Washington's instant lottery appears to be developing into a middle-class game in which the very poor and the very rich are the least likely to participate, contrary to the concern that it would be played most heavily by those who could least afford it.

According to a Washington Post poll, the highest rate of participation in the lottery appears to be among people with household incomes between $8,000 and $30,000 a year.

In those groups, which include nearly 60 percent of the city's families, 7 out of 10 persons had played the lottery at least once in its first 2 1/2 weeks of operation.

For people earning $30,000 to $50,000 a year, the poll found that 6 out of 10 had played the lottery.

The lowest rates of participation were found at the high and low ends of the income scale, according to the poll. Among those with annual household incomes under $8,000 and above $50,000, 5 in 10 people had bought at least one ticket, and persons in those groups who play the lottery tend to buy fewer tickets than more middle-income players.

Similar patterns were found in an informal survey taken by the chairman of the city's lottery commission.

U.S. Census Bureau figures, based on the city's white and black residents, indicate that in 1980, the most recent figures available, 10 percent of Washington families earn more than $50,000 a year, and about 20 percent earn $7,500 or less a year. Just more than 12 percent annually earn between $35,000 and $50,000, the data shows.

"It is not a black, ethnic game supported principally by the poor," said Jerry Cooper, a member of the D.C. Lottery and Charitable Games Control Board and chairman of its lottery committee.

Cooper, after reviewing lottery sales in each of Washington's eight wards, said he believes the greatest number of tickets are being sold in places where Washington's more well-to-do live and work.

"My initial impression is that it was a game played by people who are more affluent . . . that basically they are people who live in or visit those areas, and they are not predominantly poor," Cooper said.

The Post's finding, from a poll taken Sept. 8 and 9 of 813 prospective voters in the city's Democratic mayoral primary, is not a random survey of all people who have participated in the city's instant lottery.

It does not include Republicans, independents or Democrats who said they either were not registered to vote or did not intend to vote. But it does provide at least a rough gauge of trends that had developed among the game's players in the first weeks of the lottery.

The poll found that nearly 8 out of 10 people living in Ward 8, east of the Anacostia River, who were contacted, have bought at least one D.C. lottery ticket, making it the area with the highest percentage of people who have played.

But in terms of the numbers of tickets players have purchased, people in that generally low-income ward participate no more vigorously than those living elsewhere in the city.

In fact, the poll indicates that people living in neighborhoods around Capitol Hill and in Ward 4 (upper Northwest, east of Rock Creek) are more likely to be heavy players, having bought more than 11 tickets within the first two weeks of the game, than people living in the city's lower-income sections.

The poll shows that in Wards 1, 2, 4, 5, 6 and 7, which cover all of the city except far Northwest and most of the area east of the Anacostia, about 6 of 10 residents had bought at least one ticket. In Ward 3, the generally affluent area in far Northwest, 5 of 10 had played the game at least once.

In terms of numbers of tickets bought, the poll showed that Ward 6 had the highest percentage of heavy players, with 40 percent reporting they had bought more than 11 tickets in the first two weeks of the lottery. Ward 4 was second, with 37 percent heavy players, compared to 36 percent in Ward 8, 33 percent in wards 1 and 2, 26 percent in Ward 7, 25 percent in Ward 5, and 12 percent in Ward 3.

Tom Skarzynski, a spokesman for the Maryland State Lottery, said the typical lottery player there is also decidedly middle-class: 39 years old, a high school graduate, with two children and a combined family income of $22,000.

The Post poll and Cooper's survey suggest that many lottery players here are people like Dave Gwyer and Dan Stinnett, data processors for the Federal National Mortgage Association, who walked the block or so from their offices near Tenley Circle NW to a liquor store early this week with only one intention: to purchase D.C. instant lottery tickets.

"You'll never know when you'll hit the big one," Gwyer remarked to Stinnett, as they entered Leed's Beverages at 4201 Wisconsin Ave. NW.

Both went directly to one of the store's check-out counters and stood by patiently as the cashier tore off a strip of 11 lottery tickets. Stinnett paid for them, using a combination of winning tickets and cash.

Gwyer, dressed in a dark blue, pin-striped suit, looked on with a boyish grin. The suspense was obviously not overpowering. The two returned to work without scratching off the tickets' silver coating to see if any of them bore winning numbers.

Stinnett, who recently won $5 on a lottery ticket, promptly cashed those winnings in for more tickets because, he joked, "I don't want to win $5. I'm looking to retire."

Gwyer said he is a fairly regular player and most of his friends and the people he works with have played D.C.'s instant lottery. So, he said, he is not surprised to learn that the lottery seems to be a middle-class game.

"Everybody is looking for an easy way," he said.

The Post poll found Washington's homeowners and renters play the D.C. lottery in nearly equal percentages and frequency.

But blacks tend to be heavier players than whites, according to the poll. The Post found that 35 percent of blacks polled were medium players, having bought between 5 to 10 tickets, and 35 percent were heavy players, buying more than 11 tickets. The rest said they were light players, having bought fewer than five lottery tickets in the game's first two weeks.

On the other hand, the poll showed that 39 percent of the whites polled were medium players, 20 percent heavy players and 41 percent light players.

Even in predominantly white Ward 3, where the poll showed that only half the residents had tried the game, Nourddine Mohammed said he has seen his share of frequent lottery ticket buyers.

Mohammed, a cashier who mans the lottery check-out counter at the Peoples Drug store at 49th Street and Massachusetts Avenue NW, said he has been astounded at the number of tickets his customers will buy. With disbelief in his voice, he added that he has had some customers who will buy only one ticket at a time, but return to the drugstore over and over during the day, buying one lottery ticket each time.

"I've seen them come in and buy $70 and $80 worth," he said. "They come in to buy a pack of cigarettes and spend $15 to $20 for lottery tickets."