Tuesday afternoon, a man telephoned the general manager at Palm Beach Jai-Alai in Florida to make a special request. He asked if the establishment would accept cashier's checks from him that evening, because he and his associates were planning to make an especially large bet.

While this request was slightly unusual, the size of the transaction was going to be absolutely staggering. The gamblers would make a wager of more than $500,000. They would collect a payoff of $988,326.20, the largest in the history of American parimutuel wagering. And what made their bet all the more remarkable is that it was virtually a sure thing.

Officials at Palm Beach Jai-Alai could hardly have imagined the ramifications when they started to offer Pick Six wagering last November. The rules were the same as at Gulfstream Park and other Florida tracks. Bettors tried to select the winners of six consecutive games. If nobody succeeded, 25 percent of the money in the pool was paid out to the people with the largest number of winners. The remaining 75 percent went into a jackpot that would be paid when somebody did pick all six winners.

But there were a lot of differences between the Pick Six at Palm Beach and those at thoroughbred tracks. Palm Beach is a touristy place, and it doesn't cater to big bettors who would be making aggressive efforts to win the whole pool. Nor does jai-alai lend itself to intelligent handicapping the way horse racing does; the outcome of a game is almost a random event. With eight teams contesting each game, there are 8x8x8x8x8x8, or 262,144 possible outcomes to a jai-alai Pick Six.

With small crowds at Palm Beach betting small sums of money on the Pick Six, the chances were remote that anybody would hit it on any given night. For 146 matinee and evening programs, nobody did, and after Monday night the jackpot had grown to $551,331.

"People had been calling," fronton publicist Eric Moody said, "and asking how to bet big sums, asking how to wheel three or four or five numbers in a game." But one group of bettors saw that it was not necessary to leave anything to chance.

To cover every possible combination in the Pick Six would cost $524,288. Since the winner would get most of this money back along with the $551,331 jackpot, the bet would be very profitable as long as nobody else picked six winners on the same evening and split the pool. But the chances of that were fairly remote. Typically, the crowd at Palm Beach would bet about $20,000 on the Pick Six--$2 tickets on 10,000 of the 262,144 possible results of the Pick Six. So there was about a 1-in-26 chance that an average fan would win it. That left a 96 percent probability that the big bettors would take the whole pool with their monumental investment.

When the caller spoke to the general manager Tuesday, he said he had taken his money to a local bank and received cashier's checks. Jai-alai officials promptly called the bank to verify the transaction. That evening, the gamblers arrrived at the fronton--the people at Palm Beach won't say how many there were--and went to the window with their checks and a certain amount of cash. Once the cash was counted, they proceeded to make their bet. Because of the limitations of the computer equipment, they needed about half an hour to buy tickets that would cover every possibility in the Pick Six.

For the gamblers, the games themselves offered no suspense. All they had to do was hope that no West Palm Beach matron would play the digits in her phone number and split the pool with them.

When the public-address announcer said that the Pick Six had paid $988,326.20, Moody said, "Everybody seemed to gasp and take a breath at the same time. Everybody was buzzing." The winners went to an office at the fronton to fill out the necessary tax forms and to accept a check (plus a small amount of cash) for their winnings.

Their pre-tax profit for the evening was $464,038. The IRS withheld its standard 20 percent of the gross payoff, or $197,665, leaving them a net profit of $266,373. Assuming that the gamblers don't have a sharp accountant and a lot of tax shelters (which people with half a million dollars in ready cash usually do), the remainder of their tax liability would be $34,354. That left them with an after-tax profit of $232,019. Considering that there was virtually no risk involved, it wasn't a bad night's work.