Washington's illegal numbers racket is booming, with profits as large as they've ever been, despite the introduction of the District's first legal gambling last August, according to D.C. police officials.

D.C.'s illegal numbers trade flourishes, say police officials and lottery specialists, because it offers benefits to players that the D.C. government's game doesn't, including credit, winnings that can be hidden from income tax, the ability to make smaller wagers, and the mystique of guessing the winning three-digit number.

The "street number" also offers winners bigger payoffs than those the D.C. Lottery Board plans to offer when it introduces its own three-digit numbers game, planned for this summer, the officials and experts say.

For these reasons, matching the illegal game against the legal lottery "is like two guys in a boxing ring, one with an arm tied behind his back," said Howard Klein, associate publisher of Gaming Business magazine in New York and an expert on legal and illegal lotteries.

"We expect the illegal numbers game to continue to flourish" in spite of any legal games, Inspector Kris Coligan, chief of the D.C. police morals division, said yesterday.

"Obviously, a legalized lottery is not going to stop the illegal numbers game that we have now," said police chief Maurice Turner, citing a similar pattern in other cities where legalized gambling has been introduced. "It the illegal numbers business is a very profitable business employing hundreds of people and multimillion dollars of money."

Local police officials disagree with people who say the numbers racket is a victimless crime. "A lot of poor people have bankrupted themselves playing it," said one D.C. police official who asked not to be quoted by name. "Most of the winnings exist outside of the income tax system that we all pay into."

Police officials' statements that the illegal numbers game is thriving contradicts statements by proponents of D.C.'s legal lottery, who argued before the November 1980 city referendum that legal wagering would drastically cut the income of the underground numbers trade.

D.C. police officials estimate that the city's illegal numbers industry is enjoying gross revenues of up to $250 million a year, according to one member of the gambling squad. By comparison, the D.C. Lottery Board says its games have grossed about $54 million since it started operating last August. D.C. lottery officials say they expect the city to gross $100 million from the planned legal numbers game in its first year of operation.

The "street number" has thrived in virtually every jurisdiction where a legal lottery has started up, Klein and various police officials said. Many legal lotteries have used expensive marketing campaigns to try to persuade long-time illegal numbers bettors to switch to the legal game, by all accounts.

Illegal numbers is a decades-old tradition for many D.C. residents, especially poor people, for whom it can be a break from a humdrum existence. It's a way of life for bus drivers, teachers, housewives and others who pick their lucky number based on anything from birthdates to license plates. Legends have abounded of poor cleaning women who hit the number for $100,000 and retired to Florida.

Local prosecutors don't view the numbers racket as a top priority. Judges and juries almost never jail numbers operators, especially the lowly numbers runners, many of whom are elderly. When D.C. police arrested 20 people on lottery charges last week, for example, a number of them in their late 70s struggled into police headquarters on canes.

In most cases, D.C. police officers arrest suspected numbers runners for operating a lottery, a felony. But the U.S. Attorney's office often enters a plea bargain for a guilty plea to possession of numbers slips, a misdemeanor. The average fine is $50, officials say.

"With so many homicides and rapes in this town," said one prosecutor in the U.S. Attorney's office, "there's no way we can use our felony resources on the gambling cases."

"We don't like the disposition given to our gambling cases," said Coligan. "It does become frustrating."

Police officials say that some of the city's top numbers operators have engaged in other criminal activities such as drug trafficking. But in most respects, they say, the city's illegal numbers game resembles any well-run business, and it tries to be competitive.

None of the 17 states that have operated legal lotteries have offered credit to gamblers, lottery experts say, but almost all illegal numbers operators do.

Lotteries allow gamblers to wager as little as a nickel or a dime, but state lotteries have higher minimum bets. In its current "Loose Change" game, the D.C. Lottery Board allows only one bet, $1, and it plans to have a minimum bet of 50 cents in its numbers game.

The payoffs are generally better in the illegal games. D.C. officials say they will pay 500 to 1 in the planned numbers game. But the street number pays 600 to 1, police say.

In its current "Loose Change" game, the D.C. Lottery Board pays out 48 percent of its gross revenue in prizes to bettors, and plans to pay out 45 percent of its gross from its planned numbers game, Lottery Board spokesman Lea Adams said. By contrast, local illegal numbers operators pay out up to 60 percent of their gross to gamblers, police officials said.

The general rule is that illegal lottery winners pay the numbers runner 10 percent of their winnings. But winners in the illegal game can hide their windfall from the IRS, whereas legal lottery operators notify the government about big winners.

The Internal Revenue Service has estimated that during the late 1970s, the annual nationwide total of unreported income derived from illegal numbers games totaled some $3 billion.

D.C. police gambling investigators expect that when D.C. starts its new numbers game, the city's illegal lottery will likely counter with a new game using the daily legal number as the winning combination.

As in other jurisdictions that have introduced legal numbers games, the new illegal game would be in addition to the existing illegal numbers game, in which the winning three-digit number is computed with a complicated formula involving the winning horses at local race tracks, police say.

Such a copy-cat game would repeat what happened in 1976, when Maryland started its legal numbers game, said Sgt. Peter Edge of the Maryland State Police's gambling squad. Legal numbers "doesn't dampen the spirits of the people who run illegal lotteries one bit," Edge said.

One who disagrees is Duane Burke, president of the Rockville-based Public Gaming Research Institute, a prolegal lottery research group. Burke said he believes that legal lotteries usually eat into the profits of illegal numbers operations.

But Burke said that to be profitable, legal lotteries must compete fiercely with illegal operators for bettors. "It is directly competitive with the illegal game," Burke said. "You're setting up a competing business next door."