Derrick Davis of Baltimore, Glen DaSilva of New York and Chris Harn of Newark, Del., all 29, were accused of conspiring to violate wire-fraud laws in a complaint filed in White Plains.
The men, who had been frat brothers at Drexel University in Philadelphia, surrendered to the FBI on Tuesday.
Davis and Harn appeared before Magistrate Judge Mark Fox. DaSilva's case was put off, possibly until later in the day.
Davis and Harn did not enter a plea after the wire fraud charge was read to them, and they were released on $200,000 personal recognizance.
Prosecutors said Davis tested positive for cocaine Tuesday morning, and would be retested to confirm the results. His lawyer, Steven Allen, said his client "is dumbfounded" by the news.
Regarding the betting probe, Allen said, "My client's position is that he did nothing illegal and he's confident that after all the evidence is heard he will be found innocent of any wrongdoing."
Harn's lawyer, Daniel Conti, said "Chris maintains his innocence and nothing that happened today is going to change that."
According to the complaint, Davis used his automated New York Off Track Betting telephone account to place Pick Six bets in the Breeders' Cup, run Oct. 26 at Arlington racetrack near Chicago. To win the Pick Six, a bettor must pick the winner in each of six races.
While the races were being run, Harn, a senior programmer with Autotote, the computer wagering company, connected his company computer in Delaware to a New York OTB computer in Poughkeepsie, accessing Davis' records, the complaint said.
A fellow employee told investigators that Harn received one or more calls on his cell phone while he accessed the New York records, and the complaint says phone records show the calls came from Davis' phone.
After the races were run, Davis' computer account showed he had picked the winner in each of the first four races. He also picked every horse in the last two races. He had the only winning Pick Six tickets for a total payout of $3,067,821.60. The cost of his bets was $1,152.
The unusual bet immediately aroused suspicions of computer tampering, and the payoff has been held up pending the investigation.
The complaint says DaSilva placed wagers along the same elaborate lines on races in early October and won smaller payouts.