NEW YORK — Hillary Clinton’s problem is not her money. Despite the media flurry over a couple of awkward remarks she made, most people will understand her situation pretty quickly — she wasn’t born rich but has become very rich — and are unlikely to hold it against her. Mitt Romney did not lose the last election because of his wealth. Hispanics and Asians did not vote against him in record numbers because he was a successful businessman. Clinton’s great challenge will be to decide whether she represents change or continuity.

Clinton will make history in a big and dramatic way if she is elected — as the first woman president. But she will make history in a smaller, more complicated sense as well. She would join just three other non-incumbents since 1900 to win the White House after their party had been in power for eight years. She would be the first to win who was not the vice president or the clear protege of the incumbent president.

The examples will clarify. Since 1900, the three were William Howard Taft, Herbert Hoover and George H. W. Bush. Six others tried and lost: James Cox, Adlai Stevenson, Richard Nixon, Hubert Humphrey, Al Gore and John McCain. Interestingly, even the three successful ones had only one term in office.

A caveat: Beware of any grand pronouncements about the presidency because, in statistical terms there have not been enough examples and if you vary the criteria, you can always find an interesting pattern. The Republican Party broke almost every rule between 1861 and 1933, during which it held the presidency for 52 of the 72 years.

But the challenge for Clinton can be seen through the prism of her predecessors — should she run on change or continuity? The three who won all pledged to extend the president’s policies. They also ran in economic good times with popular presidents. That’s not always a guarantee, of course. Cox promised to be “a million percent” behind Woodrow Wilson’s policies but since Wilson was by then wildly unpopular for his signature policy, the League of Nations, Cox received the most resounding drubbing (in the popular vote) in history.

Some of the candidates had an easier time distancing themselves from unpopular presidents. McCain was clearly a rival and opponent of George W. Bush. Stevenson was very different from Harry Truman but he was, in effect, asking for not a third term for the Democrats but a sixth term — after 20 years of FDR and Truman. Shortly before the 1952 election, Stevenson wrote to the Oregon Journal that “the thesis ‘time for a change’ is the principal obstacle ahead” for his campaign. After all, if the country wants change, it will likely vote for the other party. “It’s time for a change” was Dwight Eisenhower’s official campaign slogan in 1952.

The most awkward circumstance has been for vice presidents trying to distance themselves from their bosses. Humphrey tried mightily to explain that he was different from Lyndon Johnson without criticizing the latter. “One does not repudiate his family in order to establish his own identity,” he would say. Gore faced the same problem in 2000, though many believe that he should not have tried to distance himself so much from a popular president who had presided over good times. As Michael Kinsley noted, Gore’s often fiery and populist campaign seemed to have as its slogan: “You’ve never had it so good, and I’m mad as hell about it.”

Today the country is in a slow recovery and President Obama’s approval ratings are low. This might suggest that the best course would be for Clinton to distance herself from her former boss. But Obamacare and other policies of this president are very popular among many Democratic groups. Again, the three people in her shoes who have won all ran on continuity.

Clinton’s recent memoir suggests that she has not yet made up her mind as to what course she will follow. The book is a carefully calibrated mixture of praise and criticism, loyalty and voice, such that she can plausibly go in whatever direction she chooses.

The world today is different. And Clinton is in a unique position, especially if she can truly mobilize women voters. But history suggests that choosing change or continuity will truly be her hard choice.

Fareed Zakaria is a syndicated columnist. His email address is: comments@fareedzakaria.com.