WASHINGTON — Sarah Palin demonstrated once again Friday that she is one of America’s most unconventional politicians, following an unpredictable path to an uncertain future.

That the Alaska governor has a flair for the theatrical — and plays by her own rules — was underscored anew by her stunning announcement that not only will she not seek re-election in 2010 but also that she will resign her office this month.

But are Palin’s rules those of someone with the capacity to seek and win her party’s presidential nomination in 2012, as many believe is her ultimate goal, or of someone who has flashed like a meteor across the political skies but with limited impact? That question was at the center of the discussion Friday among Republican strategists who were baffled by what they had just heard from Alaska.

Palin’s decision to exit the governorship was as sudden and unexpected as her arrival on the national stage when Sen. John McCain, R-Ariz., defied all predictions and selected her to be his 2008 vice presidential running mate. From that day in August, to Friday’s announcement that she plans to step down, she has been one of the country’s most compelling and controversial politicians — and almost always one of the most enigmatic.

Palin’s statement was ambiguous with regard to her future. “We know we can effect positive change outside government at this point in time on another scale and actually make a difference for our priorities,” she said, hinting at larger ambitions. But she also expressed weariness over what she called “superficial, wasteful, political blood sport.” Was that a hint that she intends to turn away from elective politics?

Certainly, after a week in which she was the target of new attacks over her performance in the 2008 campaign that sparked a war of words between prominent Republican strategists, slipping into the background might be a welcome tonic for Palin and her family.

But even if that were her first instinct, she will feel the tug of her passionate supporters to remain in the forefront of the debate over the party’s future, and many of them will push her to run for president.

One strategist who assumes she has aspirations to run for president called the decision to resign her office “puzzling,” and another described it as “nutty.” “If this is about running for president, it’s about as odd a way as we’ve ever seen,” said John Weaver, a Republican strategist.

Their reasoning followed conventional assumptions about what it takes to mount a national campaign — that, in surrendering the governor’s office in Alaska, she brings a conclusion to her brief tenure in statewide office, leaving behind a thin record on which to base a national campaign.

Yet, it has been obvious that Alaska is a difficult place from which to participate in the national debate, both because of its physical distance from the rest of the United States but also because of its culture and identity. Freed of the constraints of her office, Palin could, if she chooses, become a more engaged participant in the national debate.

“My contrarian take is, almost everyone I talk to thinks it’s crazy, but I wonder maybe it’s crazy like a fox,” said Bill Kristol, editor of the Weekly Standard, who has been out defending Palin this past week.

Kristol’s view is that spending another 18 months in office in Alaska will not convince skeptics that she is ready to be president. Instead, he said, she can use this time to travel the country and the world, to immerse herself in policy issues and to campaign for Republican candidates, without facing questions every time she leaves the state about whether she is shirking her responsibilities.

“It’s a heckuva gamble, but it might pay off,” Kristol said.

Few who have watched Palin doubt her ability to attract attention, command a following and make herself a force, should she choose to run for president. Democratic and Republican strategists agree that she has charisma and a personality that connects with people.

“The skills she has are formidable and unteachable,” Mark Salter, who was one of McCain’s top advisers, said after he heard the news of her impending resignation.

But along with those skills have come a host of questions, which began in the days after her selection and have continued. They include whether she has the experience and knowledge of the world required of a successful national candidate.

At critical moments in the campaign last year, she stumbled on this front, particularly in her interview with CBS anchor Katie Couric. Though she held her own in the vice presidential debate with Democrat Joe Biden, questions about her expertise dogged her throughout the campaign. By the end of the campaign, she had lost support among independents, many of whom judged her not ready to be a heartbeat away from the presidency.

Question about her also include the soundness of her judgment and the quality of the advice she receives from those around her. Veterans of the 2008 campaign, who became close to her, have felt shut out from her circle this year. She created a needless controversy this spring over whether she would be the keynote speaker at a Republican fundraising dinner in Washington, causing grumbling among GOP insiders.

Still another set of questions focused on her reliability. Those came back this past week with a lengthy Vanity Fair article in which former McCain advisers went after Palin. Other Republicans rose to her defense, but Friday’s announcement is certain to bring new questions about why she needs to step down 18 months before her term ends.

All of that may mean little to the supporters who flocked to Palin during the presidential campaign and who remain loyal to her. She had far more appeal than McCain last year and drew far bigger crowds than he ever could. How they will see Friday’s announcement is not known, but they have tended to be both protective and forgiving of Palin as she has charted her unusual course through national politics.

A Republican strategist who got to know her over the past year, and who declined to be identified in order to offer a candid opinion, said this: “She has a base in the party that’s motivated like no one else’s, and this decision won’t bother them. I don’t know if she’ll run. I don’t know if she could win if she ran. But I’m sure she has a shot.

“If she runs, she’ll face a skeptical press and a fairly stark division between her supporters and skeptics. But she commands attention, she connects with voters better than most and she’s one of the toughest-minded people I’ve met.”

He added in conclusion something with which those on both sides of the Palin divide would agree. “I imagine,” he said, “she’ll continue to surprise us.”