.”

Halep and Wozniacki would be hugely popular winners, their stories and disappointments well known to fans around the world. In her first grand slam final, at the 2014 French Open, Halep was edged out in three sets by Maria Sharapova. It is the manner of her defeat by Jelena Ostapenko in the Paris final last year, though, that still needs exorcising.

Then, she led 4-1 in the final set before Ostapenko reeled off a series of winners to deny her. Halep lost in the US Open first round but rebounded well to end the year as the world No 1 for the first time.

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Her run to the final here has echoed that of Wozniacki, though she saved match points in two matches, including two in a semi-final of the highest quality, when she wore down the former champion Angelique Kerber. After the first-round scare when she rolled her ankle, she looks to be moving at 100% again.

Wozniacki has won four of their six meetings and handed Halep a real beating when they played at the WTA Finals three months ago, dropping two games.

But Halep is still espousing the positive attitude impressed on her by her coach, Darren Cahill, the Australian who also helped Lleyton Hewitt and Andre Agassi rise to the top ranking.

“I don’t want to change anything,” she said. “I have to work. I’m ready for it. For sure it’s a big challenge. Maybe the biggest one, because all the things that were going on this tournament, first grand slam of the year, first final here. So I take it like a nice thing and with good thoughts. Nothing else.”