In Maryland and many other racing states, hard-pressed tracks have been looking desperately for answers to the financial problems that beset them.

They might find the answer -- a vision of the future of American racing -- by looking toward a harness track in Louisville. The management of Louisville Downs last week instituted a betting innovation so appealing, so logical that the wonder is that nobody ever thought of it before.

It works like this: having previously established a betting account at the track and deposited money in it, I telephone Louisville Downs and say, "This is Andrew Beyer, Code No. X254."

"Mr. Beyer," the operator responds, "you have $500 in your account. What do you wish to bet?"

"Bet $50 to win on Wampum Hanover in the first race."

"You now have $450 in your account," the operator says. "My operator number is 115. So that there will be no misunderstandings, we have tape-recorded this conversation. Thank you."

I'm in action. I take a beer from the refrigerator, turn the television to a cable channel, settle into my easy chair and watch the telecast of the first race at Louisville Downs.

There is nothing revolutionary about the concept of off-track betting, of course. It has become an article of faith in the racing industry that OTB is the remedy for its ills. But the most common vision of an OTB system resembles the one in New York, a large corporation that is a thicket of bureaucracy and political patronage.

"In many states where OTB bills have come up," said William H. King, president of Louisville Downs, "people have realized that the administration of OTB and the cost of buying up storefronts for offices would eat up most of the profits. It would scare you to know how much New York pays for administration. We've had three OTB bills fail in Kentucky. But our attendance and handle at the track have been pretty stagnant, and we felt we had to do something."

King's brainstorm was to eliminate the middle man, the OTB organization, and to deal directly with the off-track bettor. A member of his board of directors is a computer whiz who worked with a Pittsburgh-based firm called dynatote to set up what would be dubbed the Call-A-Bet system. King approached the local cable-television firm, which said it would be delighted to let Louisville Downs provide free programming for one of its channels.

At present, Call-A-Bet customers can wager only until 6:45 p.m., and then watch taped replays of the races in late evening. But by summer they will be able to bet until post time and watch each race live on television. King envisions the day when Call-A-Bet will become even more sophisticated, and operators won't be needed to take the wagers. A customer will be able to push buttons on his own telephone and transmit his bets directly into the track's computer.

Some of the track's directors worried initially that Call-A-Bet would keep at home bettors who would otherwise be spending money on admission, concessions and parking. But King argued that the cable telecasts could create new fans for the sport and stimulate attendance. So far, the early returns support his hopes; Louisville Downs' attendance and wagering have risen sharply since Call-A-Bet was begun, and tracks across the country are beginning to look at the innovation with great interest.