HARVARD, Mass. — A steady flow of customers pulled up to the Harvard General Store one recent afternoon, picking up groceries, beer and wine, or prepared foods like quiche lorraine and split pea and ham soup.

But lottery tickets, a lucrative staple of convenience and liquor stores in nearly every corner of Massachusetts, were nowhere to be found. In fact, the entire town forgoes the scratch-ticket business, standing on the sidelines of a nearly $5 billion enterprise.

At least when it comes to playing. One of just a handful of towns east of Worcester where no lottery tickets are sold, this well-to-do community of colonial farmhouses and apple orchards still received $1.3 million in state lottery aid last year, more than the total of a half-dozen surrounding towns.

Stores in those towns along the Interstate 495 beltway, including Ayer, Boxborough, Lancaster, Littleton and Shirley, sold almost $25 million in lottery tickets last year, and most are larger and less affluent than Harvard.

But in an anachronistic quirk of the lottery aid formula, a complex calculation that determines how $1 billion in lottery proceeds is divvied up among cities and towns, Harvard receives credit for population it had in the 1990s, when Fort Devens was an active duty military base.

"We're lucky," Harvard Selectman Stu Sklar said of the town's lottery aid, which last year fully financed the town's police department. "Those are the rules. We didn't make them up."

While an outlier, Harvard's lottery subsidy speaks to a broader problem, critics say. By not accounting for ticket sales, the formula generally favors wealthier towns, where residents buy fewer tickets. Towns with high per-capita lottery spending wind up receiving less in aid than they paid in.

"I don't think that's fair," said state Representative Steven Howitt, a Seekonk Republican. Howitt and state Senator James Timilty, a Walpole Democrat, are sponsoring legislation that would cut lottery revenue to any town that "does not provide opportunity for sales" of lottery tickets.

Seekonk, a town of 13,500 on the Rhode Island border, is more than twice Harvard's size and has much lower property values, Howitt said. Its lottery sales, $20 million last year, ranked among the top 20 percent in the state.

Yet Seekonk received $1.1 million in lottery aid, $200,000 less than Harvard.

"I just think there should be some weight given to sales," Howitt said.

But the likelihood of change may be slim. The lottery formula has come under criticism for years for shortchanging the towns that play the most. But legislators have been reluctant to overhaul the system, realizing some communities will be incensed.

By giving weight to population and real estate values, the formula seeks to distribute money to the communities that need it most. But lawmakers have long upheld the principle that cities and towns that have come to rely on a certain level of lottery funds should not be penalized for circumstances beyond their control, like a base closing.

As a result, Harvard still receives credit for thousands of personnel once stationed at Fort Devens, which also lies in Ayer and Shirley.

Timothy Bragan, the Harvard town administrator, said he has heard grumbling about the town's lottery share before, but doubts lawmakers will do much tinkering with the formula. Opposition, he said, would be swift.

"Of course Harvard would fight it," he said. "We would be on the phone immediately with our state senator and state representative."

A town of about 6,000, Harvard has only three retail outlets, which choose not to sell lottery tickets.

"It's not up to the town to peddle lottery tickets, or push it on retailers," Bragan said. "We don't say it's not good for the community. We take no position."

Geoffrey Beckwith, executive director of the Massachusetts Municipal Association, which represents cities and towns, dismissed the idea of considering sales in the distribution formula.

"These are communities that are rural and have no commercial base," he said. "But their residents play the lottery someplace else."

Revising the formula would pit communities against another, he said, describing Harvard as an anomaly.

"It's a big state," he said. "You will always be able to find an outlier or two."

Scott Hayward, owner of the Harvard General Store, said he has been meaning to add lottery sales, even though he can't recall a single customer asking for tickets in recent years. But it's a pretty low priority, and he hasn't gotten to it just yet.

Joe Hutchinson, a Harvard resident who stopped at the store, said lottery sales would run counter to the "authentic" character of the store, which stands between Harvard Common and an 18th century cemetery.

Plus, in a state with 351 towns, the next one over is never too far.

"Not many people in Harvard want to buy lottery tickets," said Kenneth Morin, who works at the store. "And if they do want them, they can just drive up the road to other towns."

(Click to display full-size in gallery)An example of the disparity in lottery distribution of money to communities.