In the face of legal competition from Maryland's lottery, gamblers in Washington have started a second illegal numbers game -- this one based on the Maryland number.

The new nightly numbers game in the city has become so popular that law enforcement sources believe it has increased by as much as one-third the take on the $200-million-a-year illegal numbers business.

For years the illegal daytime numbers game in the city has attracted thousands who place bets with a "runner" who provides door-to-door service, or with their cleaners, shoeshine man or contact in government offices and courthouses.

The business here has been overseen by a handful of gamblers who are described by law enforcement sources as astute businessmen. They select the winning three-digit number by often complex formulas based on results at nearby racetracks.

After the state of Maryland began a daily lottery three years ago, backers of gambling organizations in the city observed that some of Maryland's most faithful customers were Washington residents who went to the supermarkets and liquor stores along the Maryland-D.C. line to bet the number legally.

The city gamblers decided, in response, to offer the nightly service themselves -- using the Maryland number. Persons familiar with the gambling business here say that numbers operators now often accept bets for the nighttime number at the same time they accept bets for the daytime number. Others make themselves available to bettors a second time to see if they want to bet the nighttime game.

In the illegal games, bettors place their money -- nickels and dimes in the past, but now usually in the 25 cents to $1 range -- on a three-digit number.

If the bettor wins, he is paid off on what gamblers compute as 600-to-1 odds. Law enforcement officials say the odds are usually considerably lower because gamblers often decide not to allow bets on certain numbers that have been bet heavily in the past.

In the illegal daytime game, news of the winning number filters back to the streets. One advantage of the night game is that bettors learn of the number by watching it be drawn on television by agents of the official Maryland lottery system.

Another advantage, sources said, is that the Maryland lottery is perceived to be an honest system that would be difficult to manipulate. Gamblers mistrust some racetracks and often switch the tracks they use to compute the daytime number and change the way it is calculated. Currently, the daytime number is computed on the combined results of six daily races at Timonium racetrack north of Baltimore.

Law enforcement sources said the nighttime numbers business has become so popular in Washington that some gambling organizations have had to expand or set up separate subsidiaries to handle the increased business.

Evidence seized in one recent raid of a gambling organization in the city indicated that the nighttime take accounted for about one-third of its business, law enforcement sources said.

Some gamblers have said that the nighttime numbers business has become so attractive that they are considering eliminating the illegal daytime game altogether, sources said.

If such a change occurred -- and law enforcement officials doubt that it will because of the tradition of the daytime numbers business here -- it would be the most significant change in recent memory in the decades-old numbers business here.

"The majority [of gamblers] have found that if you deal with both [the daytime and nighttime numbers] you can make a hell of a lot more money" said Washington gambling squad detective Walter Staples. He said it is difficult to determine what percentage of the Washington gambling business is based on the nighttime number, but he noted that it has been growing in recent months.

Staples said that one investigation showed that one gambling organization split into two parts recently, one to handle the daytime business and the other to handle the nighttime flow.

The illegal gamblers who use the nighttime number offer numerous advantages over the legal system, various law enforcement officials said.

Illegal gamblers will provide credit to their customers, will allow them to bet the same number (known as "keep-ins") for an indeterminate amount of time, and will accept bets by telephone or through intermediaries or runners. To bet the legal system, customers must make a trip to Maryland and pay cash.

Maryland's lottery turned over an estimated $120 million last year to the state treasury and about $145 million to winners.

The District of Columbia government had planned a referenderendum on legalized gambling this fall for the purpose of establishing similar lottery. The referendum was postponed after vigorous objections from the city's politically powerful Baptist ministers.