The D.C. Lottery Board announced yesterday that it will start its third instant-winner lottery game next week, a contest in which for the first time some players will win free lottery tickets in addition to cash prizes.

Tickets for the game, called Loose Change, will be sold starting March 9 and will differ somewhat from those used in the first two scratch-off ticket games that the lottery board has sold since it started legalized gambling in Washington last August.

In the new game, players purchasing the $1 tickets will scratch off the surface of five circles resembling coins to determine if the total is more--or less--than $1.

If the value of the five coins is more than $1, the player will win the prize listed in the ticket's Prize Box--a free ticket to play again or cash awards of $2, $5, $10, $20, $100, $10,000 or $20,000. If the value of the five coins is less than $1, the ticket is a loser.

In the new game, which will run for eight to 10 weeks, players will have a 1-in-5 chance of winning at least a free ticket and a 1-in-10 chance of winning cash, according to Gloria A. Decker, general manager of Games Production Inc., the private firm hired by the lottery board to run its instant-ticket games.

At the end of the game, the lottery board also plans to stage a drawing in which one person who has won a $100 prize during the Loose Change game also will win $1 million in $50,000 increments over 20 years. Three others will win $100,000, $25,000 or $10,000; and 16 will pocket $1,000.

The lottery board's current D.C. Double instant game, in which players must match like amounts on a scratch-off ticket in order to win that amount, ends tomorrow. Decker said about 23 million tickets will have been sold in the four-month-long game, well short of the 30 million ordered by the lottery board.

About 19.1 million tickets were sold in less than two months in the city's first instant game last year.

Chester C. Carter, the board's executive director, said the lesson learned by comparing the first two games "is that you can't let a game go too long." Carter said the Loose Change game will be ended after eight weeks if sales are lagging.

Games Production yesterday unveiled its newest symbol--a man wearing a costume that looks like a U.S. nickel and bears the inscription, "Loose Change Adds Up." Decker said several people dressed that way will roam D.C. streets next week to pass out literature on the new game.

In the D.C. Double game, Games Production instituted a losers' drawing for players who submitted at least 10 losing tickets, but ticket sales did not pick up appreciably. Decker said there are no plans for losers' drawings in the Loose Change game.

The final D.C. Double losers' drawing is scheduled Friday, and one winning loser will drive away in a 1983 Cadillac. Some time next month a drawing will be held to give away million-dollar prizes to two lottery players who have bought $100 or $200 winning tickets in the D.C. Double game.

The lottery board has purchased 22,080,000 tickets for the Loose Change game, which, if all are sold, would yield $19,872,000 in revenue. Some 2,208,000 tickets would be given away as prizes.

A total of $9,705,000 would be awarded in cash prizes, which equals 48.83 percent of the revenue raised. Expenses and administrative costs will eat up another 24 percent and the rest, about $5.4 million or 27.17 percent, will go to the city treasury.