Prof. William T. Ziemba has an imposing set of academic credentials. His resume includes a long list of books and papers he has published, and even most of the titles are incomprehensible to a layman:

Ziemba and Vicksons, eds., "Stochastic Optimization Models in Finance" (1975). Ziemba and Schaible, eds., "General Concoavity in Optimization and Economics" (1981). Ziemba and Hausch, "Beat the Racetrack" (1984).

People in the academic world do a predictable double take when they see that last title, and they look on Ziemba with considerable curiosity because of his interest in the horses. But he makes no apologies for his latest scholarly pursuit.

"I think this book is as good as anything I've ever done," the professor said of "Beat the Racetrack." "It uses all the power of all the stuff I know from mathematics and finance. But a lot of people think it's cute or strange because it's about gambling."

Ziemba got his Ph.D. in business at Cal-Berkeley and has taught for the past 15 years at the University of British Columbia. His main interest is the application of high-powered mathematics to the management of investments. Ziemba knew colleagues who were using computer technology to analyze stocks, options and other financial markets.

Why not the race track? Having been a casual racing fan for years, Ziemba started to analyze the myriad factors that determine the outcome of races.

"I got nowhere," he said. Ziemba finally came to the conclusion that other mathematically oriented students of the game had reached before him: The race track is an efficient market. Odds created by the betting public reflect a horse's chances of winning with amazing accuracy.

Over any reasonable period of time, 3-to-1 shots will win more often than 7-to-2 shots, and 7-to-2 shots will win more often than 4-to-1 shots.

What about the place and show pools? Here, Ziemba thought there might be potential. Horses aren't always bet in the same strength to win, place and show. A favorite could, conceivably, take 35 percent of the money in the win pool, 40 percent in the place pool and 27 percent in the show pool. But if we assume that the win pool is "correct," that it most accurately reflects a horse's chances of winning, then the other pools may be "incorrect" -- or, as an economist would put it, inefficient. Could money be made by playing horses the public has underbet to place and show?

Ziemba and a young mathematician, Donald Hausch, set their computers whirring to tackle that question. Their answer consumes 400 pages of "Beat the Racetrack," published last month by Harcourt Brace Jovanovich.

What they did, in essence, was to look at horses who were bet less heavily to place or show than to win, and to calculate when they would get a mathematical edge by betting these horses. They expressed this edge as a precise percentage; a particular situation might be said to offer a 17 percent advantage.

Then they employed a money-management system that would dictate the percentage of their bankroll to be bet in the situation.

Because all the calculations are cumbersome and time-consuming, Ziemba programmed a hand-held computer to perform them. He demonstrated it on a recent visit to the Meadowlands.

Suppose that $25,000 is bet on a favorite to win, out of a pool of $75,000. But only $10,000 of the $50,000 in the show pool is bet on him. Ziemba punched these four figures into his computer, which promptly flashed the number 1.28. This meant the bettor has a 28 percent edge; betting in this situation would show a 28 percent profit over the long run. Now Ziemba tells the computer that his bankroll is $1,000. The computer answers: $283. This is the optimal size of a show bet.

Mechanical systems that purport to beat the races are mostly hokum, although horse players keep buying them and wanting to believe in them. Ziemba's system may be quite different. It may well be sound and legitimate, and yet few horse players are likely to embrace it. "Most bettors like high payoffs," Ziemba acknowledged. "They don't like place and show."

Indeed, it is hard to become rapturous about the prospect of collecting $2.60 on a horse who should, by all rights, be paying $2.40 to show. But the slowness of the action doesn't faze Ziemba. Any man who has spent much of his life dealing with stochastic optimization models is well equipped to handle a certain amount of tedium at the race track.