WASHINGTON IS a town for games, be it real estate, the dinner party or the White House leak. Sometimes a game itself is the game. One of them, a daring sport of intrigue and power, is now as big as the Prince racket; it's the garden variety of what Jimmy Connors plays and is correctly referred to as: Social Tennis.

Consider the case of Lee Fentress, who was an assistant in the U.S. attorney's office when Bobby Kennedy called one day in 1966. Would Fentress, a nationally ranked tennis player and a former All-American at Tulane University, like to play? Fentress was a political fledgling, but he knew how fast to say yes. And later, no. As he recalls: "Once I had an invitation to play with Spiro Agnew on the White House courts, and it took me about a second to figure out a conflict on my schedule." Now Fentress, who says that tennis was how he first met the Kennedys, enjoys their influential friendship, is a partner in a powerful law firm and has his own tennis court in Potomac.

Not everyone is as fortunate. Consider Jean Barbiere, a British secretary who was left by then-secretary of state Alexander Haig with her racket cooling. At the recent Versailles summit, The Wall Street Journal reported that the tennis-addicted Haig was searching for suitable partners. An American Embassy official, assigned to the hunt, turned up Barbiere, a former junior competitor at Wimbledon. Barbiere was put on immediate alert. She received a call on June 2 saying to be ready at 6:30 a.m. on June 3, only to receive a call on June 3 saying to be ready at 6:45 a.m. on June 4. (She also took her tennis gear to work, just in case.) On June 4, the call came. No game.

Or, as she puts it, "I was told Mr. Haig preferred playing with men."

Social tennis can be both bewildering and amusing, but never lighthearted. "If you want to get to meet all the powerful people, you've got to play tennis," Sondra Gotlieb, the nonplaying Canadian ambassador's wife, told a reporter recently. "It gave me access to certain things," says an administration member who played with Haig. "You become a part of the entourage."

Admittedly, tennis is fun. But why else is there a 10-year waiting list at St. Albans, a tennis club where the courts are adequate, the play acknowledged by the club pro as "second class"--and the membership stellar?

The serious player knows how much social tennis can do. For example:

* David Bates, a 30-year-old assistant at the Commerce Department, doesn't have the kind of job that would give him access to the vice president. But Bates, a terrific tennis player, grew up on the courts of the Houston Country Club, where George Bush used to play. Now he's one of the vice president's frequent partners. Before coming to Commerce, he worked for Bush's unsuccessful presidential campaign. "I think maybe his tennis helped him get the job in the first place," says Sen. Bennett Johnston (D-La.), who plays with Bates as well. "It certainly didn't stand against him. The vice president is interested in tennis. But please understand--David is a very competent guy. Still, it is awfully nice to be able to play tennis with someone with whom you work."

* Jim Bayless, a 30-year-old deputy assistant secretary at the Commerce Department, also doesn't have the kind of job that would make it natural to spend off-hours with the powers of the U.S. Senate. But he's a former nationally ranked tennis player and was on the University of Texas team when it was among the top 10 in the country. Now he plays with Sens. Paul Laxalt (R-Nev.), John Heinz (R-Pa.), George Mitchell (D-Maine), Lowell Weicker (R-Conn.) and Johnston.

* Larry Barrett, Time magazine's White House correspondent, has a job that depends largely on good relations with administration advisers. Like a few other reporters, Barrett plays tennis with White House Chief of Staff James Baker. Does this help Barrett cover his beat?

"Sure, there's no question about it," responds Barrett, whose journalistic colleagues noticed him whacking balls with Baker on Barbados, site of the president's Easter vacation. "Tennis, like fishing or golf, is a good way to get to know people outside of a formal setting . . . you're more likely to get a call back in time for deadline."

One young player, who regularly smashes balls at senators, puts it this way: "You do meet a lot of people who ostensibly might provide some sort of mileage. Six months down the road you have a problem and you can call them. But it doesn't always manifest itself in a tangible reward system. And I'm disinclined to do that. It sort of reeks."

