Gambling in America is going to the dogs.

Once considered an unfashionable, grubby poor relation of the thoroughbred sport, greyhound racing has achieved respectability and prosperity. In the 14 states where it is now legal, more than 20 million people attended dog races last year and wagered more than $1.5 billion.

Yet the recent growth of dog racing is only a harbinger of things to come. The sport is certain to boom in the near future because it has so many economic advantages over horse racing. In the last few years, several tracks -- Green Mountain, Wheeling Downs and Lincoln Downs -- have gone out of business with thoroughbreds and switched to the dogs to survive.

The business of these tracks had suffered for a variety of reasons, most notably the increased competition for the parimutuel dollar, and they could not withstand a drop in their attendance and handle because their fixed costs were so high. Even minor-league tracks have to maintain a large physical plant, a large stable area and a large racing strip. And they have to pay out a high percentage of their income in purse money, because horses are so expensive to maintain and their owners need ample purses to stay in business.

The experience of Green Mountain, a pretty little track in Vermont, was typical. Green Mountain does not have a large or affluent population from which to draw, but in 1976 its patrons bet an average of $190,000 a day. That sounds like a respectable figure, but it was not adequate. Green Mountain lost $2 million that year.

The next season, Green Mountain was offering dog racing with its small racing strip, small kennel area and -- most important -- its small purses. "In our last year with horses," a track official said, "we had a July 4 double-header and paid out $24,000 in purses. The next July 4, with dogs, the purses came to $3,000."

With their lower overhead, the track owners calculated that they could make a profit with a handle of only $125,000 a night. Because of such arithmetic, Green Mountain has been able to survive and other greyhound tracks have become tremendously successful.

"Dog racing has done well in every area where it's been introduced," said Perrine Palmer, general manager of Hollywood Greyhound Track. "There has never been a single failure of a dog track."

Greyhound racing has yet to be introduced in the Washington area. The closest dog track for Washingtons is in Plainfield, Conn.

States are continually searching for new sources of revenue and legalizing new forms of gambling, and many of them will turn toward dog racing because the thoroughbred game is already suffering from the effects of overexpansion. There are too few race horses and too many races and, as a result, tracks have to put on programs with the six and seven-hourse fields that most bettors find unappealing. But there is no such shortage of greyhounds. Nature has provided that while a broodmare can produce only one foal at a time, a bitch may have a litter of as many as a dozen pups.

Another aspect of greyhound racing that many states will find attractive is the adaptability of the sport to existing facilities. Indoor arenas and outdoor stadiums can be converted into greyhound tracks. Hwite City Stadium, a mammoth structure built for the 1924 Olympics in London, is a dog track now.This country has debt-ridden football stadiums for which dog racing could be a salvation. "Greyhounds are the only things that can save the Superdome in New Orleans," says Barney O'Donnell, owner of one of the country's largest kennels.

The chief obstacle inthe way of dog racing's growth is opposition from horse-racing interests. In 1977, the thoroughbred indurstry helped deal a sound defeat to a referendum that would have legalized greyhound racing in California.

But the thoroughbred-racing opposition is only delaying the inevitable. Too many people want dog racing. It is very profitable for track owners. It is a source of substantial revenue for the state. It is lucrative for people who own and race dogs. And -- underlying the whole success of the sport -- it is a marvelous gambling game, which appeals to casual fans because of its fast action and to serious bettors who consider it easier to beat than any other form of racing.

FRIDAY: A professional dog bettor .