The District of Columbia's instant lottery is spending a greater percentage of its total revenue on administrative and overhead costs and giving a smaller percentage to the city government than all but two of the 17 other lotteries in the country.

Of the $40 million that the D.C. lottery board has collected in its first five months of operating the instant lottery, it has spent 24 percent of that amount on costs, including advertising, sales promotion, tickets, a consultant's advice and workers' salaries.

Only Maine and Vermont, both with much smaller lotteries than the District, spend the same or a higher percentage than the local lottery on administration and overhead, 25.7 and 24 percent respectively.

At the same time, by sending 30 percent of its total revenue to the city government, the D.C. lottery also ranks 16th among the nation's 18 lotteries in the percentage of revenue that goes to government coffers, again leading only Maine and Vermont, where 25 percent of lottery revenues are sent to the state treasuries.

The D.C. lottery board returns 46 percent of its revenue to players in the form of cash prizes, a lower percentage than all but three states--New York (44.4 percent) and Washington and Arizona (both 45 percent).

In general, smaller lotteries have higher administrative and overhead costs and return less money to government treasuries. But in both categories the District ranks behind some smaller operations, such as that of Rhode Island, for example, which takes in less than half the annual revenues of the D.C. lottery but spends only 16.2 percent of that amount on overhead.

The chief reason the D.C. lottery board spends so much on administration and overhead is that, unlike any other lottery in the country, it has contracted with a private firm--a joint venture of a Washington firm named Games Production Inc. and Scientific Games Inc. of Atlanta--to run its first four instant lottery games, and possibly a fifth.

Under the joint venture's agreement with the lottery board, Games Production is paid 7.8 percent of the proceeds from all ticket sales, which possibly could amount to $7.8 million in the first year of the lottery's operation, assuming the purchase of $100 million worth of lottery tickets.

Scientific Games, the dominant company in the lottery ticket industry, also is paid 1.2 percent of the total revenue to act as a consultant to Games Production and the D.C. lottery and about 3 percent for the tickets.

"It's a very rich contract," said lottery board Chairman Brant Coopersmith.

Coopersmith said the contract to operate the instant lottery games was awarded to the Games Production-Scientific Games joint venture despite the fact that it presented the highest bid--by about 2 percent--among the three firms seeking the contract.

But he justified the contract award on grounds that the combination was "the best simply because they had Scientific Games. They were just better experienced. They knew their business better."

The lottery board chairman also defended the hiring of a private firm to operate its instant lottery games.

"We did it because we wanted to be on the street quickly" with the instant lottery game, Coopersmith said. "It was difficult to develop a management capacity [so the city government could run its own game]. We would've been a lot longer getting on the street.

"Scientific Games had started 11 of the first 15 states" with instant games, Coopersmith said. "We had to start well. If we got off poorly, the press would have killed us and Congress would have killed us."

In addition to the amounts paid Games Production and Scientific Games, a Games Production subcontractor, LaMancha Inc., receives 4 percent of the gross revenue for advertising and promotion. Six percent more is paid in commissions to storekeepers who sell the lottery tickets, while the remaining 2 percent goes for salaries and expenses of the five-member lottery board and their 40 staff employes.

Coopersmith acknowledged that the D.C. lottery's overall 24 percent overhead was high, in part because of necessary start-up costs, and said that such expenses would have been cut if the lottery board had not hired a contractor to run its games.

However, he said that if it had taken longer to start the first game, and if it had been run solely by the city government, the city's percentage share might have been higher but the total revenues would have been sharply lower, and so would the amount sent to the city treasury.

The lottery board expects to send $26 million to the cash-strapped city treasury in the current fiscal year and more than $40 million in fiscal year 1984, which starts Oct. 1.

Gloria A. Decker, Games Production's general manager, said the firm's pact with the city is a "costly contract for Games Production. It isn't something you do without overhead."

Decker described the 7.8 percent paid to Games Production as "a fair figure," and said the overall 24 percent overhead figure is "very much in line" compared to a small state. "Compared to Pennsylvania, New York and New Jersey, it seems high," she said."

While currently preoccupied with consideration of the bids by three firms who want to run the city's planned daily numbers game, the lottery board eventually will have to decide whether it wants to continue to have a private company operate the instant lottery games, or possibly to take over some of the functions that Games Production now handles.

Decker said that Games Production warehouses the lottery tickets, distributes them, keeps accounting records, trains lottery sales agents and transfers revenue to the city.

The D.C. lottery's revenues are expected to climb sharply with the expected summer start-up of the daily numbers game similar to the one now operating in Maryland. In this form of betting, players select their own three-digit number and then wait to see if it is selected as the winning number in a daily drawing.

Since the daily numbers game does not require as many people to operate as the instant lottery games, D.C. lottery officials said, the percentage of overhead and administrative costs should decline.

As the District gains more experience in the overall management of its lottery, Coopersmith said, "the big policy issue will be what percentage of total revenues goes to the city and how much to the players. We're going to experiment giving more money to players to see if they buy more tickets. We may just up it to 55 percent," from the present 46 percent.

The lottery board recently announced that it would try to renegotiate downward the percentage that Games Production and the city would receive during the fourth instant game, which likely will be in operation next summer, so that in addition to cash, free tickets could be awarded.