Still, some tennis partners have built solid political alliances from the dust on the courts. Both Baker and Bush were new to Houston in 1957. "Neither one of us had a doubles partner in the country club tournament," Baker recalls. "So that's how we ended up being friends."

And in 1976, when Walter Mondale returned to Capitol Hill triumphant after his vice presidential nomination, he was taken aside by Sen. Charles Percy (R-Ill.)

"There's one important thing you can do to smooth relations with the Senate," Percy said to him solemnly.

"What's that, Chuck?"

"Let us play on the vice president's court." No Aces, Please

Social tennis is also a calling card, a sport where a strong forehand is as much an indication of your pedigree as the cuffs on your khakis. Among Washington's well-to-do, it is one of life's necessities. Georgetown fund-raiser Polly Fritchey recalls telling a new-to-Washington Leah Rabin, the wife of the former Israeli prime minister, that "the thing I can offer you is the best dentist in the world and a good tennis coach."

Social tennis is never played midday. Who wants to look so idle and out of demand? The earlier the better. Former World Bank president Robert McNamara plays at 7 a.m. at St. Albans. "You've got to get there at 5 to 7 or every court is gone," says Jack Valenti, the movie industry spokesman who plays there, too. Only people who can officially sleep in--spouses and journalists--play at 8.

Social tennis is never to be confused with real tennis. "It's like going to a party," says Lee Rawls, who plays competitively at the Edgemoor Club. "Or if you're an Olympic swimmer, like going to a friend's pool. You make sure nobody gets blitzed, and if there's somebody weak on the other side, you don't embarrass them. If you do too steady a diet of it, your game can atrophy a bit."

Finally, social tennis is a fine game for political rivalries. Some years after the 1968 national election, when Eugene McCarthy was still mad at Mondale for backing Hubert Humphrey, he found Mondale playing on the adjacent court.

McCarthy, whispering to his partner, said, "Make me look good." The White House

The First Tennis Court is at the White House. Situated on a low patch of land on the South Lawn, it is surrounded by shrubbery and is undetectable to sidewalk tourists. Staffers who play there know the country club will never be the same again. "There's this overwhelming feeling of smugness," recalls Hendrik Hertzberg, Jimmy Carter's chief speechwriter. "Because even if you're losing, you can look up and say, 'Isn't this wonderful.' And it makes you feel even more like a character in a Washington novel if you get a call on the court."

Haig, while secretary of state, played on occasion at the White House. Now he's lost not only a job but the court as well. He may have to spend more time at one club he favors, the Regency Racquet Club in McLean, where, according to staff there, he places last-minute calls for court reservations.

"He never calls personally," says Edgar Lee, the Regency tennis director, who was interviewed before Haig resigned. "Someone from his office calls. It's normally a he. He always says, 'The secretary of state would like to play. What is the availability of courts?'

"We sometimes have to tell him," says Lee, "that there are no courts available. So he says, 'Will you please try to accommodate him?' Then he calls back. He's very persistent."

Wait a minute. Lee told the secretary of state that there were no courts available?

"This is a very exclusive club," says Lee. "We're in McLean, Va."

He told Haig there were no courts available?

"Sometimes a Saudi prince is in town," says Lee. "And if he books a court, you can't just go down there and say, 'Hey. The secretary of state wants to play.' "

At the previous White House, Carter himself was well-known for his desire to oversee the tennis court schedule. This became a frequently repeated example of a president too immersed in minutiae to see the large picture. Once when Carter was traveling to make a speech, then-chief speechwriter Jim Fallows actually put in a call to presidential secretary Susan Clough on Air Force One. Could he use the courts? The message came back from the president as yes--provided Fallows came up with four good jokes for the speech. Fallows put in a quick call to jokester Jerry Doolittle, who delivered. Fallows can't remember the punch lines and in fact can't even remember the jokes. "In any case," he says, "we used the courts."

