The gambling initiative on Tuesday's ballot will give District voters an opportunity to vote yes or no on legalizing city-operated numbers and periodic lottery games; parimutuel wagering on commercially operated jai alai and dog racing; bingo and raffles conducted by charitable and other nonprofit organizations, and social betting, such as private poker games.

The legislation, drafted by gambling proponents, comes after City Council refused last year to act on the issue. The D.C. Committee on Legalized Gambling, the city's chief pro-gambling organization, collected 21,462 signatures from registered District voters to guarantee the question's place on the ballot. The signatures of 12,241 registered voters, 5 percent of the total as of May 1979, were required.

Proponents say legalized gambling will:

Provide the financially troubled District with as much as $30 million in revenue now spent on the Maryland lottery.

Provide money for unfunded service programs in the District.

Bring as much as $25 million into the District from new D.C. players who have not tried the Maryland game, and from Maryland and Virginia residents.

Discourage D.C. residents from spending additional dollars in retail establishments outside the District when they go to buy lottery tickets.

Curb illegal betting (numbers) operations.

Opponents say legalized gambling will:

Encourage gambling among the aged, poor and minorities, those least able to afford it.

Contribute to an increase in crime.

Discourage people from seeking employment, thereby adding to the welfare rolls.

Pave the way for casinos and other large-scale gambling operations, and open the door to possible corruption.

Allow the loosely defined Commission on Gaming , a five-member board which would be appointed to oversee the operations, to function as a separate governmental entity without stringent guidelines for its supervision or control. The board's executive director would be a GS-16 and make no less than $47,900; the board chairman would earn $18,000, and each board member, $15,000.