As he explained earlier in the year, there were good reasons for choosing it.
It was the first number he raced with as a nine-year-old karter in his native Perth, and he used it when he moved up to single seaters.
It was also the number the late 'Intimidator' Dale Earnhardt, a boyhood hero, used for most of his career as NASCAR's 'Man in Black' on his way to seven Winston Cup championships.
Left unsaid was another excellent reason: Three is better than two when your team mate has the champion's number one on his car.
No Formula One driver wants to be labelled a 'Number Two', even if it is a tag the 24-year-old Australian already faces as he takes the hottest seat in Formula One as partner to a four times champion only two years older than him.
Mark Webber, Vettel's Australian team mate until the end of last season, had to race with the two on his car for years because the numbers were allocated according to the constructors' championship.
"Not bad for a number two driver," Webber famously declared in a barbed comment directed at his team when he won at Silverstone in 2010.
Under the new rules, Ricciardo can choose for himself and three makes a statement: Not the number one but never a number two either.
The Australian faces a tough challenge ahead. Vettel eclipsed Webber last season, with the German controversially disregarding team orders in Malaysia and then going on to win the last nine races in a row.
He will expect to be calling the shots again this year while Ricciardo, who has graduated from sister team Toro Rosso, does not even have a podium finish to his credit so far and has plenty to learn. But he will not be pushover.
"Obviously I don't expect to be treated like God. I'm not the world champion but at the same time I've been reassured I'm going to get the equal side, the same length of straw, whatever you want to say," the Australian told reporters.
"I've got to earn my place in the team as well. It's nice to know we're going to have equal stuff but I definitely want, after some time, let the team know that I'm capable to hopefully get some top results as well."
The immediate task is to learn as much as he can from the man in the adjacent garage.
"It's a bit of a privilege I guess to have a four time world champion alongside me, to be able to see his data and what he's doing on track and to try and better myself learning off him," said Ricciardo.
"I'd love to be as competitive as soon as possible but I'll just take it step by step and learn what I can from Seb," he said at the end of January.
If he knows his place in the pecking order, the team has high hopes for the young Australian with the constant smile and endless optimism.
"I think he could really pose a surprise on occasion this year. It's going to take him time to settle in and develop but the underlying fact is that he's extremely fast," said team principal Christian Horner.
Webber, now racing for Porsche in sportscars, also expects his compatriot to give Vettel a run for his money.
"He'll go well," the older Australian told the March edition of Britain's Motor Sport magazine. "I think he'll give Seb a real hard time in qualifying - it'll be 50:50 in the first year, I reckon.
"I took a few off Seb last year...I think Daniel will be fine, and it certainly won't hurt him that he's come through the Red Bull system. I just hope he gets better starts than I did."
Pre-season testing has been difficult for the champions, with Vettel and Ricciardo heading for Melbourne without having done a proper race simulation in the new car.
If the first few races show the champions on the back foot, rivals do not expect that situation to last given Red Bull's resources and reserves of talent. Ricciardo remains confident he will have a chance to shine.
"If we do our homework here and back in the factory, Red Bull will start the season in Melbourne in style - though probably not as dominant as we've been last year," he told the formula1.com website at last week's final test in Bahrain.
No Australian has ever won his home race and even without Red Bull's current difficulties Ricciardo would not be lining up in Melbourne as a favourite.
He will still be the only local in the race, however, and that alone fills him with excitement.
"I won't need much psyching up," he said. "I think Melbourne will take care of that. Always the first race of the year is big but now being a home race for me and the sole Australian...
"I'm sure there's going to be a lot of attention and people will call it pressure. I guess for me, I just call it excitement. And some added adrenaline. I've just got to channel that, control that and use it to my advantage on track."
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