If James Quigley had lived to see the introduction of computerized betting equipment at the nation's race-tracks, he would be enjoying some happy memories now.

The new technology has caused money shortages in Florida, the cancellation of a race in California and mechanical breakdowns in New York, but Quigley could attest that this is nothing new. He could remember earlier in the century when electronic totalizer machines were replacing crude manual methods of wagering, and they caused trouble at first, too.

It was this last technological revolution that enabled Quigley to participate in an outrageous betting coup, and gave him what may have been his most profitable day during four decades around the tracks. He told friends about the coup before his death in 1974. While some of the details have been blurred, the story is still one that would make any conspiratorial better drool with envy.

Quigley trained a few horses in New York, and took them each winter to Caliente Race Track in Tijuana, Mexico. There, he struck up a fateful conversation with a stranger, a bespectacled little man who took a great interest in one of Quigley's horses.

The colt, whom we'll call Big Champ, had run well in high-class competition at Jamaica and totally outclassed every thoroughbred on the grounds at Caliente.But Quigley didn't plan to run him until he went back home in the spring.

The little man apologized for his lack of knowledge about racing; he said he was an accountant by training and was working in the new totalizer equipment at the track. But he couldn't understand why Quigley wouldn't want to run Big Champ at Caliente.

Quigley explained patiently that the purses at Caliente were too small.

"Well, you could bet the horse," the little man suggested.

Quigley laughed. "I don't think it would be worth betting him at 1 to 10."

"What if you could get 3 to 1 on him?" the stranger demanded."Would you run him?"

"You bet," Quigley said.

Quigley forgot about this conversation until two days later, when the little man approached him and said, "I've been thinking over your proposition."

"What proposition?" Quigley asked, mystified.

"You'll get your 3 to 1," the little man said. "How soon can you get Big Champ ready?"

Quigley said he could have his colt ready for a minor stakes race two weeks hence. But he insisted, "We can't possibly get 3 to 1 on this horse."

"Anything can happen down here," the little man said.

Quigley did not see the stranger again until the day Big Champ was entered, and still he offered no explanation of what he had in mind. He only told the trainer that everything was ready, and he hoped Big Champ was ready, too.

When the betting opened, Big Champ was 3 to 1, as the little man had promised. So quigley went to the windows, bet $1,000 to win, and watched the odds board, waiting to see his horse's price plummet. But when the board flashed and the odds fluctuated, Big Champ stayed 3 to 1.

Quigley went back and bet $1,500, and watched the board again. The price didn't budge. Quigley deduced by now that the accountant knew things about the new totalizator equipment that weren't in the book. He bet again, $2,000, but Big Champ was still holding firm at 3 to 1 when he went into the gate.

The colt ran as well as he was supposed to, drawing away from the outclassed Caliente horses to win, under wraps, by a dozen lengths. He paid $8 to win.

After Quigley collected his winnings, he looked for his benefactor so he could thank him, but he could find no trace of the little man. Within a few days, track officials had discovered that the books didn't quite balance for Big Champ's race, and they, too, were looking for their erst-while employe. They never found him.