Complex sentence: She is also known as the former girlfriend of Barry Greenstein, who not only taught her how to play poker, but also convinced her to compete in tournaments; until the mid-to-late 1990s she had been exclusively a side-game player.
Split into simpler sentences: She is also known as the protégé and former girlfriend of Barry Greenstein, who taught her how to play poker. Greenstein also convinced Tran to compete in tournaments; until the mid-to-late 1990s she had been exclusively a side-game player.