Many liquor store owners in Washington have an added interest in this year's campaign for mayor. The reason: a few weeks after the crucial Sept. 14 primary, the city government will decide on which liquor and grocery stores and other businesses will be awarded terminals for the city's new legal lottery.

Many expect the terminals to be the biggest plus for the liquor stores since the end of Prohibition--not in profits from selling lottery tickets, but rather from the spinoff business of selling beer, liquor, soda and other goods to those who come in to buy lottery tickets.

Some predict that any store with one of the coveted terminals could triple or even quadruple its business. That has been the case in neighboring Maryland, which for years has had a legal lottery and numbers game--to the envy of many Washington merchants, especially those with stores near the District line.

The lottery is expected to generate big bucks--at least $1 million a week in gross sales. Of that amount, 50 percent would go back to the bettors as winnings at a payoff of 500-to-1, another 30 percent would go into the city's coffers and the rest would be used for lottery operations. Barry has already included $26 million in the city budget for fiscal year 1983 from anticipated lottery revenues.

City store owners would like to get in on that game, but the catch is, you gotta have a terminal to win.

Brant Coopersmith, chairman of the D.C. Lottery and Charitable Games Control Board, says there will be only 200 terminals. The city has 355 liquor stores alone, not to mention the thousands of grocery stores, drugstores, novelty shops and newsstands also looking to boost business.

Coopersmith says the board alone will select the sites for the terminals--not the mayor or the mayor-elect. The final decisions will be made in October or November, he says.

With that in mind, several liquor store owners have given generously to the reelection campaign of Mayor Marion Barry--the man who will be in power when the decisions are made, regardless of the outcome of the primary. Barry has attracted more than a dozen contributions from liquor dealers in the first seven weeks of fund-raising, including the maximum contribution of $2,000 from one liquor dealer. Some of those who gave acknowledge in private that they gave to Barry with an eye toward improving their prospects for being awarded a terminal.

"I'm hoping the process won't be political," says Douglas Gordon, the executive director of the gambling board. "But I'm not naive. I'm not so foolish that I don't think there will be an attempt to make it political. The board will have to deal with that."

"They are wasting their money if they think they're buying a lottery terminal with campaign contributions," says Coopersmith. "The 200 will be chosen by objective criteria--economic criteria: Where is the biggest play likely? Where is there the most traffic of people who want to buy the tickets? . . . I admit, liquor stores are very good for this kind of thing."

The board will have some help in finding out which outlets could sell the most lottery tickets when the city begins an instant lottery game in early August. The instant game, like the lottery to come later, is expected to generate big money--about $20 million in gross sales in eight to 10 weeks, according to Coopersmith. Tickets for that game can be sold by any business in the city.

Theoretically, every business would also have a shot at one of the 200 lottery terminals. "Any retail establishment or service establishment will be eligible," says Coopersmith, "so long as they have a business that is not dependent on the lottery."

Businesses that lose in the first round could get a second chance. Coopersmith says there would be an undetermined number of hardship cases--instances where store owners complain that they are losing money because a neighboring competing store has been given the advantage of having one of the first 200 lottery terminals.

In such cases, a terminal may be given to the merchant who claims hardship. Coopersmith says he favors leaving the distribution of such terminals to special task forces in each ward of the city.

Coopersmith concedes that those task forces could become highly political playgrounds. But, he says, the mayor will not have a seat on any task force, so any politics should be on a neighborhood level--not the citywide type.

The most logical place for any citywide politics to occur is in awarding the 200 main terminals by the five-person commission--whose members all are appointed by the mayor. But Coopersmith says that shouldn't happen either. The mayor, he says, will play no part in the decision making.

Some of those liquor store owners who contributed to Barry are saying, "Well, maybe, maybe not." Like many other businessmen in town who have given generously to Barry's reelection drive, they don't see any danger in covering themselves with a bet on the incumbent.