What are your chances of winning one of the thousands of contests and sweepstakes, offered every year by advertisers in order to promote their products? You hear about them on the radio, see them in many newspapers and magazines, get them in the mail, find entry blanks in supermarkets. All those prizes have to be won by someone.

In the biggest sweepstakes, the odds are long--maybe 20 million to one for the grand prize. But other contests have shorter odds, especially those that are locally run. "You can win contests if you keep at it," says Carolyn Tyndall who, with her husband Roger, publishes the monthly Contest News-Letter, probably the largest-selling newsletter in the country. "If you don't bother to enter, your odds are zero."

Who enters contests? Practically everybody, the Tyndalls say. Some of us occasionally drop our names into a big, national sweepstakes; others faithfully enter every contest they come across.

Many contests are simple sweepstakes, where you send in your name and a winner is drawn in a random lottery. Some contests ask you to answer simple questions (often the answers are printed on the label of the company's product, to induce you to buy it). Winners are drawn from among those who answered correctly. Some contests require skill--you may have to write recipes or limericks, or bake a gingerbread house.

The Tyndalls say that, in their experience, the contests are fair. They are not stacked in favor of the owner's daughter or the judge's nephew. The companies employ independent judging agencies, or judge entries themselves in an open and impartial way. Sponsors of contests seek public attention and goodwill, and cannot afford to be caught stacking the deck.

The prizes can be stupendous--vacations, cars, appliances, cash, cash and more cash. Although any win remains a long shot, the Tyndalls say that there are ways you can improve your chances:

* Enter often. When winners are chosen in random drawings, the judging agencies may pick a handful of entries from each mailbag and put them into a drum for the final drawing. Or the mailbags may be numbered, and a drawing held to see from which bag the winner will be picked.

If you mail many entries over the life of the contest you'll be represented in many different mailbags, hence will have a better chance of being chosen. Sometimes more names are picked from mailbags that arrive in the week or two before the contest closes, so it doesn't hurt to increase your entries during that time.

* Follow the rules. If the rules say hand-print your entry, hand-print it. Written, typed or rubber-stamped entries will be disqualified. If the rules say enter on a 3-by-5 card, use a card, not a piece of paper. If the rules ask for an envelope, do not use a postcard. Follow every instruction minutely.

* Don't be suspicious. Many contests let you enter either on an official entry blank or a plain white card. Contestants fear that the judges will give preference to the official form--and multiple forms may be hard to find (photocopies are normally not accepted.) "But if the rules say you can enter on a card, it's just as good as an official form," Roger Tyndall says. Sweepstakes often ask you to enclose either a product label with your entry or a plain white card with the name of the product printed on it, and both entries have an equal chance of winning.

* Don't feel that you have to decorate your envelope or bend your card in order to be a winner. The Tyndalls say that some people win with eye-catching envelopes and some win with plain envelopes; it doesn't seem to make much difference. But decorated envelopes don't hurt your chances, either, so if you like them, use them.

The Tyndalls advise against entering contests that require money up front. These may be mail-order sales operations that incorporate the price of your apparent "prize" into the cost of the merchandise you buy.

The Contest News-Letter keeps track of new contests, gives tips on winning, and exhorts contest fanatics to keep on trying. Cost: $12.95 a year. You can get a free copy by sending a self-addressed, stamped, business-size envelope (follow the rules) to The Contest News-Letter, P.O. Box 1059, Fernandina Beach, Fla. 32034.