Carter also had to share his courts with Mondale. Eventually, a hint of tennis rivalry developed between the two. Once when a reporter remarked to Carter than Mondale had a strong backhand, Carter was said to have replied: "I'm not afraid of it." Around Town

The courts of the St. Albans Tennis Club are generally considered the most social in town, a tradition started when the Kennedy crowd arrived there in 1962. Allie Ritzenberg, the longtime pro, had been giving Jackie Kennedy lessons at the White House the year before. "Not bad," Ritzenberg once said of Jackie's tennis. "She ran well." Soon Ritzenberg and St. Albans were it. Now the line to get in would stretch miles past the nearby intersection of Garfield and 35th streets NW.

("The only reason to join," says one St. Albans veteran, "is that it's hard to get in.") It is. Barrett, the White House reporter who plays with Baker, has been trying or, as he says, has "made his interest known." No luck yet, though.

Ritzenberg, a tanned and shaggy 63, was talking about his club one recent ay as the pleasant ponk, ponk of tennis balls sounded in the afternoon sun. "Oh, God," he says. "You get 30 letters from people who want somebody in. They're pressure letters. It's just part of Washington, and it doesn't mean they're going to get in. I keep saying in my annual letter to stop writing that so-and-so is a great guy and he should get in. Everybody's a great guy." He complains that the press' interest in his club has always been for the names, not the sport, yet he flips through the membership book, reeling off the chosen:

Columnists Carl Rowan and Clayton Fritchey, CBS reporter Fred Graham, former transportation secretary Brock Adams, former health, education and welfare secretary Joe Califano, Rep. Les Aspin (D-Wis.), Sen. Howard Metzenbaum (D-Ohio), Sen. Larry Pressler (R-S.D.), Sen. Ernest Hollings (D-S.C.), Sen. Lloyd Bentsen (D-Tex.), Walter and Joan Mondale, journalists Elizabeth Drew, Mel Elfin, Seymour Hersh, James Reston and Daniel Schorr, former protocol chiefs Lloyd Hand and James Symington, Rep. Tim Wirth (D-Colo.), FBI Director William Webster, Washington Post Co. chairman of the board Katharine Graham, banker William Fitzgerald, artist Sam Gilliam and Attorney General William French Smith.

William French Smith? What about the 10-year wait? "People like that are only here for a few years, and they're making contributions to the country or the city," says Ritzenberg. "You're not going to say no."

More select than St. Albans are the private courts. They offer less of the social tennis hustle because most guests, to be invited in the first place, are either old friends or people who have successfully completed the hustle. Ethel Kennedy's court at Hickory Hill and Teddy Kennedy's down the road are very in, followed closely by the courts belonging to British Ambassador Nicholas Henderson and Swedish Ambassador Wilhelm Wachtmeister.

"Ethel's is the most fun place to play tennis in town," says Dorrance Smith, executive producer of the ABC Weekend News. "You have the stereo blasting at 90 mph (usually ABBA, Andy Williams, Dolly Parton or the Police), there are usually three or four dogs on the court, the phone's ringing--and she's beating you." This is followed, according to Smith, "by a light lunch with a lot of Pouilly-Fuisse and banter."

Ethel Kennedy, adds Smith, "prefers men . . . her ideal is her and three men. Doubles, always doubles. She loves to hit it down your alley. She gets a great thrill out of that."

Her brother-in-law's is more sedate. No dogs, no stereo. Ted Kennedy also prefers strong players and, over the years, has acquired a few to improve his game. One well-known local competitive player remembers being called by Kennedy 12 years ago, just like that. He played, and then was asked back, and asked back again. "Once he gets your telephone number and feels familiar with you," says this player, "he'll keep calling." Does he ever see him in any other context?

"No," says the player, who begs for anonymity. "I don't even tell people I play tennis with him. If my name were linked with his, I don't think he'd invite me to play anymore." Match Point

Of course, not everyone can play at Teddy's or Ethel's. But it doesn't matter; social tennis can happen anywhere. "The tennis court in Washington is like the pool hall in Chicago," says Mark Plotkin, a D.C. City Council candidate who has haunted Washington courts for a decade. "It's where you hang out."

Just remember. In social tennis, it's not whether you win or lose--but with whom you play the game.