Two minutes before Tuesday's third race at Keystone Race Track, a young man walked up to a betting window and said, quietly, "Give me three thousand to show on No. 6." When the clerk had punched out the tickets, the young man said, "Now, give me three thousand more."

The seller was able to punch out only $4,700 worth of tickets before betting was halted and the race began. His customer paid and disappeared into the crowd. Only then did the seller have a chance to contemplate what an insane wager this had been. Clean Air had lost his last race against weaker competition by 19 lengths. He had never finished in the money in nine career starts.

Clean Air ran as expected, straggling home a distant fourth, while the even-money favorite, House Speaker, won easily. The losing bettor never reappeared. "Nobody knew him," said Keystone's mutuel manager, Allen Henry. "Nobody had ever seen him before."

Whoever he was, or wherever he went, the young man was not weeping over the results of the race. Quite the contrary. He and a group of youthful confederates had just executed a deft, ingenious and legal betting coup that won an estimated $60,000 from bookmaking establishments throughout Nevada.

The gamblers' tactics were a variation on an old theme, a type of coup known as a "builder play," which is based on the most elementary fact of parimutuel wagering: when a large sum of money is bet on one horse, his odds will drop and the odds on his opponents will rise.

One builder play, which occurred at Caliente Race Track in 1932, has become part of racing legend. The track was located just over the Mexican border, and most of its customers came from Los Angeles on a train that didn't arrive until after the first race.

One day, when a horse named Linden Tree was the odds-on favorite in the first event, a pair of gamblers bet on him heavily with bookmakers throughout the United States. Then they went to Caliente and bet heavily on another horse. With so little money in the wagering pool, they were able to push Linden Tree's odds up to 9 to 1.

He won and paid $21.40. A bookie who had calmly accepted a $2,000 bet, thinking that he was risking a loss of $1,200 or so on the favorite, would be stunned to find that he instead owed his customer $21,400.

While illegal bookmakers don't accept much serious action on horses any more, the legal establishments in Las Vegas do. They pay track odds, and thus offer possibilities for a builder play. It would be easy for a gambler to distort payoffs on a slow day at a small track, especially in the show pool, where so little money is wagered. Builder plays have been executed with some success on races at Pimlico and Bowie this year. But the Keystone coup was the masterpiece of the genre.

The gamblers knew that on a Tuesday there would ordinarily be only $3,000 or so in the entire show pool for any race. Betting just a few thousand dollars on a horse who finished out of the money could inflate the payoff on a solid, short-priced favorite. Tuesday's third race looked like a perfect situation: House Speaker appeared overwhelmingly superior in the maiden race and Clean Air looked like a hopeless case.

On Tuesday morning, the young strangers began visiting every race book in the state of Nevada. "The bookies here almost all said they looked like college kids," reported Chuck DiRocco, editor of Sports Form, the Las Vegas gambling paper. One of them spoke with an accent and said he was Australian. Some of them operated singly, others in pairs.

But all of them asked to bet $500 to win and $5,000 to show on House Speaker in the third race at Keystone. All of them were denied a bet of this size, but many of the bookmakers did take as much as $3,000 to show on the favorite. The gamblers got down bets at 20 of the 22 bookmaking establishments in Las Vegas and Reno.

To people who have visited these sports books, this may seem implausible. The books are notoriously cautious; they might turn down an innocuous $100 bet on a 10-to-1 shot. But DiRocco said, "The books are not lacking in greed. When somebody comes in to bet a favorite to show, they're thinking that at most they're risking 20 or 40 cents on the dollar. To them, that's like found money."

But the bookmakers realized that they were not dealing with sucker bets from a bunch of innocent kids when the third at Keystone was official. The payoffs were flashed by wire to Las Vegas and they saw that House Speaker had paid $4 to win, $2.60 to place and (gasp!) $6.40 to show. The young men who had managed to place a $3,000 show bet were receiving $9,600 instead of a pittance, as well as the satisfaction of having outwitted the wiliest professionals in Las Vegas.