The winning formula for Tuesday's special D.C. City Council election probably won't be one copied from the few pages of the city's young political history. But it may not write a chapter of its own either because the election itself is unique.

It will be the first special election in modern city history. It will take place in the middle of the hot summer vacation season. Only one office is at stake and only one election victory is necessary to win it.

With 10 candidates in the field and fewer than 25.000 persons expected to vote, as few as 6,000 votes could win the race and fill the at-large Council vacancy created by the March 23 death of Julius Hobson Sr.

So this campaign has been one of novel approaches and uncanny political game plans. Even some of the four leading candidates -- not one of whom has run for citywide public office before -- have political strategies that go somewhat against the grain of this city's still young local political tradition:

Paul Hays, the Republican candidate has virtually ignored ward three make up his small party base in this overwhelmingly Democratic city may be on vacation on election day. So Hays has placed a heavy emphasis during his campaigning on absentee ballots.

Independent candidate Barbara Sizemore's campaign strategists hope to score a coup on the city's established political "experts." Their candidate has virtually ignored ward three, the largely white area west of Rock Creek Park. Conventional wisdom has in that a good showing in ward three is essential to any citywide campaign because that ward has more voters than any other in the city and they go to the polls in higher percentages than anyone else.

Instead, Sizemore is concentrating on Northeast and Southeast Washington -- specifically wards five and seven mostly black largely working class areas where voting strength has grown significantly in the past several years.

By contrast Hilda Mason the endorsed D.C. Statehood Party candidate and independent Susan Truitt both have more conventional strategies. Both have focused on ward three and ward four, the mostly black, middle to upper middle-income area of Northwest Washington east of Rock Creek Park.

Truitt lives in the Cleveland Park area of ward three and has the sup-area of some highly visible community residents in ward tour. Mason has twice been elected to the school board from ward four and has the support of Democrat Polly Shackleton the current City Council member from ward three.

Adding an interesting sidelight to the race is the fact that two of the city's traditional power bases have lined up behind opposing candidates. Most of the city's top elected officials have endorsed Mason, while many of the city's black clergy appear to be solidly behind Sizemore.

"This is going to be a very funny election." Mason said recently.

"It's a good thing," said Sizemore campaign manager Chuck Green "that nobody owns this town."

The other candidates in the race are Leo A. Murray and Frank E. Sewell Jr. of the Statehood Party, independents Richard R. Clark and Wade H. Jefferson, Susan Pennington of the U.S. Labor Party and James Clark of the Jii Lunaa (Black Poor People's) Party.

Hilda Mason, a 61-year-old former school board member got a slight jump on the other candidates when the Statehood Party's central committee chose her to be Hobson's interim successor as provided by city law.

Mason has campaigned almost like an incumbent avoiding controversial stands on issues and arguing that through her long involvement in city human rights efforts and her experiences on the school board she has the best background for the job.

Her political base is in ward four from which she was twice elected to the school board. In order to broaden that base and that of the Statehood Party -- which has only 1.692 registered voters -- she has turned to the city's Democratic Party. No Democrat is running in this election because the party already holds the maximum at-large representation allowed on the Council by city law.

So ranking individual Democrats --including five City Council members, Del Walter E. Farmroy and most of the party's state committee leadership --bringing with them workers, political contacts and a few additional funds.

Among the most active Democrats in the Mason campaign is Council member Marion Barry, a possible mayoral candidate in 1978 who considers his own reputation on the line. The campaign has become a grudge war of sorts involving Barry and one of his arch enemies on the Council, Douglas E. Moore, the outcast Democrat.

"The motivation of many Democrats is not against Barbara Sizemore," Barry said. "It'sDoug and the other people who are supporting Sizemore that other Democrats want to get at."

Trappings of Moore's political style abound in the Sizemore campaign from her frequently stated assertion that she will be "unbought and unbossed" to the very campaign strategy itself which appears to be partially based on Moore's 1974 election.

In that year, Moore outpolled 16 other candidates for at-large council, seats including Barry. He did it on a low budget campaign -- like Sizemore's --in Northeast and Southeast Washington.

Sizemore, the 49-year-old former superintendent of the city's schools, picked up a major boost last week when she got the unanimous support of the Baptist Ministers Conference of Washington, D.C. representing more than 50 churches mostly in the city.

Sizemore whom one supporter described as a "going to-church-on-Sunday Baptist" had very high visibility at the churches and was generally received well. Her opposition to legalized gambling decriminalization of marijuana and Gay Pride Day whom her support among ministers.

Sizemore, an independent, probably has greater name recognition than any of the other candidates as the result of the well-publicized two stormy years she served as head of the city's schools. Some of her support is expected to come from those who feel the city school board was wrong when it fired her in 1975 charging her with inept administration.

Hays, Republican candidate and Truitt, an independent who has secured some Republican support and financial backing are sure top carve up the predominantly white, middle to upper income ward three and parts of ward four, conservative and moderate blacks live, political observers say.

Hays, chairman of the D.C. Republican Central Committe, has engaged the party machine in his attempt to win the Council seat. For months, party workers have been calling the city's estimated 28,000 registered Republicans, 45 per cent of whom live in ward three Hays said, urging them to vote.

"We intend to reach every Republican by mail or by phone by election day," he said.

Hays is also seeking votes in ward two, the ward with the second highest number of Republicans, and support in ward seven and ward six, his home ward.

During his campaign, Hays has urged those Republicans who will be out of town during the election, to vote by absentee ballot.

Truitt, who is hoping that her exposure as a television reporter for two local stations will win her support in all areas of the city, has focused on wards three and four as well.

"But I'm counting on pockets of support throughout the city," Truitt said. "Wherever I go, in any part of the city, I've run into people who say 'Hey -- aren't you the girl who used to be on TV?'"

The remaining six candidates in the campaign are not as well known as the major four, but some feel their chances for winning have been improved because there are so many candidates in the race and so few voters are expected to turn out.

Some of those candidates, who have been campaigning on broader goals of social change, economic prosperity and the need for openness in government, have been reluctant to discuss their campaign strategies with reporters.

When asked specifically what wards her winning votes would come from, Pennington said, "You're not going to get me to answer a bourgeois question like that."

Richard Clark wouldn't discuss campaign strategy either, saying, "Would a general reveal his battle plan?"

While some at-large candidates in the past have raised as much as $40,000 for their campaigns, money was scarce in this election, with most of the bigger contributions coming from the candidates themselves. Mason gave $14,000 towards her $21,452 campaign fund. Truitt's $16,685 was included $9,000 loaned by the candidate to her campaign organization.

Even these amounts were astronomical when compared to those of other candidates. Sewell, for example, had spent only $30 on his campaign last week. James Clark tried to cut campaign costs by using hand-made campaign signs and paraphernalia.

In candidates' forums, there have been no single issues that have sharply divided candidates, although voters have been concerned about rent control, high property taxes, delivery of city services and improving the city's tax base.