After graduating from Bogan High School, he earned a bachelor degree in computer science from the University of Illinois at Urbana-Champaign. He studied for a PhD in mathematics, but never defended his completed dissertation.

According to his book, Ace on the River, Greenstein was doing quite well playing poker, but figured a more conventional job would improve his chances of adopting his stepchildren, so he went to work for the new startup company Symantec, where he developed their first product Q&A. He retired from the company in 1991 at age 36.

Greenstein has two children and four stepchildren, and he resides in Rancho Palos Verdes, California. His stepson, Joe Sebok, with whom he started PokerRoad, a poker strategy and entertainment website, is also a professional poker player.

Greenstein has appeared in each of the first three series of Poker Superstars Invitational Tournament and all six seasons of the GSN series High Stakes Poker. He has also appeared in the first three seasons of the late night series Poker After Dark on NBC. Greenstein has also won two World Poker Tour (WPT) titles: the Fifth Annual Jack Binion World Poker Open ($1,278,370), and 2006 WPT Invitational at the Commerce Casino ($100,000). He has also won two other WPT titles in special events: WPT Father and Sons Tournament, 2006 World Poker Finals; and WPT Poker by the Book: Chapter 2. As of 2008, he began donating his net winnings to charity. At the 2008 World Series of Poker (WSOP), Greenstein cashed in six events for a total of $768,461. He also finished second in the 2008 WSOP Player of the Year standings, behind Erick Lindgren. As of 2010, his total live tournament winnings exceed $7,000,000. His 44 cashes at the WSOP account for $2,259,097 of those winnings.

In 2005, Greenstein wrote a book titled Ace on the River. Tuan Le, a WPT Season 3 champion, claims that book showed him how to succeed on the poker circuit. Greenstein is known for giving away a free copy of his book to the player who eliminates him in a tournament, including his autograph and details of the hand. Greenstein taught former girlfriend Mimi Tran how to play poker in exchange for her teaching him how to speak Vietnamese. He also plays online at PokerStars, under the alias "barryg1" and is a member of the cardroom's Team PokerStars.

He accepted a bet of $10,000 from 2+2 Poker Forums to say "lol donkaments" on an episode of High Stakes Poker, which he did after winning a hand against Erick Lindgren. After the initial $10,000, he also received a further $45,000 in donations from other charitable poker players who were amused by the bet.

As of 2010, his total live tournament winnings exceed $7,100,000. His 46 WSOP cashes account for $2,285,120 of those winnings.

After winning $770,000 at Larry Flynt’s $1 million Seven-Card Stud event in 2003, he donated $440,000 to Children, Incorporated - a gift of $1,000 to each of the charity's 440 employees. In 2006, Greenstein announced that he would be donating net earnings from tournaments to charity. "Until now, I was donating the pay-off each time I cashed but I can't afford to continue doing that. I didn't anticipate the growth and expense of tournament poker,” he said.