Marion S. Barry Jr., though wounded by the scandals that have bedeviled his administration, shouldn't have much trouble winning a third term as mayor. But when it comes to a fourth term, the advice here is: don't even think about it.

This outrageously unscientific opinion is supported by no political poll, no expert analysis, no insider information -- nothing at all except the sense I get from talking to a lot of Washingtonians.

Barry, who by most accounts, has been a good mayor with no apparent desire to enrich himself illegally, has been hurt by the two things: the sense that too many people who work for him are on the take and the sense that the mayor himself is not seen as moving firmly enough to clean house. But if his wounds are somewhat more than superficial, they are somewhat less than disabling. Which is why City Council Chairman Dave Clarke and council members John Wilson and Charlene Drew Jarvis, all of whom harbor ambitions for the city's top job, apparently have decided to bide their time -- this time. (The only announced candidates to date, Mattie Taylor, Dennis Sobin, Brian Moore and Calvin Gurley, are thought not to have much of a chance.)

But four years from now could be a battle royal -- even if Barry decides to run again.

How can a man who is virtually unbeatable in 1986 project as so vulnerable in 1990?

My feeling, based on what people across the city are saying, is that while there is a predisposition to give Barry a third shot at leadership, there is no desire to install him as mayor-for-life. Indeed an extraordinary number of Washingtonians were, until fairly recently, under the impression that the D.C. mayorship had a two-term limit.

These same conversations reveal Barry not as some Reagan-like Mayor Teflon, but only as Mr. Lucky. Whether President Reagan is above the fray, as his supporters seem to think, or merely out of it, as his detractors would have it, he continues to escape any real responsibility for the insensitivity, the lack of compassion, the counterrevolutionary zeal and the sheer racism that infects his administration. But in Barry's case, damage to the integrity of his administration is damage to the mayor himself. The sense is that he has steered clear of scandal more through luck than through probity.

And so his challengers sit back and wait.

But what of the fact that Clarke, the chief among these challengers, is white? Is it really possible that this black-majority electorate would install a white man as mayor?

The answer appears to be: yes. Clarke himself hints that he might be tempted to make a run this year if he could achieve a head-to-head contest. His reluctance, he says, is the fear that a three-or four-way race would split the vote and reelect Barry. It was a three-way split, with former mayor Walter Washington and former council chairman Sterling Tucker, that helped Barry to victory the first time around.

But wasn't it a similar split that produced Clarke's chairmanship victory against Tucker and former councilman Arrington Dixon? And wouldn't that same sort of split help Clarke in a mayoral bid?

Not according to Clarke. By his reckoning, Tucker, the third-place finisher in 1982, hurt rather than helped the Clarke candidacy. He feels certain that he would have won most of the votes that went to Tucker had Tucker not been in the race, giving him an outright majority. (Clarke won with 44 percent of the vote.)

Jarvis, herself a formidable candidate, won't make the concession, but my sense of it is that if Clarke can avoid appearing too eager and too white, while keeping his Mr. Clean image for the next four years, he could wind up as that rare political phenomenon: a white mayor of an overwhelmingly black city.