Varkonyi first started playing poker as an undergraduate at the Massachusetts Institute of Technology. After his graduation in 1983, he was an investment banker in Brooklyn, New York for a number of years before beginning to play tournament poker.
Varkonyi is most well known for winning the 2002World Series of Poker main event, taking the $2 million prize. Because he was a relative newcomer and considered dead money, commentator and fellow poker player Phil Hellmuth agreed to have his hair shaved off for charity if Varkonyi won. Hellmuth made good on his promise, and even allowed Varkonyi to shave some of it off.
Since his win Varkonyi has become a columnist for Card Player magazine.
Varkonyi currently resides in Great Neck, New York with his wife Olga, who also plays poker, and daughter.
Robert graduated from MIT with one degree in computer science and another in management.
Finally in 2000, Varkonyi decided to take a step back from his career; after 15 years of hard work and careful savings, he decided it was the right time to focus on other interests.